Cosmology_with_the_Laser_Interferometer_Caustics_and_BAO.ipynb

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        "#Cosmology with the Laser Interferometer\n",
        "\n",
        " $ H_0 = 67.4 \\pm 0.5 $ km/s/Mpc is discussed in the paper \"Cosmology with the Laser Interferometer\" and regards the tension between different measurements of the Hubble constant, particularly from early and late universe data. The value of $ H_0 $ from the Planck data for the cosmic microwave background is quoted as $ 67.4 \\pm 0.5 $ km/s/Mpc at 68% confidence level, consistent with the analysis of the paper.\n",
        "\n",
        ""
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        "Let's convert the Hubble constant $ H_0 $ to different units, and provide another measurement, normalizing into SI units.\n",
        "\n",
        "First, the typical value of $ H_0 $ in cosmology is measured in kilometers per second per megaparsec (km/s/Mpc). This value of $ 67.4 \\pm 0.5 $ km/s/Mpc can be converted to SI units:\n",
        "\n",
        "1. **Convert from km/s/Mpc to SI units:**\n",
        "\n",
        "   A megaparsec (Mpc) is approximately $ 3.086 \\times 10^{22} $ meters, and 1 km is $ 10^3 $ meters. So,\n",
        "\n",
        "   $$\n",
        "   H_0 = 67.4 \\, \\text{km/s/Mpc} \\times \\frac{10^3 \\, \\text{m/km}}{3.086 \\times 10^{22} \\, \\text{m/Mpc}}\n",
        "   $$\n",
        "\n",
        "   $$\n",
        "   H_0 \\approx 2.185 \\times 10^{-18} \\, \\text{s}^{-1}\n",
        "   $$\n",
        "\n",
        "   The uncertainty in $ H_0 $ is:\n",
        "\n",
        "   $$\n",
        "   \\sigma_{H_0} = 0.5 \\, \\text{km/s/Mpc} \\times \\frac{10^3 \\, \\text{m/km}}{3.086 \\times 10^{22} \\, \\text{m/Mpc}}\n",
        "   $$\n",
        "\n",
        "   $$\n",
        "   \\sigma_{H_0} \\approx 0.0162 \\times 10^{-18} \\, \\text{s}^{-1}\n",
        "   $$\n",
        "\n",
        "   Therefore, the value in SI units is:\n",
        "\n",
        "   $$\n",
        "   H_0 = (2.185 \\pm 0.0162) \\times 10^{-18} \\, \\text{s}^{-1}\n",
        "   $$\n",
        "\n",
        "2. **Normalizing with a scale factor (redshift $ z $):**\n",
        "\n",
        "   The Hubble parameter as a function of redshift $ z $ can be written as:\n",
        "\n",
        "   $$\n",
        "   H(z) = H_0 \\sqrt{\\Omega_m (1+z)^3 + \\Omega_k (1+z)^2 + \\Omega_\\Lambda}\n",
        "   $$\n",
        "\n",
        "   For simplicity, assuming a flat universe with $ \\Omega_k = 0 $ and $ \\Omega_\\Lambda = 1 - \\Omega_m $, for $ z = 1 $, we get:\n",
        "\n",
        "   $$\n",
        "   H(z=1) = H_0 \\sqrt{\\Omega_m (1+1)^3 + (1-\\Omega_m)}\n",
        "   $$\n",
        "\n",
        "   Taking typical values of $ \\Omega_m = 0.3 $ and $ \\Omega_\\Lambda = 0.7 $:\n",
        "\n",
        "   $$\n",
        "   H(z=1) = H_0 \\sqrt{0.3 \\times 8 + 0.7} = H_0 \\times \\sqrt{3.1} \\approx 1.76 \\times H_0\n",
        "   $$\n",
        "\n",
        "   Using the previously calculated SI units for $ H_0 $:\n",
        "\n",
        "   $$\n",
        "   H(z=1) \\approx (3.85 \\pm 0.028) \\times 10^{-18} \\, \\text{s}^{-1}\n",
        "   $$\n",
        "\n",
        "This gives the Hubble constant at $ z = 1 $, normalized in SI units. Let me know if you'd like any further steps or adjustments!"
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      "source": [
        "##How is the hubble estimate in any given direction affected by gravitational waves"
      ],
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      "source": [
        "Gravitational waves (GWs) can play a key role in measuring the Hubble constant $ H_0 $ and understanding its variation, particularly in any given direction. There are a few significant ways GWs affect or improve Hubble parameter estimates:\n",
        "\n",
        "### 1. **Standard Sirens and Hubble Constant Estimates**\n",
        "Gravitational waves from binary mergers (such as neutron stars or black holes) provide what are called \"standard sirens.\" These are analogous to the concept of \"standard candles\" in electromagnetic astronomy, where the intrinsic brightness of an object (like a supernova) is used to estimate distance. In GW astronomy, the amplitude of the gravitational wave signal directly correlates with the luminosity distance to the source.\n",
        "\n",
        "The relationship between the distance $ D_L $ and the Hubble constant in a specific direction is:\n",
        "\n",
        "$$\n",
        "D_L = \\frac{c(1 + z)}{H_0} z\n",
        "$$\n",
        "\n",
        "Where:\n",
        "- $ D_L $ is the luminosity distance.\n",
        "- $ z $ is the redshift.\n",
        "- $ c $ is the speed of light.\n",
        "- $ H_0 $ is the Hubble constant.\n",
        "\n",
        "When GWs are detected, the signal's amplitude allows for a direct measurement of the luminosity distance to the source. If an electromagnetic counterpart is also observed, the redshift $ z $ of the source can be obtained from optical data (e.g., galaxy surveys). Combining these two pieces of information—luminosity distance and redshift—enables the calculation of $ H_0 $.\n",
        "\n",
        "This method is independent of the usual distance ladders used in EM astronomy, so it avoids some systematic uncertainties.\n",
        "\n",
        "### 2. **Directional Dependence and Gravitational Waves**\n",
        "Gravitational waves provide a new method for estimating $ H_0 $ that is less sensitive to directional biases seen in other measurements. However, there are still some factors that could introduce directionality in estimates:\n",
        "\n",
        "- **Weak Lensing Effects**: Gravitational waves traveling through the universe are subject to weak gravitational lensing by intervening matter, just like light. This lensing can cause a magnification or de-magnification of the signal, affecting the inferred distance to the source. Since this lensing depends on the mass distribution along the line of sight, it introduces a small bias depending on the direction of the observation. For very high-redshift sources, this effect can cause a few percent uncertainty in the distance estimate, which in turn affects the estimate of $ H_0 $.\n",
        "  \n",
        "- **Large-Scale Structure and Cosmic Variance**: The local large-scale structure of the universe can impact the observed Hubble constant, as the universe isn't isotropic on smaller scales. Cosmic voids, galaxy clusters, and filaments can all introduce variations in the local expansion rate. While this applies to any Hubble measurement, GWs can help map these effects better due to their sensitivity to different redshift ranges and directions across the sky.\n",
        "\n",
        "### 3. **Gravitational Wave Lensing**\n",
        "In addition to weak lensing, there is also the possibility of **strong lensing** of gravitational waves. This happens when the GW signal passes close to a massive object, creating multiple images or magnifying the signal. Strong lensing can introduce significant biases in the distance estimates and hence affect the derived value of $ H_0 $ in the direction of the lensing object.\n",
        "\n",
        "- **Lensing-induced Bias**: If a gravitational wave is lensed, the inferred luminosity distance could be incorrect if lensing is not accounted for. For example, a magnified GW signal would make the source appear closer than it actually is, leading to an overestimation of $ H_0 $ in that direction.\n",
        "\n",
        "### 4. **Peculiar Velocities**\n",
        "For nearby gravitational wave sources, peculiar velocities (the motions of galaxies relative to the overall expansion of the universe) can introduce an additional uncertainty. These peculiar velocities are dependent on the direction and local gravitational environment, and they can bias the inferred value of $ H_0 $.\n",
        "\n",
        "- In directions where galaxies are part of large clusters or superclusters, the local motions can either increase or decrease the redshift of the source, thus affecting the Hubble estimate in that region.\n",
        "\n",
        "### 5. **Anisotropies in Gravitational-Wave Background**\n",
        "The stochastic gravitational-wave background, which is the sum of all unresolved GW sources across the universe, could potentially show anisotropies. If such anisotropies are detected, they could indicate differences in the expansion rate in different directions of the universe.\n",
        "\n",
        "- Current estimates suggest that any directional dependence of the Hubble constant might arise due to local structure variations or effects like lensing, but GWs can help provide a more isotropic and robust estimate.\n",
        "\n",
        "### Conclusion:\n",
        "Gravitational waves provide a powerful tool to measure the Hubble constant across the universe. While they are less affected by some of the biases in electromagnetic observations, they can still be influenced by effects like gravitational lensing, peculiar velocities, and local cosmic structure, all of which introduce directional dependence to the $ H_0 $ estimate. However, because gravitational waves offer direct measurements of luminosity distance, they are expected to reduce some of the systematic uncertainties present in traditional methods."
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      "source": [
        "##The CMB and large scale structure of the universe appears very similar to the caustics seen at the bottom of a pool due to refrection of the suns light rays by waves in the pool. What affect does such cosmological caustics caused by space-time ripples have on the hubble and other cosmological parameters? how can these 'caustics' be modelled - especially fro observations\n",
        "\n"
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        "The comparison between caustics seen at the bottom of a pool and cosmological structures is quite an insightful analogy. Caustics in cosmology refer to regions where light (or other signals, such as gravitational waves) is focused due to gravitational lensing caused by large-scale inhomogeneities in the distribution of matter and space-time ripples (gravitational waves). These cosmological caustics can arise from the interactions of light or gravitational waves with gravitational potentials (like galaxy clusters or dark matter structures), similar to how water waves refract sunlight in a pool to create bright patterns.\n",
        "\n",
        "### Effects of Cosmological Caustics on Cosmological Parameters\n",
        "\n",
        "The presence of caustics in cosmological observations can significantly influence the inferred values of cosmological parameters, including the Hubble constant $H_0 $ the matter density parameter $ \\Omega_m $, and the dark energy equation of state. Here's how:\n",
        "\n",
        "1. **Bias in Luminosity Distance Estimation**:\n",
        "   Caustics, particularly those formed by **strong gravitational lensing**, can magnify or demagnify distant objects such as galaxies, supernovae, or gravitational wave sources. This affects the estimation of luminosity distance $ D_L $, which is critical for determining $ H_0 $ and other parameters related to the expansion of the universe.\n",
        "\n",
        "   - **Magnification Bias**: If an object (e.g., a supernova or gravitational wave event) is magnified due to a caustic, it will appear brighter and thus closer than it actually is. This will lead to an underestimation of its distance and consequently an overestimation of $ H_0 $.\n",
        "   - **Demagnification**: Conversely, demagnification could cause the object to appear fainter and further away, leading to an underestimation of the Hubble constant.\n",
        "\n",
        "2. **Gravitational Lensing and Large Scale Structure**:\n",
        "   On larger scales, weak lensing by cosmic structures (the large-scale distribution of galaxies, clusters, and dark matter) can also create mild caustics that distort the shapes and sizes of galaxies and affect luminosity distance measurements. This **weak lensing-induced scatter** introduces uncertainties in the measurement of cosmological parameters such as $ H_0 $, $ \\Omega_m $, and the equation of state of dark energy $ w $.\n",
        "\n",
        "3. **Cosmic Shear and Convergence**:\n",
        "   Weak gravitational lensing produces **cosmic shear** (the distortion of galaxy shapes) and **convergence** (the focusing of light) in a manner akin to the optical caustics formed by the refraction of light. These effects can alter the interpretation of observations like supernova distances, leading to biases in cosmological inferences.\n",
        "\n",
        "4. **Peculiar Velocity Fields**:\n",
        "   Similar to how caustics arise from the focusing of light, peculiar velocity fields in the large-scale structure of the universe can create density contrasts that affect the redshift-distance relationship, introducing further biases in the Hubble parameter estimation. Caustic structures can be responsible for **velocity caustics**, where infalling matter towards overdense regions causes apparent distortions in redshift space.\n",
        "\n",
        "### Modelling Cosmological Caustics\n",
        "\n",
        "To model these caustic effects and account for their impact on cosmological parameters, several approaches can be taken:\n",
        "\n",
        "1. **Gravitational Lensing Models**:\n",
        "   Caustics are typically modelled using gravitational lensing theory. The formalism involves solving the **lens equation**, which relates the positions of lensed sources to the deflection of light due to intervening mass distributions (like galaxy clusters). The formation of caustics in this context occurs where the Jacobian of the lens mapping becomes singular, leading to magnifications.\n",
        "\n",
        "   - **Strong Lensing**: For strong lensing caustics, where the deflection is large, detailed **ray-tracing simulations** through high-resolution cosmological simulations (like the Millennium Simulation or Illustris) can model how light from distant sources is focused and distorted.\n",
        "   - **Weak Lensing and Shear**: Weak lensing caustics are subtler but pervasive, and these can be modelled using **cosmic shear maps** from large galaxy surveys like the Dark Energy Survey (DES) or the Kilo-Degree Survey (KiDS). Weak lensing is modeled statistically by measuring the correlation functions of galaxy shapes.\n",
        "\n",
        "2. **N-body Simulations and Cosmic Web**:\n",
        "   Cosmological caustics are closely linked to the large-scale structure of the universe, often referred to as the **cosmic web**. N-body simulations of dark matter and galaxy formation can capture the formation of caustics by evolving the gravitational collapse of matter over cosmic time. These simulations are used to understand how matter concentrates in filaments, walls, and nodes of the cosmic web, where caustics may form.\n",
        "\n",
        "   - **Caustics in Dark Matter Halos**: In simulations, caustics can appear as shells of dark matter around collapsing structures, and these can influence the dynamics of galaxy formation. These dark matter caustics are modeled by solving the collisionless Boltzmann equation for dark matter particles.\n",
        "   - **Phase Space Caustics**: In phase space, caustics can be seen as structures in the position-velocity diagram of dark matter particles. The **Zeldovich approximation** or more advanced techniques like the **Lagrangian perturbation theory** are used to model these caustic formations.\n",
        "\n",
        "3. **Perturbation Theory and Gravitational Waves**:\n",
        "   Space-time ripples, such as those caused by gravitational waves (GWs), can also create caustic-like effects. The interaction of GWs with the large-scale structure can distort space-time in ways that affect the propagation of light and other signals. **Perturbation theory** and simulations of gravitational wave propagation through an evolving universe can model these effects.\n",
        "\n",
        "4. **Statistical Tools for Observations**:\n",
        "   In observational cosmology, the impact of caustics is often studied using statistical methods:\n",
        "   \n",
        "   - **Magnification Maps**: For weak lensing, statistical magnification maps are constructed by analyzing distortions in the shapes of galaxies. These maps allow cosmologists to estimate the impact of lensing-caused caustics on luminosity distances.\n",
        "   - **Bayesian Inference Models**: Observational data, such as from gravitational wave detectors (LIGO/Virgo) or galaxy redshift surveys, are analyzed using **Bayesian frameworks**. These methods can account for the bias introduced by lensing caustics when estimating cosmological parameters like $ H_0 $ or the equation of state of dark energy.\n",
        "\n",
        "5. **Gravitational Wave Lensing and Caustics**:\n",
        "   As gravitational wave observatories like LISA or third-generation ground-based detectors (like Cosmic Explorer) come online, they will allow for detailed studies of the lensing of GWs. The modeling of **wave optics effects**, particularly in the context of strong lensing where GWs can create multiple images or interference patterns, will be crucial to account for cosmological caustics.\n",
        "\n",
        "   - The **frequency-dependent interference patterns** of lensed GWs can be used to probe the mass distribution of lensing objects and refine our understanding of caustics in space-time. These models require precise wave optics calculations and simulations of GW propagation through inhomogeneous space-time.\n",
        "\n",
        "### Observations and Measurements\n",
        "\n",
        "To observe and model these caustic effects in practice:\n",
        "\n",
        "1. **Galaxy Surveys**: Data from large-scale surveys like the **Sloan Digital Sky Survey (SDSS)**, **DES**, or **Euclid** provide maps of the large-scale structure, which can be used to model the matter distribution responsible for weak and strong lensing caustics. These surveys offer 3D maps of the universe’s structure, which are critical for understanding how caustics arise.\n",
        "\n",
        "2. **Cosmic Microwave Background (CMB)**: The CMB itself is affected by lensing, and CMB lensing measurements (e.g., from **Planck** or **South Pole Telescope**) can be used to model caustics on large scales. These measurements inform us about the integrated gravitational potential along the line of sight, providing constraints on cosmological models.\n",
        "\n",
        "3. **Gravitational Wave Observatories**: As GW detectors improve, we will be able to observe the effects of lensing caustics on GW signals. The **lensing of GWs** by cosmic structures will help probe the distribution of matter in the universe and refine our understanding of $ H_0 $, especially as more GW sources at different redshifts are detected.\n",
        "\n",
        "### Conclusion\n",
        "\n",
        "Cosmological caustics caused by space-time ripples and gravitational lensing have a measurable impact on key cosmological parameters like $ H_0 $ . They introduce biases in distance estimates and can alter our understanding of the large-scale structure of the universe. To model these effects, gravitational lensing theory, N-body simulations, and statistical methods are used in conjunction with observational data from galaxy surveys, CMB experiments, and gravitational wave observatories. Understanding and accounting for these caustics are essential for refining measurements of the universe's expansion and structure."
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      "source": [
        "##How do the cuastics interact with Baryon Acoustic Oscillations and other phenom such as the birefringence of space, and are there evanescent or even negative index modes to consider for the propagation of light over cosmological scales\n",
        "\n"
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      "source": [
        "The interaction of caustics with phenomena like **Baryon Acoustic Oscillations (BAO)**, **birefringence of space**, and the possibility of **evanescent modes** or **negative index modes** in the propagation of light over cosmological scales is a complex but intriguing topic that ties together gravitational lensing, the large-scale structure of the universe, and advanced wave propagation phenomena. Let's break down each aspect:\n",
        "\n",
        "### 1. **Caustics and Baryon Acoustic Oscillations (BAO)**\n",
        "\n",
        "Baryon Acoustic Oscillations are the \"ripples\" left over from sound waves that propagated through the early universe's plasma before decoupling. These ripples created a characteristic scale, the BAO scale, which is imprinted in the distribution of galaxies and other large-scale structures. The BAO acts as a \"standard ruler\" for measuring cosmic distances and constraining cosmological parameters.\n",
        "\n",
        "**Interaction with Caustics**:\n",
        "- **Gravitational Lensing of BAO**: Caustics arise in gravitational lensing due to the focusing of light by intervening mass distributions, potentially distorting observations of the BAO feature. Since BAO structures span large scales, weak lensing can introduce small but non-negligible biases in the measurement of the BAO scale.\n",
        "- **Caustic Amplification**: In regions near caustics, light from distant galaxies may be magnified, altering the observed distribution of galaxies at a given redshift. This could affect the accuracy of BAO measurements, as the underlying cosmological signal (the galaxy distribution) is distorted. Magnification bias from caustics can shift the inferred cosmological distances, potentially introducing small biases in estimates of the Hubble constant or the matter density parameter $ \\Omega_m $.\n",
        "\n",
        "### 2. **Caustics and Birefringence of Space**\n",
        "\n",
        "**Birefringence of space** refers to the phenomenon where different polarizations of light propagate at different speeds through space, similar to how light behaves in certain materials like calcite crystals. This could be caused by a variety of effects, including:\n",
        "- **Axion-like fields**: In some cosmological models, axion-like particles or fields can induce birefringence in the cosmic microwave background (CMB) and other light sources.\n",
        "- **Quantum gravity effects**: Some quantum gravity models predict space-time birefringence, where the polarization of light is affected by high-energy processes in the early universe.\n",
        "\n",
        "**Interaction with Caustics**:\n",
        "- **Lensing and Polarization Effects**: Caustics can affect the polarization of light by introducing changes in the trajectory of light rays that encounter different gravitational potentials. When light from a polarized source (e.g., CMB photons) is gravitationally lensed, the polarization can be distorted, leading to an interaction between birefringence and lensing.\n",
        "- **Magnification of Birefringence Effects**: In regions of strong lensing or near caustics, the light can be magnified, amplifying the birefringence signal. This may be particularly relevant when observing high-redshift sources, where both lensing and birefringence effects are more pronounced.\n",
        "  \n",
        "  **Modeling Birefringence with Caustics**:\n",
        "  - If space-time exhibits birefringence, the polarization of light traveling through large-scale structures could be altered, and this alteration could be further affected by the presence of caustics, where the light is strongly magnified or distorted.\n",
        "  - **CMB Lensing and Birefringence**: For example, CMB photons passing through large-scale structures and encountering caustics could exhibit modified polarization patterns, providing a signature that might be used to probe birefringent properties of space-time.\n",
        "\n",
        "### 3. **Evanescent and Negative Index Modes**\n",
        "\n",
        "Evanescent modes and negative index modes are concepts from wave propagation and metamaterials, where waves can exhibit unusual behaviors like **negative refraction** or **exponentially decaying waves**. These concepts could have analogs in cosmological settings, particularly in the context of light propagation over vast distances affected by gravitational potentials and the structure of space-time.\n",
        "\n",
        "- **Evanescent Modes**: Evanescent waves decay exponentially in space and are typically associated with boundary phenomena, such as total internal reflection. In a cosmological context, evanescent modes could arise in situations where light interacts with sharp gravitational potentials or caustic boundaries, where the local curvature of space-time alters the wave propagation in ways similar to evanescent decay.\n",
        "  \n",
        "  - **Implication for Light Propagation**: If evanescent modes exist on cosmological scales, they would introduce a decay in the intensity of light over short distances (relative to the cosmic scale), potentially affecting how we perceive distant objects in regions with strong gravitational potentials or near caustics. These modes might be linked to gravitational lensing, where certain light paths are highly suppressed due to space-time curvature.\n",
        "  \n",
        "- **Negative Index Modes**: Negative index of refraction is a phenomenon in metamaterials where waves bend in the opposite direction compared to normal materials. In cosmology, such behavior could theoretically arise in exotic space-time configurations or in the presence of certain types of dark energy or modified gravity theories. Negative index modes could lead to unusual gravitational lensing effects, such as light bending in unexpected directions or causing novel interference patterns.\n",
        "  \n",
        "  - **Implication for Lensing and Caustics**: If negative index modes exist, they could lead to the creation of exotic caustics where light is focused in unusual patterns, possibly causing **superlensing** (extreme magnification) or creating regions where light is completely blocked or bent away. This could fundamentally alter how we interpret lensing data and might introduce additional bias into distance measurements if not properly accounted for.\n",
        "\n",
        "  - **Wave Optics in Gravitational Lensing**: Gravitational lensing at cosmological scales is usually treated using the geometric optics approximation, but when considering wave optics, the propagation of light through caustics and regions with strong gravitational fields could lead to interference effects. If negative index modes exist, they could introduce additional wavefront distortions or shift the caustic structures in unexpected ways.\n",
        "\n",
        "### 4. **Wave Optics and the Propagation of Light over Cosmological Scales**\n",
        "\n",
        "While traditional lensing models use geometric optics, at very large distances and when light interacts with complex gravitational potentials (like in caustics), **wave optics** must be considered. This brings several potential consequences:\n",
        "  \n",
        "- **Interference and Diffraction**: Near cosmological caustics, light can undergo interference and diffraction, similar to how waves interact with obstacles or apertures in classical optics. These effects could lead to **diffraction fringes** around lensed images, and in the case of gravitational waves, even **beat patterns** could appear due to interference from multiple lensed paths.\n",
        "  \n",
        "- **Frequency Dependence**: Both evanescent and negative index modes could introduce frequency-dependent propagation effects, where different wavelengths of light (or gravitational waves) are focused or dispersed differently near caustics. This would have observational consequences, as the same object could appear differently in various parts of the electromagnetic spectrum.\n",
        "  \n",
        "  - **Gravitational Wave Lensing**: For gravitational waves, wave-optics effects in the vicinity of caustics or strong lenses could produce interference patterns, potentially observable by detectors like LIGO, Virgo, and the upcoming LISA. These patterns would reveal details about the intervening mass distribution and might also hint at exotic space-time phenomena, including the possibility of negative index-like behavior.\n",
        "\n",
        "### Conclusion\n",
        "\n",
        "The interaction between cosmological caustics and phenomena like BAO, birefringence, evanescent modes, and negative index modes introduces new layers of complexity in the study of cosmology. These effects can introduce biases or novel signatures in the measurement of cosmological parameters like $ H_0 $, $ \\Omega_m $, and the equation of state of dark energy. Caustics, particularly those created by gravitational lensing, can amplify or distort signals from distant sources, leading to both challenges and opportunities in refining our models of the universe.\n",
        "\n",
        "Understanding these effects requires sophisticated modeling using both **geometric and wave optics**, advanced simulations of large-scale structure, and precise observations from galaxy surveys, CMB experiments, and gravitational wave detectors. As these tools improve, we may be able to better account for or even exploit these phenomena to gain deeper insights into the nature of space-time and the evolution of the universe."
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      "cell_type": "markdown",
      "source": [
        "##What observational evidence is there for actual space-time caustics?\n",
        "\n"
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      "cell_type": "markdown",
      "source": [
        "Observational evidence for **space-time caustics** arises primarily from the field of **gravitational lensing**, where light from distant sources (such as galaxies, quasars, or supernovae) is bent and magnified by massive objects like galaxy clusters or dark matter structures. These lensing events sometimes result in the formation of **caustics**—regions where light is highly concentrated, leading to dramatic magnification or multiple images of the same source.\n",
        "\n",
        "Here are key examples of observational evidence for space-time caustics:\n",
        "\n",
        "### 1. **Strong Gravitational Lensing and Multiple Images**\n",
        "In strong gravitational lensing, light from a distant source is bent by the gravitational field of a massive object (e.g., a galaxy or galaxy cluster), often producing multiple images of the same object. In some cases, these multiple images form along **caustic curves**, which are locations where the magnification becomes formally infinite in the ideal case (though realistically, it can be extremely large).\n",
        "\n",
        "- **Examples of Multiple Image Formation**:\n",
        "  - **Einstein Cross**: The Einstein Cross is a famous gravitational lensing system where a quasar appears as four images arranged symmetrically around a foreground galaxy. This configuration occurs because the quasar's light is bent along a caustic curve.\n",
        "  - **Quasar Lens Systems**: Several lens systems involving quasars show multiple images due to caustics. These images can appear distorted, magnified, or stretched, revealing the underlying caustic structure of the lensing mass.\n",
        "\n",
        "- **Observations**: Gravitational lens systems such as the **SDSS J1004+4112** and **Abell 1689** lensing clusters provide excellent examples of strong lensing and caustics. In these cases, the light from distant galaxies is magnified and split into multiple images, often forming arcs or rings that trace the caustic structures of the gravitational lens.\n",
        "\n",
        "### 2. **Giant Arcs and Fold Caustics in Galaxy Clusters**\n",
        "Giant arcs are elongated images of distant galaxies created by strong gravitational lensing from galaxy clusters. These arcs often form along **fold caustics**, which occur when a source crosses a caustic curve in the lensing potential, leading to extreme magnification and stretching.\n",
        "\n",
        "- **Example: Abell 2218**: The **Abell 2218** galaxy cluster is famous for producing multiple giant arcs around its center, caused by gravitational lensing. These arcs are highly magnified images of background galaxies, and their shape and location are consistent with the presence of fold caustics.\n",
        "  \n",
        "- **Caustic Theory and Giant Arcs**: The theory of caustics in gravitational lensing predicts the formation of giant arcs when a source moves near or across a fold caustic, leading to sudden increases in magnification. These arcs have been observed in many clusters, providing evidence for the underlying caustic structures.\n",
        "\n",
        "### 3. **Critical Curves and Caustics in Lensing Maps**\n",
        "In gravitational lensing, **critical curves** are the loci on the sky where the magnification of a source becomes very large. When projected into the source plane, these curves map onto **caustics**. The location of these curves and caustics depends on the mass distribution of the lens.\n",
        "\n",
        "- **Lensing in Abell 1689**: The **Abell 1689** galaxy cluster is one of the best-studied lensing systems. Detailed lensing maps have been created using the distribution of multiple images, and these maps show the location of critical curves and caustics. Observations from instruments like the **Hubble Space Telescope (HST)** and **ground-based telescopes** have confirmed the existence of these structures in galaxy clusters.\n",
        "\n",
        "### 4. **Weak Lensing and Cosmic Shear**\n",
        "In **weak gravitational lensing**, the light from distant galaxies is slightly distorted by large-scale structures in the universe (like dark matter halos). While the effects are not as dramatic as in strong lensing, they can still reveal the presence of caustic-like features when combined across many sources.\n",
        "\n",
        "- **Cosmic Shear and Caustics**: Weak lensing surveys, such as those conducted by the **Dark Energy Survey (DES)**, **Kilo-Degree Survey (KiDS)**, and the **Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS)**, measure the statistical distortions (shear) in the shapes of galaxies due to weak lensing by large-scale structures. While weak lensing does not directly produce caustics observable in individual images, the cumulative effect of weak lensing by large-scale structure can be mapped, and caustic-like features can emerge in certain regions of these maps where the density of lensing structures is high.\n",
        "  \n",
        "### 5. **Gravitational Lensing of Gravitational Waves**\n",
        "While still a relatively new area of study, there is potential evidence for space-time caustics in the context of **gravitational wave lensing**. Gravitational waves, like light, can be lensed by massive objects. Caustics could lead to **amplified or multiple gravitational wave signals** when a source passes near or through a caustic region.\n",
        "\n",
        "- **Potential for Future Evidence**: As gravitational wave observatories like **LIGO**, **Virgo**, and future detectors like **LISA** (Laser Interferometer Space Antenna) continue to observe gravitational waves from merging black holes and neutron stars, there is a possibility that gravitational waves lensed by intervening mass could show caustic-related amplification effects. The detection of **multiple, time-delayed gravitational wave signals** from the same event could provide direct evidence of space-time caustics for gravitational waves.\n",
        "\n",
        "### 6. **Cosmic Microwave Background (CMB) Lensing Caustics**\n",
        "The **Cosmic Microwave Background (CMB)**, the relic radiation from the early universe, is also affected by gravitational lensing due to large-scale structures. Lensing of the CMB can produce small-scale distortions in the temperature and polarization maps.\n",
        "\n",
        "- **CMB Lensing**: Lensing of the CMB has been observed by experiments such as **Planck**, **ACT (Atacama Cosmology Telescope)**, and **SPT (South Pole Telescope)**. While caustics in the CMB are not as easily observed as in optical gravitational lensing, the lensing effects seen in the CMB provide indirect evidence of the large-scale structure and potential caustics that exist in the universe.\n",
        "  \n",
        "- **Polarization Caustics**: In some models, lensing of the CMB could also lead to caustics in the polarization field of the CMB, providing further evidence for the interaction of caustics with cosmic light on large scales.\n",
        "\n",
        "### 7. **Dark Matter Caustics**\n",
        "There is a theoretical prediction that dark matter forms **caustics** in the halos of galaxies. These caustics would occur where dark matter streams converge and overlap, leading to higher densities in certain regions. These caustics are expected to occur in both the outer and inner regions of galaxies.\n",
        "\n",
        "- **Evidence for Dark Matter Caustics**: While direct observational evidence of dark matter caustics is still lacking, there have been hints from **rotation curve** anomalies in galaxies, which suggest the presence of additional mass in certain regions that could be explained by dark matter caustics. Additionally, N-body simulations of dark matter in galactic halos often show caustic-like structures where the density of dark matter becomes highly concentrated due to gravitational collapse.\n",
        "\n",
        "### Conclusion\n",
        "\n",
        "The observational evidence for space-time caustics comes largely from **gravitational lensing phenomena**, particularly the formation of **multiple images**, **giant arcs**, and **critical curves** in galaxy clusters. Strong gravitational lensing provides the clearest examples of caustics, where light from distant sources is magnified and split along caustic curves. While evidence for caustics in **dark matter** and **gravitational waves** is still emerging, future observations and improved detection techniques will likely uncover more examples of space-time caustics, especially as new tools like **LISA** and next-generation telescopes become operational."
      ],
      "metadata": {
        "id": "cK3zCcrTIoJb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##What would/do these caustics look like, and can we model the spacetime distortion that creates the caustics? give me the theory plesase\n",
        "\n"
      ],
      "metadata": {
        "id": "vcdM17N9IsPD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Caustics and Their Appearance in Space-Time\n",
        "\n",
        "**Caustics** in the context of space-time refer to regions where light (or other waves, including gravitational waves) is focused due to gravitational lensing or space-time distortions, leading to high magnification and sometimes multiple images of a distant source. These caustics can take various forms depending on the gravitational potential that causes them.\n",
        "\n",
        "The appearance of caustics can be likened to the patterns of light on the bottom of a pool: concentrated bright spots or lines where waves converge. In gravitational lensing, caustics manifest as **arcs**, **Einstein rings**, or **multiple image systems**.\n",
        "\n",
        "#### Common Forms of Caustics in Cosmology:\n",
        "1. **Fold Caustics**: These occur when a light source crosses a smooth caustic surface, causing a sudden increase in magnification. The most common manifestation is **giant arcs** seen in galaxy clusters.\n",
        "2. **Cusp Caustics**: Cusp caustics arise from the merging of fold caustics, producing sharp peaks of magnification. This often results in multiple images clustered together, such as in **quasar lensing systems**.\n",
        "3. **Caustic Networks**: In the case of dark matter caustics in galactic halos, these appear as shells or layers where the dark matter density increases due to the convergence of cold dark matter streams.\n",
        "\n",
        "### Theory of Caustics in Gravitational Lensing\n",
        "\n",
        "The formation of caustics in gravitational lensing is rooted in **general relativity**, which describes how mass bends space-time, and hence light, around it. To understand the theory, we begin with the **lens equation**, which relates the position of a source to its observed, lensed position:\n",
        "\n",
        "$$\n",
        "\\boldsymbol{\\beta} = \\boldsymbol{\\theta} - \\boldsymbol{\\alpha}(\\boldsymbol{\\theta})\n",
        "$$\n",
        "\n",
        "Where:\n",
        "- $ \\boldsymbol{\\beta} $ is the position of the source.\n",
        "- $ \\boldsymbol{\\theta} $ is the observed, lensed position of the source.\n",
        "- $ \\boldsymbol{\\alpha}(\\boldsymbol{\\theta}) $ is the deflection angle of light caused by the lensing mass.\n",
        "\n",
        "The lensing potential $ \\psi(\\boldsymbol{\\theta}) $ describes the gravitational potential responsible for deflecting light, and the deflection angle $ \\boldsymbol{\\alpha} $ is derived from it as:\n",
        "\n",
        "$$\n",
        "\\boldsymbol{\\alpha} = \\nabla \\psi(\\boldsymbol{\\theta})\n",
        "$$\n",
        "\n",
        "The key to understanding caustics is the **Jacobian matrix** of the lens mapping, which describes how the positions of the lensed images change with respect to the source position. This matrix is:\n",
        "\n",
        "$$\n",
        "A = \\frac{\\partial \\boldsymbol{\\beta}}{\\partial \\boldsymbol{\\theta}} = \\mathbb{I} - \\frac{\\partial \\boldsymbol{\\alpha}}{\\partial \\boldsymbol{\\theta}} = \\mathbb{I} - \\nabla^2 \\psi(\\boldsymbol{\\theta})\n",
        "$$\n",
        "\n",
        "The **magnification** of the lensing event is given by the inverse of the determinant of this Jacobian matrix:\n",
        "\n",
        "$$\n",
        "\\mu = \\frac{1}{|\\det(A)|}\n",
        "$$\n",
        "\n",
        "Caustics occur where the magnification becomes very large, i.e., where $ \\det(\\mathcal{A}) = 0 $. These are the **critical curves** in the lens plane (the 2D plane where the deflecting mass lies). When mapped back to the source plane (the plane where the distant source lies), these critical curves become **caustic curves**.\n",
        "\n",
        "### Types of Caustics:\n",
        "1. **Fold Caustics**: These occur when the source crosses a smooth curve of critical points in the lens plane. The magnification diverges near the caustic but remains finite in real systems. Fold caustics are the simplest and most common form of caustic.\n",
        "   \n",
        "2. **Cusp Caustics**: These arise at the intersections of fold caustics and represent points of even higher magnification. Cusp caustics can create multiple images of the same source close together.\n",
        "\n",
        "3. **Elliptical and Spherical Lenses**: If the lensing mass is symmetric, such as a singular isothermal sphere or an elliptical potential, the caustic structures take on a corresponding symmetry. For example, a perfect **Einstein ring** is a circular caustic formed when a source lies exactly behind a spherically symmetric lens.\n",
        "\n",
        "### Modelling the Space-Time Distortion and Caustics\n",
        "\n",
        "To model caustics, we use the **geometric optics approximation** of general relativity, where light rays follow null geodesics (the paths of light in curved space-time). The following elements are key in constructing models of space-time caustics:\n",
        "\n",
        "#### 1. **Metric of Space-Time**:\n",
        "The metric describes the curvature of space-time around a massive object (the lens). For a point mass lens, the simplest form of the metric is the **Schwarzschild metric**:\n",
        "\n",
        "$$\n",
        "ds^2 = -\\left(1 - \\frac{2GM}{r}\\right) dt^2 + \\left(1 - \\frac{2GM}{r}\\right)^{-1} dr^2 + r^2 (d\\theta^2 + \\sin^2\\theta \\, d\\phi^2)\n",
        "$$\n",
        "\n",
        "Here, $ G $ is the gravitational constant, $ M $ is the mass of the lens, and $ r $, $ \\theta $, and $ \\phi $ are spherical coordinates. This metric describes the bending of space-time due to a static, spherically symmetric mass.\n",
        "\n",
        "For more complex lensing systems, such as galaxy clusters, the metric would be derived from the mass distribution of the cluster, often modeled using the **Navarro-Frenk-White (NFW)** profile for dark matter halos.\n",
        "\n",
        "#### 2. **Lens Equation and Potential**:\n",
        "The lens equation is solved numerically or analytically for simple cases to find the positions of images and to map out the critical and caustic curves. The potential $ \\psi(\\theta) $ of a lensing mass is calculated based on the mass distribution, and the deflection angle $ \\alpha(\\theta) $ is derived from it.\n",
        "\n",
        "In simple cases like the **singular isothermal sphere (SIS)**, the potential is proportional to the logarithm of the distance:\n",
        "\n",
        "$$\n",
        "\\psi(\\theta) = \\theta_E^2 \\ln|\\theta|\n",
        "$$\n",
        "\n",
        "Where $ \\theta_E $ is the Einstein radius, which defines the size of the Einstein ring.\n",
        "\n",
        "#### 3. **Perturbation Theory for Wave Optics**:\n",
        "While geometric optics describes the deflection of light as rays, **wave optics** is needed when considering interference effects near caustics. In wave optics, light is treated as a wave, and the **Huygens-Fresnel principle** is applied. This can produce diffraction patterns in the vicinity of caustics, which can be modeled using **Fermat's principle** and **wave propagation equations**.\n",
        "\n",
        "The wavefront distortion near caustics can be described using the **Keller-Maslov index theory**. This theory uses catastrophe theory, particularly **Arnold’s classification**, to model the formation of fold, cusp, and higher-order caustics in wavefronts.\n",
        "\n",
        "#### 4. **Dark Matter Caustics**:\n",
        "In the context of dark matter, caustics arise due to the convergence of dark matter streams in galactic halos. The theory behind dark matter caustics is based on **cold dark matter (CDM)** dynamics, where the collisionless nature of dark matter allows for the formation of thin, dense shells or filaments at certain radii in the galaxy.\n",
        "\n",
        "- **Zeldovich Approximation**: This is used to model the formation of large-scale structures in the universe, including caustics. It assumes that the motion of matter can be approximated as moving along straight lines until gravitational collapse forms dense structures like caustics.\n",
        "\n",
        "The theory predicts **inner caustics** (near the galactic center) and **outer caustics** (in the outskirts of galaxies), where the dark matter density spikes. These can be modeled numerically using **N-body simulations**, which track the evolution of dark matter particles under gravity.\n",
        "\n",
        "### Mathematical Models and Catastrophe Theory\n",
        "\n",
        "Caustics can be mathematically modeled using **catastrophe theory**, which studies how small changes in parameters can lead to sudden changes in the behavior of a system. In gravitational lensing, this corresponds to changes in the position of the source relative to the lens causing a sudden increase in magnification.\n",
        "\n",
        "#### Catastrophe Types:\n",
        "1. **Fold Catastrophe**: This is the simplest type of caustic, occurring when a single image splits into two. It is described by the equation:\n",
        "\n",
        "   $$\n",
        "   F(x) = x^3 - ax\n",
        "   $$\n",
        "\n",
        "   Where $ a $ is a control parameter. This describes the formation of a fold caustic as the parameter $ a $ changes.\n",
        "\n",
        "2. **Cusp Catastrophe**: This occurs when three images merge into one. It is described by the equation:\n",
        "\n",
        "   $$\n",
        "   C(x, y) = x^4 + y^2 - ax - by\n",
        "   $$\n",
        "\n",
        "   Where $ a $ and $ b $ are control parameters. As $ a $ and $ b $ change, a cusp caustic forms.\n",
        "\n",
        "These catastrophe models are used to predict the shapes and behavior of caustics in gravitational lensing, and they have been applied extensively in both theoretical and observational lensing studies.\n",
        "\n",
        "\n",
        "\n",
        "### Conclusion\n",
        "\n",
        "Caustics in space-time, particularly in the context of gravitational lensing, arise from the magnification and focusing of light due to the curvature of space-time by massive objects. The theory behind their formation is grounded in general relativity, geometric optics, and catastrophe theory. These caustics can be modeled using the lens equation, the Jacobian of the lens mapping, and wave optics when interference effects become significant. Observational evidence, particularly in strong gravitational lensing systems like galaxy clusters, confirms the existence of these caustic structures, and numerical simulations further help refine our understanding of their formation and effects on cosmological parameters."
      ],
      "metadata": {
        "id": "BCaKaAssIyyI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Jupyter notebook example, to ingest observational data such as  gaia and then search for and analyse actual caustics.\n",
        "\n"
      ],
      "metadata": {
        "id": "-NXkcOWpKDB6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here's a workflow you can implement in a Jupyter notebook to ingest observational data (such as from the **Gaia mission**) and analyze gravitational lensing caustics. This example will guide you through ingesting data, performing basic pre-processing, and searching for caustics in gravitational lensing phenomena. You can adapt it for more specific datasets or models as needed.\n",
        "\n",
        "### Step-by-Step Workflow\n",
        "\n",
        "1. **Install Required Libraries**:\n",
        "   First, you'll need libraries for handling astronomical data, numerical analysis, and plotting. These can be installed via `pip` if necessary:\n",
        "\n",
        "   ```bash\n",
        "   pip install numpy matplotlib astropy astroquery pandas scipy\n",
        "   ```\n",
        "\n",
        "2. **Import the Libraries**:\n",
        "\n",
        "   ```python\n",
        "   import numpy as np\n",
        "   import matplotlib.pyplot as plt\n",
        "   from astropy.io import fits\n",
        "   from astropy.table import Table\n",
        "   from astroquery.gaia import Gaia\n",
        "   from scipy.optimize import minimize\n",
        "   ```\n",
        "\n",
        "3. **Query and Load Data from Gaia**:\n",
        "\n",
        "   You can use `astroquery` to fetch data from the Gaia mission. Gaia provides detailed positional, distance, and motion data for billions of stars, which could serve as background sources for lensing studies.\n",
        "\n",
        "   Here's how you can query a specific region of the sky and retrieve a list of sources:\n",
        "\n",
        "   ```python\n",
        "   # Define the region of interest in RA, Dec (in degrees)\n",
        "   ra = 180.0  # Right Ascension\n",
        "   dec = 0.0   # Declination\n",
        "   radius = 0.1  # Search radius in degrees\n",
        "\n",
        "   # Gaia query for sources in the region of interest\n",
        "   query = f\"\"\"\n",
        "   SELECT source_id, ra, dec, parallax, pmra, pmdec, phot_g_mean_mag\n",
        "   FROM gaiadr3.gaia_source\n",
        "   WHERE 1=CONTAINS(\n",
        "     POINT('ICRS', ra, dec),\n",
        "     CIRCLE('ICRS', {ra}, {dec}, {radius})\n",
        "   )\n",
        "   \"\"\"\n",
        "   job = Gaia.launch_job(query)\n",
        "   results = job.get_results()\n",
        "\n",
        "   # Convert results to a pandas DataFrame for easier manipulation\n",
        "   data = results.to_pandas()\n",
        "   ```\n",
        "\n",
        "4. **Pre-process the Data**:\n",
        "\n",
        "   You may want to filter out stars with high parallax errors or other issues. You can filter the data based on quality:\n",
        "\n",
        "   ```python\n",
        "   # Filter out sources with poor parallax measurements\n",
        "   filtered_data = data[data['parallax_error'] < 0.1]\n",
        "\n",
        "   # Display a few rows of the filtered data\n",
        "   print(filtered_data.head())\n",
        "   ```\n",
        "\n",
        "5. **Simulate a Simple Lens (SIS Model)**:\n",
        "\n",
        "   In gravitational lensing studies, a common model is the **Singular Isothermal Sphere (SIS)**, which approximates the gravitational potential of a galaxy cluster. We will set up a simple model for a lensing galaxy or galaxy cluster:\n",
        "\n",
        "   ```python\n",
        "   def deflection_angle(theta, theta_e):\n",
        "       \"\"\" Deflection angle for SIS model \"\"\"\n",
        "       return theta_e / np.abs(theta)\n",
        "\n",
        "   def lens_equation(theta, beta, theta_e):\n",
        "       \"\"\" Lens equation for SIS model: theta - alpha(theta) = beta \"\"\"\n",
        "       return theta - deflection_angle(theta, theta_e) - beta\n",
        "\n",
        "   # Example values\n",
        "   theta_e = 1.0  # Einstein radius (arcseconds)\n",
        "   beta = 0.5     # Source position (arcseconds)\n",
        "\n",
        "   # Solving for the lensed image positions\n",
        "   def solve_lens_eq(beta, theta_e):\n",
        "       # Minimize the lens equation to find the lensed image position\n",
        "       sol = minimize(lambda theta: np.abs(lens_equation(theta, beta, theta_e)), x0=[beta])\n",
        "       return sol.x[0]\n",
        "\n",
        "   theta_lens = solve_lens_eq(beta, theta_e)\n",
        "   print(f\"Lensed image position: {theta_lens} arcseconds\")\n",
        "   ```\n",
        "\n",
        "6. **Search for Caustics**:\n",
        "\n",
        "   To search for caustics, you need to calculate the magnification of the lensed images using the Jacobian of the lens equation. The magnification is the inverse of the determinant of the Jacobian matrix. For the SIS model, the magnification \\( \\mu \\) is:\n",
        "   $$\n",
        "   \\mu = \\frac{1}{1 - \\frac{\\theta_e}{|\\theta|}}\n",
        "   $$\n",
        "\n",
        "   Here's how to compute it:\n",
        "\n",
        "   ```python\n",
        "   def magnification(theta, theta_e):\n",
        "       \"\"\" Magnification for SIS lens model \"\"\"\n",
        "       return 1 / np.abs(1 - (theta_e / np.abs(theta)))\n",
        "\n",
        "   # Calculate magnification for the lensed image\n",
        "   mu = magnification(theta_lens, theta_e)\n",
        "   print(f\"Magnification: {mu}\")\n",
        "   ```\n",
        "\n",
        "7. **Visualize the Caustics**:\n",
        "\n",
        "   You can visualize the caustics by plotting the source and lensed image positions along with the critical curve. Here's how you can plot the system:\n",
        "\n",
        "   ```python\n",
        "   theta_range = np.linspace(-2, 2, 1000)\n",
        "   image_positions = [solve_lens_eq(b, theta_e) for b in theta_range]\n",
        "   magnifications = [magnification(theta, theta_e) for theta in image_positions]\n",
        "\n",
        "   plt.figure(figsize=(8, 6))\n",
        "   plt.plot(theta_range, image_positions, label='Lensed Image Positions')\n",
        "   plt.plot(theta_range, magnifications, label='Magnification', linestyle='--')\n",
        "   plt.axvline(x=0, color='gray', linestyle=':', label='Lens Center')\n",
        "   plt.title('Lensed Image Positions and Caustics')\n",
        "   plt.xlabel(r'Source Position $\\beta$ (arcseconds)')\n",
        "   plt.ylabel(r'Lensed Position $\\theta$ (arcseconds)')\n",
        "   plt.legend()\n",
        "   plt.grid(True)\n",
        "   plt.show()\n",
        "   ```\n",
        "\n",
        "8. **Apply the Model to Real Data**:\n",
        "\n",
        "   You can now take the Gaia data, assume some of the stars are lensed, and apply the SIS model to each star to compute its lensed position and magnification. You would look for signs of **high magnification**, indicating proximity to a caustic.\n",
        "\n",
        "   ```python\n",
        "   # Example: apply lensing model to the first star in the dataset\n",
        "   star = filtered_data.iloc[0]\n",
        "   star_ra = star['ra']\n",
        "   star_dec = star['dec']\n",
        "   star_mag = star['phot_g_mean_mag']\n",
        "\n",
        "   # Calculate lensed image and magnification\n",
        "   beta = star_ra  # Simplified for demonstration, normally you'd transform coords\n",
        "   theta_lens = solve_lens_eq(beta, theta_e)\n",
        "   mu = magnification(theta_lens, theta_e)\n",
        "\n",
        "   print(f\"Star RA: {star_ra}, Dec: {star_dec}, Magnification: {mu}\")\n",
        "   ```\n",
        "\n",
        "9. **Refine and Expand**:\n",
        "   - You can refine the model to account for more complex lensing systems (e.g., elliptical lenses, galaxy clusters) or use other gravitational lensing models such as **NFW halos** for dark matter-dominated lenses.\n",
        "   - Expand the dataset to use more stars or combine Gaia data with other surveys (e.g., **DES**, **Hubble**, or **SDSS**) to improve the analysis.\n",
        "   - You can also integrate observational data with simulations using N-body models or ray-tracing tools to look for more subtle lensing signals or dark matter caustics.\n",
        "\n",
        "### Data Sources for Further Study:\n",
        "- **Gaia**: Offers precise astrometry of stars, useful for tracking lensed stars and searching for microlensing events.\n",
        "- **SDSS (Sloan Digital Sky Survey)**: Provides galaxy spectra and imaging data, ideal for searching for lensed galaxies.\n",
        "- **Hubble Space Telescope (HST)**: High-resolution imaging, especially useful for detailed lensing studies.\n",
        "\n",
        "This workflow provides a starting point for searching for gravitational lensing caustics using real data. You can scale up the analysis by applying it to larger datasets and more complex lensing models."
      ],
      "metadata": {
        "id": "L2Ss_nVMKvmf"
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    },
    {
      "cell_type": "code",
      "source": [
        "!pip install numpy matplotlib astropy astroquery pandas scipy"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bBQtOCPVLIx4",
        "outputId": "b188907f-e219-4783-87ea-765b76d9baee"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "Collecting astroquery\n",
            "  Using cached astroquery-0.4.7-py3-none-any.whl.metadata (7.2 kB)\n",
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            "  Using cached pyvo-1.5.3-py3-none-any.whl.metadata (4.7 kB)\n",
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            "Installing collected packages: pyvo, astroquery\n",
            "Successfully installed astroquery-0.4.7 pyvo-1.5.3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from astropy.io import fits\n",
        "from astropy.table import Table\n",
        "from astroquery.gaia import Gaia\n",
        "from scipy.optimize import minimize\n",
        "# Define the region of interest in RA, Dec (in degrees)\n",
        "ra = 180.0  # Right Ascension\n",
        "dec = 0.0   # Declination\n",
        "radius = 0.1  # Search radius in degrees\n",
        "\n",
        "# Gaia query for sources in the region of interest\n",
        "# Added parallax_error to the query\n",
        "query = f\"\"\"\n",
        "SELECT source_id, ra, dec, parallax, pmra, pmdec, phot_g_mean_mag, parallax_error\n",
        "FROM gaiadr3.gaia_source\n",
        "WHERE 1=CONTAINS(\n",
        "  POINT('ICRS', ra, dec),\n",
        "  CIRCLE('ICRS', {ra}, {dec}, {radius})\n",
        ")\n",
        "\"\"\"\n",
        "job = Gaia.launch_job(query)\n",
        "results = job.get_results()\n",
        "\n",
        "# Convert results to a pandas DataFrame for easier manipulation\n",
        "data = results.to_pandas()\n",
        "# Filter out sources with poor parallax measurements\n",
        "filtered_data = data[data['parallax_error'] < 0.1]\n",
        "\n",
        "# Display a few rows of the filtered data\n",
        "print(filtered_data.head())\n",
        "def deflection_angle(theta, theta_e):\n",
        "    \"\"\" Deflection angle for SIS model \"\"\"\n",
        "    return theta_e / np.abs(theta)\n",
        "\n",
        "def lens_equation(theta, beta, theta_e):\n",
        "    \"\"\" Lens equation for SIS model: theta - alpha(theta) = beta \"\"\"\n",
        "    return theta - deflection_angle(theta, theta_e) - beta\n",
        "\n",
        "# Example values\n",
        "theta_e = 1.0  # Einstein radius (arcseconds)\n",
        "beta = 0.5     # Source position (arcseconds)\n",
        "\n",
        "# Solving for the lensed image positions\n",
        "def solve_lens_eq(beta, theta_e):\n",
        "    # Minimize the lens equation to find the lensed image position\n",
        "    sol = minimize(lambda theta: np.abs(lens_equation(theta, beta, theta_e)), x0=[beta])\n",
        "    return sol.x[0]\n",
        "\n",
        "theta_lens = solve_lens_eq(beta, theta_e)\n",
        "print(f\"Lensed image position: {theta_lens} arcseconds\")\n",
        "\n",
        "def magnification(theta, theta_e):\n",
        "    \"\"\" Magnification for SIS lens model \"\"\"\n",
        "    return 1 / np.abs(1 - (theta_e / np.abs(theta)))\n",
        "\n",
        "# Calculate magnification for the lensed image\n",
        "mu = magnification(theta_lens, theta_e)\n",
        "print(f\"Magnification: {mu}\")\n",
        "\n",
        "theta_range = np.linspace(-2, 2, 1000)\n",
        "image_positions = [solve_lens_eq(b, theta_e) for b in theta_range]\n",
        "magnifications = [magnification(theta, theta_e) for theta in image_positions]\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(theta_range, image_positions, label='Lensed Image Positions')\n",
        "plt.plot(theta_range, magnifications, label='Magnification', linestyle='--')\n",
        "plt.axvline(x=0, color='gray', linestyle=':', label='Lens Center')\n",
        "plt.title('Lensed Image Positions and Caustics')\n",
        "plt.xlabel(r'Source Position $\\beta$ (arcseconds)')\n",
        "plt.ylabel(r'Lensed Position $\\theta$ (arcseconds)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 836
        },
        "id": "181HQQ1uLkg3",
        "outputId": "3c3aa58b-6a0d-4ee3-d39d-c08fe89f3a98"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              SOURCE_ID          ra       dec  parallax       pmra      pmdec  \\\n",
            "6   3795032797804395008  179.930722 -0.027623  0.821255 -22.783260  -8.186590   \n",
            "11  3795033244480995072  179.980733 -0.003938  0.516995 -28.621633  -0.850522   \n",
            "15  3795033278840733568  179.984545 -0.001041 -0.025869  -2.650933  -1.608555   \n",
            "46  3602878297443569920  180.068776 -0.071511  2.660761 -84.533533 -14.423515   \n",
            "52  3602878572320135296  180.040133 -0.045332  1.479696 -10.968584  10.682266   \n",
            "\n",
            "    phot_g_mean_mag  parallax_error  \n",
            "6         15.803629        0.054967  \n",
            "11        16.730806        0.087755  \n",
            "15        16.626635        0.085772  \n",
            "46        15.504142        0.067355  \n",
            "52        16.268152        0.083714  \n",
            "Lensed image position: 1.2807764027212944 arcseconds\n",
            "Magnification: 4.56155285952796\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the RA and Dec of sources in the region\n",
        "plt.figure(figsize=(10, 8))\n",
        "plt.scatter(filtered_data['ra'], filtered_data['dec'], c=filtered_data['phot_g_mean_mag'], s=10, cmap='viridis', marker='o')\n",
        "plt.colorbar(label='G-band Magnitude')\n",
        "plt.xlabel('Right Ascension (degrees)')\n",
        "plt.ylabel('Declination (degrees)')\n",
        "plt.title('Spatial Distribution of Gaia Sources in the Selected Region')\n",
        "plt.gca().invert_xaxis()  # Invert RA for proper sky view\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "id": "y-owiNjRMAhq",
        "outputId": "c0a01eec-1e80-42c5-a0fb-4200f91a3a92"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from astroquery.skyview import SkyView\n",
        "\n",
        "# Define the target coordinates and survey\n",
        "survey = 'DSS2 Red'  # You can also try 'DSS2 Blue', 'DSS2 IR', etc.\n",
        "position = f\"{ra} {dec}\"\n",
        "\n",
        "# Fetch the image\n",
        "try:\n",
        "    images = SkyView.get_images(position=position, survey=survey, radius=0.05 * coords.degree)\n",
        "    # Display the first image in the result\n",
        "    plt.figure(figsize=(8, 8))\n",
        "    plt.imshow(images[0][0].data, cmap='gray', origin='lower')\n",
        "    plt.colorbar(label=\"Pixel values\")\n",
        "    plt.title(f\"DSS Image of Region (RA: {ra}, Dec: {dec}) - {survey}\")\n",
        "    plt.show()\n",
        "except Exception as e:\n",
        "    print(f\"Could not retrieve image: {e}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rbfFF6TBMRoW",
        "outputId": "5e369f31-d86b-4b08-a96a-bb1b573b3a16"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Could not retrieve image: name 'coords' is not defined\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: apply lensing model to the first star in the dataset\n",
        "star = filtered_data.iloc[0]\n",
        "star_ra = star['ra']\n",
        "star_dec = star['dec']\n",
        "star_mag = star['phot_g_mean_mag']\n",
        "\n",
        "# Calculate lensed image and magnification\n",
        "beta = star_ra  # Simplified for demonstration, normally you'd transform coords\n",
        "theta_lens = solve_lens_eq(beta, theta_e)\n",
        "mu = magnification(theta_lens, theta_e)\n",
        "\n",
        "print(f\"Star RA: {star_ra}, Dec: {star_dec}, Magnification: {mu}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oJ8ux5KpKq5N",
        "outputId": "3143a583-df08-4b3f-d71d-81521a3aac21"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Star RA: 179.9307217645084, Dec: -0.02762257736685463, Magnification: 1.005588581611386\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from astropy.io import fits\n",
        "from astropy.table import Table\n",
        "from astroquery.gaia import Gaia\n",
        "from astroquery.sdss import SDSS\n",
        "from astroquery.skyview import SkyView\n",
        "#from astroquery.image_cutouts.pan_starrs import PanSTARRS\n",
        "from astropy import coordinates as coords\n",
        "from scipy.optimize import minimize\n",
        "\n",
        "# Define the region of interest in RA, Dec (in degrees)\n",
        "ra = 180.0  # Right Ascension\n",
        "dec = 0.0   # Declination\n",
        "radius = 0.1  # Search radius in degrees\n",
        "\n",
        "# Gaia query for sources in the region of interest, including parallax error\n",
        "query = f\"\"\"\n",
        "SELECT source_id, ra, dec, parallax, pmra, pmdec, phot_g_mean_mag, parallax_error\n",
        "FROM gaiadr3.gaia_source\n",
        "WHERE 1=CONTAINS(\n",
        "  POINT('ICRS', ra, dec),\n",
        "  CIRCLE('ICRS', {ra}, {dec}, {radius})\n",
        ")\n",
        "\"\"\"\n",
        "job = Gaia.launch_job(query)\n",
        "results = job.get_results()\n",
        "\n",
        "# Convert results to a pandas DataFrame for easier manipulation\n",
        "data = results.to_pandas()\n",
        "# Filter out sources with poor parallax measurements\n",
        "filtered_data = data[data['parallax_error'] < 0.1]\n",
        "\n",
        "# Display a few rows of the filtered data\n",
        "print(filtered_data.head())\n",
        "\n",
        "# Plot the RA and Dec of sources in the region\n",
        "plt.figure(figsize=(10, 8))\n",
        "plt.scatter(filtered_data['ra'], filtered_data['dec'], c=filtered_data['phot_g_mean_mag'], s=10, cmap='viridis', marker='o')\n",
        "plt.colorbar(label='G-band Magnitude')\n",
        "plt.xlabel('Right Ascension (degrees)')\n",
        "plt.ylabel('Declination (degrees)')\n",
        "plt.title('Spatial Distribution of Gaia Sources in the Selected Region')\n",
        "plt.gca().invert_xaxis()  # Invert RA for proper sky view\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "# Function for retrieving and displaying an SDSS image\n",
        "def display_sdss_image(ra, dec):\n",
        "    position = coords.SkyCoord(ra, dec, unit=\"deg\", frame=\"icrs\")\n",
        "    try:\n",
        "        hdu_list = SDSS.get_images(coordinates=position, radius=0.05 * coords.degree)\n",
        "        plt.figure(figsize=(8, 8))\n",
        "        plt.imshow(hdu_list[0][0].data, cmap='gray', origin='lower')\n",
        "        plt.colorbar(label=\"Pixel values\")\n",
        "        plt.title(f\"SDSS Image of Region (RA: {ra}, Dec: {dec})\")\n",
        "        plt.show()\n",
        "    except Exception as e:\n",
        "        print(f\"Could not retrieve SDSS image: {e}\")\n",
        "\n",
        "# Function for retrieving and displaying a DSS image\n",
        "def display_dss_image(ra, dec):\n",
        "    position = f\"{ra} {dec}\"\n",
        "    try:\n",
        "        images = SkyView.get_images(position=position, survey='DSS2 Red', radius=0.05 * coords.degree)\n",
        "        plt.figure(figsize=(8, 8))\n",
        "        plt.imshow(images[0][0].data, cmap='gray', origin='lower')\n",
        "        plt.colorbar(label=\"Pixel values\")\n",
        "        plt.title(f\"DSS Image of Region (RA: {ra}, Dec: {dec}) - DSS2 Red\")\n",
        "        plt.show()\n",
        "    except Exception as e:\n",
        "        print(f\"Could not retrieve DSS image: {e}\")\n",
        "\n",
        "# Function for retrieving and displaying a Pan-STARRS image\n",
        "def display_pan_starrs_image1(ra, dec):\n",
        "    position = coords.SkyCoord(ra, dec, unit=\"deg\", frame=\"icrs\")\n",
        "    try:\n",
        "        cutout = PanSTARRS.get_images(coordinates=position, size=240, filter='r')\n",
        "        plt.figure(figsize=(8, 8))\n",
        "        plt.imshow(cutout[0][0].data, cmap='gray', origin='lower')\n",
        "        plt.colorbar(label=\"Pixel values\")\n",
        "        plt.title(f\"Pan-STARRS Image of Region (RA: {ra}, Dec: {dec}) - r-band\")\n",
        "        plt.show()\n",
        "    except Exception as e:\n",
        "        print(f\"Could not retrieve Pan-STARRS image: {e}\")\n",
        "\n",
        "# Function for retrieving and displaying a Pan-STARRS image using SkyView\n",
        "def display_pan_starrs_image(ra, dec):\n",
        "    position = f\"{ra} {dec}\"\n",
        "    try:\n",
        "        images = SkyView.get_images(position=position, survey='PanSTARRS1 r', radius=0.05 * coords.degree)\n",
        "        plt.figure(figsize=(8, 8))\n",
        "        plt.imshow(images[0][0].data, cmap='gray', origin='lower')\n",
        "        plt.colorbar(label=\"Pixel values\")\n",
        "        plt.title(f\"Pan-STARRS Image of Region (RA: {ra}, Dec: {dec}) - r-band\")\n",
        "        plt.show()\n",
        "    except Exception as e:\n",
        "        print(f\"Could not retrieve Pan-STARRS image: {e}\")\n",
        "\n",
        "# Display images from different sources\n",
        "display_sdss_image(ra, dec)\n",
        "display_dss_image(ra, dec)\n",
        "display_pan_starrs_image(ra, dec)\n",
        "\n",
        "\n",
        "# Display images from different sources\n",
        "display_sdss_image(ra, dec)\n",
        "display_dss_image(ra, dec)\n",
        "display_pan_starrs_image(ra, dec)\n",
        "\n",
        "# Lens model and analysis (example SIS lens model)\n",
        "def deflection_angle(theta, theta_e):\n",
        "    \"\"\" Deflection angle for SIS model \"\"\"\n",
        "    return theta_e / np.abs(theta)\n",
        "\n",
        "def lens_equation(theta, beta, theta_e):\n",
        "    \"\"\" Lens equation for SIS model: theta - alpha(theta) = beta \"\"\"\n",
        "    return theta - deflection_angle(theta, theta_e) - beta\n",
        "\n",
        "# Example values for lensing\n",
        "theta_e = 1.0  # Einstein radius (arcseconds)\n",
        "beta = 0.5     # Source position (arcseconds)\n",
        "\n",
        "# Solving for the lensed image positions\n",
        "def solve_lens_eq(beta, theta_e):\n",
        "    # Minimize the lens equation to find the lensed image position\n",
        "    sol = minimize(lambda theta: np.abs(lens_equation(theta, beta, theta_e)), x0=[beta])\n",
        "    return sol.x[0]\n",
        "\n",
        "theta_lens = solve_lens_eq(beta, theta_e)\n",
        "print(f\"Lensed image position: {theta_lens} arcseconds\")\n",
        "\n",
        "def magnification(theta, theta_e):\n",
        "    \"\"\" Magnification for SIS lens model \"\"\"\n",
        "    return 1 / np.abs(1 - (theta_e / np.abs(theta)))\n",
        "\n",
        "# Calculate magnification for the lensed image\n",
        "mu = magnification(theta_lens, theta_e)\n",
        "print(f\"Magnification: {mu}\")\n",
        "\n",
        "# Plotting the lens model results\n",
        "theta_range = np.linspace(-2, 2, 1000)\n",
        "image_positions = [solve_lens_eq(b, theta_e) for b in theta_range]\n",
        "magnifications = [magnification(theta, theta_e) for theta in image_positions]\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(theta_range, image_positions, label='Lensed Image Positions')\n",
        "plt.plot(theta_range, magnifications, label='Magnification', linestyle='--')\n",
        "plt.axvline(x=0, color='gray', linestyle=':', label='Lens Center')\n",
        "plt.title('Lensed Image Positions and Caustics')\n",
        "plt.xlabel(r'Source Position $\\beta$ (arcseconds)')\n",
        "plt.ylabel(r'Lensed Position $\\theta$ (arcseconds)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "IHYqJzE_Mr5_",
        "outputId": "808895c4-2775-4ef4-a322-554cba6d4731"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              SOURCE_ID          ra       dec  parallax       pmra      pmdec  \\\n",
            "6   3795032797804395008  179.930722 -0.027623  0.821255 -22.783260  -8.186590   \n",
            "11  3795033244480995072  179.980733 -0.003938  0.516995 -28.621633  -0.850522   \n",
            "15  3795033278840733568  179.984545 -0.001041 -0.025869  -2.650933  -1.608555   \n",
            "46  3602878297443569920  180.068776 -0.071511  2.660761 -84.533533 -14.423515   \n",
            "52  3602878572320135296  180.040133 -0.045332  1.479696 -10.968584  10.682266   \n",
            "\n",
            "    phot_g_mean_mag  parallax_error  \n",
            "6         15.803629        0.054967  \n",
            "11        16.730806        0.087755  \n",
            "15        16.626635        0.085772  \n",
            "46        15.504142        0.067355  \n",
            "52        16.268152        0.083714  \n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Could not retrieve SDSS image: module 'astropy.coordinates' has no attribute 'degree'\n",
            "Could not retrieve DSS image: module 'astropy.coordinates' has no attribute 'degree'\n",
            "Could not retrieve Pan-STARRS image: module 'astropy.coordinates' has no attribute 'degree'\n",
            "Could not retrieve SDSS image: module 'astropy.coordinates' has no attribute 'degree'\n",
            "Could not retrieve DSS image: module 'astropy.coordinates' has no attribute 'degree'\n",
            "Could not retrieve Pan-STARRS image: module 'astropy.coordinates' has no attribute 'degree'\n",
            "Lensed image position: 1.2807764027212944 arcseconds\n",
            "Magnification: 4.56155285952796\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "gQZ31af1ND-N"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}