ST4_2020_Cosmology_TD1.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ST4-2020-Cosmology-TD1.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOh1pC9xWdCMSRYn4IbDS2m",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jchamilton75/CS-ST4-Cosmo-2020/blob/master/ST4_2020_Cosmology_TD1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vtDmPTLZcgkh"
      },
      "source": [
        "# Centrale-Supélec - ST4 - Cosmology - TD1\n",
        "\n",
        "## General Instructions (copied from G. Mention's TD1)\n",
        "To do this homework, you have to download it on your own \"Google Colaboratory\" space (see in the \"File\" menu, \"save a copy in your Google Drive\", you will have to create a gmail account if you don't already have one) so that you can modify it as you wish. You need to train with Google Colaboratory as you will be using it for the Challenging Week (Enseignement d'Intégration).\n",
        "\n",
        "Once you did indeed save this notebook on your own Google drive, you can modify it and save it again. If you corrupt anything by mistake, you have automatic recording of previous version which you can still acess to get back. Anyway you can still start from scratch with the default notebook if you experience really weird things with your current version.\n",
        "\n",
        "On the Help menu above, (menu \"Aide\" in French) you can switch the language of the interface. For this lectures I set it to English.\n",
        "\n",
        "\n",
        "## Overview\n",
        "Welcome this this first practicle work in cosmology. The aim of this practicle work is to further familiarize you with python and Google Colaboratory. Remember that you will have to use this for the Enseignement d'Intégration, so you really want to get trained before...\n",
        "\n",
        "In this first Practicle work we will address the following topics:\n",
        "\n",
        "\n",
        "1.   Simple Plots with cosmological parameters\n",
        "2.   Calculating distances and age of the Universe\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9rHbV8tKeGdo"
      },
      "source": [
        "## Simple Plots with cosmological parameters\n",
        "In a python notebook, there a cells that can be \"code\" or \"text\". The code cells can be recognized by the \"In[xx]\" at the beginning (xx is a number that depends on the order of execution of the cells)). They can be executed by pressing \"Shift+Enter\" and the code they contain is executed by the machine. If there is an output, it is displayed in another cell below the input one, a cell that starts with \"Out[xx]\".\n",
        "\n",
        "Before starting, one usually needs to set-up a few parameters for the notebook so that the plots are good-looking and that usual librairies are imported. This is obtained by executing the cell below:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B0G-WGDYdXHW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1f663734-ac44-4eac-87ef-3c61f14174d3"
      },
      "source": [
        "import sys\n",
        "print(\"Using Python {}\".format(sys.version_info[0]))\n",
        "\n",
        "from pylab import *\n",
        "import numpy as np\n",
        "%matplotlib inline\n",
        "from matplotlib import rc\n",
        "from importlib import reload\n",
        "rc('figure',figsize=(10,5))\n",
        "rc('font',size=12)\n",
        "rc('text',usetex=False)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Using Python 3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kORl7BNleTkg"
      },
      "source": [
        "### Densities as a function of redshift\n",
        "We will now do our first plot, which is related to cosmology. We want to plot the evolution of the density of various species (Radiation, Matter and Cosmological constant) as a finction of redshift. This was shown is the first lecture. We use the following values for the various densities as expressed today:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z7p42t67eKju"
      },
      "source": [
        "h_0 = 0.7\n",
        "omega_l_0 = 0.7\n",
        "omega_r_0 = 4.3 * h_0**(-2) * 1e-5\n",
        "omega_m_0 = 0.3 - omega_r_0 "
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZXTSKPuLerPG"
      },
      "source": [
        "We recall that: $$\\Omega(z) = \\Omega_r (1 + z)^4 + \\Omega_m (1 + z)^3 + \\Omega_\\Lambda$$\n",
        "\n",
        "We define a array containg the redshifts that we want to look at with logarithmic spacing between 1e-1 and 1e4 and 1000 elements."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RolrcvH-enzT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "87f1b278-30a2-4073-9d0c-00cfe689bb13"
      },
      "source": [
        "z = np.logspace(-1, 4, 1000)\n",
        "\n",
        "### Let's print the first 10 elements\n",
        "print(z[0:10])"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.1        0.10115911 0.10233166 0.1035178  0.10471768 0.10593148\n",
            " 0.10715934 0.10840144 0.10965793 0.11092899]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pEl6_XzifGu_"
      },
      "source": [
        "We can directly calculate the densities using the redshift array as the following:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IhQRvSpbfD0D"
      },
      "source": [
        "om_r = omega_r_0 * (1 + z)**4\n",
        "om_m = omega_m_0 * (1 + z)**3\n",
        "# the operation below is just a trick to have om_l be an array with the same \n",
        "# number of elements as the others\n",
        "om_l = omega_l_0 + z*0       \n",
        "total = om_r + om_m + om_l"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OpqTaWnrfeTg"
      },
      "source": [
        "Now let's do our first plot:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uh-a09qPfbb0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 515
        },
        "outputId": "a02be515-0280-48ad-f8ba-a57074527db3"
      },
      "source": [
        "rc('figure',figsize=(10,5))\n",
        "xscale('log')\n",
        "yscale('log')\n",
        "xlabel('Redshift')\n",
        "ylabel(r'$\\Omega(z)$')\n",
        "plot(z,om_l, 'b', label = r'$\\Omega_\\Lambda(z)$')\n",
        "plot(z,om_r, 'k', label = r'$\\Omega_R(z)$')\n",
        "plot(z,om_m, 'g', label = r'$\\Omega_{NR}(z)$')\n",
        "plot(z,total, 'r', lw=2, label = 'Total')\n",
        "legend(loc='upper left', fontsize=13)\n",
        "title('Densities as a function of Redshift')"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Densities as a function of Redshift')"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O60kkPcSfvM6"
      },
      "source": [
        "***Question 1:*** Find numerically the values of the redshift of matter-radiation equality and of lambda domination, store them into a variable and print them."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LQCYvXHKfgxZ"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iKNi32iKgOBk"
      },
      "source": [
        "***Question 2:*** Now replot the initial plot and materialize with dotted vertical lines the values you found before. You are also requested to display the redshifts you found in the legend using python's formatted output. \n",
        "\n",
        "As an example for printing $\\pi$ with maximum 5 characters and 2 digits:\n",
        "```\n",
        "print('pi is {0:5.2f}'.format(np.pi))\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1OPB8YWwf2yC"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "koTTEAN3g1ru"
      },
      "source": [
        "Note the way of adding numerical values from a variable in the plot. This will be useful later.\n",
        "\n",
        "Now you know how to make a simple plot from an array, and how to manipulate arrays and make operations with them.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ob8_zLMXhFRq"
      },
      "source": [
        "## Cosmological Distances\n",
        "\n",
        "### quick recap\n",
        "\n",
        "Let's recall that distances in cosmology are not as straighforward as in our everyday life because of the effect of the expansion of the Universe. One needs to calculate distances on the curved and expanding manifold whose metric is given by the Friedman-Lemaître-Robertson-Walker  metric:\n",
        "$$ds^2 = dt^2 - a^2(t)\\left[\\frac{dr^2}{1-kr^2} + r^2 d\\theta^2 + r^2\\sin^2\\theta d\\phi^2\\right]$$  \n",
        "where we have set $c=1$ and $k$ is the curvature parameter and can take the values -1, 0 or 1 corresponding respectively to open, flat and closed Universes.\n",
        "\n",
        "The radial space coordinate difference between a point at 0 and a point at radius $r$ is:\n",
        "$$\\Delta r(z) = \\int_0^r \\frac{dr'}{\\sqrt{1-kr'^2}}$$\n",
        "\n",
        "For a photon, the travel is made at the speed of light whatever the referential (Relativity princinple) and the invariant $ds^2$ is therefore equal to zero:\n",
        "$$ds^2 = 0 = dt^2-a^2\\frac{dr^2}{1-kr^2}$$\n",
        "so that\n",
        "$$\\frac{dr}{\\sqrt{1-kr^2}}=\\frac{dt}{a}$$\n",
        "We also recall the definition of the redshift: $$1+z = \\frac{a0}{a}$$ and differientate it with respect to time:\n",
        "$$\\frac{dz}{dt}= -\\dot{a}\\frac{a_0}{a^2}$$ implying $$\\frac{dt}{a} = -\\frac{dz}{a_0}\\times\\frac{a}{\\dot{a}}$$, so finally introducing the Hubble parameters $H=\\frac{\\dot{a}}{a}$, we can rewrite the coordinate difference as:\n",
        "$$\\Delta r(z) = \\frac{1}{a_0}\\int_0^z \\frac{dz'}{H(z')}$$.\n",
        "\n",
        "Multiplying this coordinate difference by the scale factor today $a_0$, one get the *proper comoving distance*: $$D_P(z) = a_0 \\Delta r(z) = \\int_0^z \\frac{dz'}{H(z')}$$\n",
        "\n",
        "The latter can be multiplied by $1+z$ to obtain the *Luminosity Distance* or divided by $1+z$ to obtain the angular diameter distance."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_BZ60nrDhagd"
      },
      "source": [
        "### Luminosity distance calculation\n",
        "We will first calculate and plot H(z) with 1000 values of z between 0 and 1 linearly spaced (function to use is linspace()) using the formula in the course for H(z) and the cosmological parameters set to the same values as above. You can also play with cosmological parameters to see the change. We recall that $$H(z)=H_0\\sqrt{\\Omega_k(1 + z)^2 + \\Omega_\\Lambda + \\Omega_m (1 + z)^3}$$\n",
        "\n",
        "***Question 3:*** Do it yourself in the following cell, the variable H(z) should be called \"hz\". You are then requested to plot H as a function of z. Do not forget to put labels on your axes as well as a legend."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rvwLatV-grIm"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n5YXbf4ehuHc"
      },
      "source": [
        "Now we calculate the luminosity distance $$D_l(z) = c(1+z)\\int_0^z \\frac{\\mathrm{d}z'}{H(z')}$$ using the numerical integration features of the scipy library (trapezoidal cumulative integral):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bnkk1b78hqwJ"
      },
      "source": [
        "import scipy.integrate\n",
        "dp = np.zeros(len(z))\n",
        "dp[1:] = scipy.integrate.cumtrapz(1./hz, z) * 3e5"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iGisXWWhhzRV"
      },
      "source": [
        "***Question 4:*** You are asked to make a plot of Luminosity distance as a function of redshift in the following cell (remember that $D_L(z) = (1+z)\\times D_p(z)$. You will call the variable containing luminosity distance \"dl\":"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q9X6SM1Shwht"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I2NjpaZth8vV"
      },
      "source": [
        "### Using the cosmolib library\n",
        "In order to simplify our lives, I have prepared a library for the purpose of this course called \"cosmolib.py\" which is in the same directory. I encourage you to have a look at the various codes that we will be using from this library in order to see how such tools can be simply coded.\n",
        "\n",
        "The library requires installing two public libraries: emcee and iminuit before:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v3hMGa1Sh1sN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4110ec7c-6265-48fc-d301-5fe6a2f553a8"
      },
      "source": [
        "!pip install emcee\n",
        "!pip install iminuit"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting emcee\n",
            "  Downloading emcee-3.1.4-py2.py3-none-any.whl (46 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m46.2/46.2 kB\u001b[0m \u001b[31m4.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from emcee) (1.22.4)\n",
            "Installing collected packages: emcee\n",
            "Successfully installed emcee-3.1.4\n",
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting iminuit\n",
            "  Downloading iminuit-2.21.3-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (382 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m382.1/382.1 kB\u001b[0m \u001b[31m14.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: numpy>=1.21 in /usr/local/lib/python3.10/dist-packages (from iminuit) (1.22.4)\n",
            "Installing collected packages: iminuit\n",
            "Successfully installed iminuit-2.21.3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_jdwu2vwjXOK"
      },
      "source": [
        "Now let's retrieve the cosmolib.py from GitHub directly using Google Colaboratory.\n",
        "\n",
        "Note that we first remove a possible version of the file in the local Google Colab directory, then download it using wget, list the content of the directory. All these commands are typical unix commands that are run from Google Colaboratory by prepending an exclamation mark to tell it that it should run unix commands:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NnP2JxQwjjx-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "282cd71a-acc6-46f5-af81-0412bad48ca2"
      },
      "source": [
        "!rm -rf cosmolib.py*\n",
        "!wget --no-check-certificate https://raw.githubusercontent.com/jchamilton75/CS-ST4-Cosmo-2020/master/cosmolib.py\n",
        "!ls -lrt"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "--2023-05-10 16:43:37--  https://raw.githubusercontent.com/jchamilton75/CS-ST4-Cosmo-2020/master/cosmolib.py\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.111.133, 185.199.108.133, 185.199.109.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.111.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 15812 (15K) [text/plain]\n",
            "Saving to: ‘cosmolib.py’\n",
            "\n",
            "\rcosmolib.py           0%[                    ]       0  --.-KB/s               \rcosmolib.py         100%[===================>]  15.44K  --.-KB/s    in 0s      \n",
            "\n",
            "2023-05-10 16:43:38 (52.1 MB/s) - ‘cosmolib.py’ saved [15812/15812]\n",
            "\n",
            "total 20\n",
            "drwxr-xr-x 1 root root  4096 May  9 13:35 sample_data\n",
            "-rw-r--r-- 1 root root 15812 May 10 16:43 cosmolib.py\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BtA4EQacoMI0"
      },
      "source": [
        "Now let's import the library and give it the namespace 'cs' so that everytime we'll call one of its function it will be as:\n",
        "```\n",
        "cs.myfunction()\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oQVZYoDjoacH"
      },
      "source": [
        "import cosmolib as cs"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YwYalOwoiXBO"
      },
      "source": [
        "It contains a function for Luminosity Distances that is slightly more precise than the one we just calculated above, but the differences are very small.\n",
        "\n",
        "It is called in the follwing manner that uses a dictionnary to specify the value of the cosmological parameters. The three parameters that are accepted are:\n",
        "- *h* for the Hubble constant at redshift 0 divided by 100\n",
        "- *omega_M_0* for $\\Omega_m$ today at redshift 0\n",
        "- *omega_lambda_0* for $\\Omega_\\Lambda$ at redshift 0\n",
        "- *w0* for the equation of state of Dark Energy. \n",
        "\n",
        "**Note:** The Dark Energy equation of state was not discussed in the lectures due to the lack of time. It is however one of the main challenges of observational cosmology to measure it today. SNIa are a sensitive probe for this parameter. The equation of state is the ratio between pressure and density of Dark Energy (as for a perfect gaz). However in the case of Dark Energy or Csomological Constant the ratio is negative (you need negative pressure to have an accelerated expansion as can be seen in the second Friedman Equation - see lectures). For a perfect Cosmological constant w=0 and for Dark Energy models it can have other values, and possibly vary with redshift. Do not worry with this now and just keep it fixed to -1."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1PzAQJBNiKAu"
      },
      "source": [
        "z = np.linspace(0,1,1000)\n",
        "cosmo_lcdm = {'h':0.7, 'omega_M_0':0.3, 'omega_lambda_0':0.7, 'w0':-1.}\n",
        "dlnew = cs.lumdist(z, cosmo_lcdm)"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sRvltPU6ojgp"
      },
      "source": [
        "As you see the Cosmological Parameters values are specified using a Python Dictionnary, a very useful tool in Python when one needs containers of various data types with labels for each.\n",
        "\n",
        "***Question 5:*** In the follwing cell, you are expected to superimpose both of the luminosity distances we have calculated (if you want to play, you can also have a look at the difference or relative difference between both)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZFdE2L0GnF0a"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cqv_9gohjjHW"
      },
      "source": [
        "### Angular distance:\n",
        "Similarly to the luminosity distance, the cosmolib library has a angdist() function that is called the same way. We calculate it and compare to the previously calculated luminsotity distance in the following cell:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ocgi0a0LjktG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "outputId": "22e40671-b1aa-4749-f1ba-b8ee6a2a7b4c"
      },
      "source": [
        "dang = cs.angdist(z, cosmo_lcdm)\n",
        "plot(z, dlnew, 'red', label='Luminosity Distance')\n",
        "plot(z, dang, 'blue', label='Angular Distance')\n",
        "xlabel('Redshift')\n",
        "ylabel('Distance [Mpc]')\n",
        "legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ffb7b628e48>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4sa7ktJDr-Zx"
      },
      "source": [
        "### Overplotting Cosmological models to observational data:\n",
        "Let's assume you have ran an experiment that measured angular distances  (using Baryonic Acoustic Oscillations) at various redshifts and obtain the following measurements (this is taken from the SDSS-3 Boss experiment https://arxiv.org/abs/1607.03155 with a slight conversion to make your life easier):\n",
        "\n",
        "| Redhift | Angular Distance [Mpc] | Uncertainty on $D_A$ [Mpc] |\n",
        "| --- | --- | --- |\n",
        "| 0.38 | 1081 | 15 |\n",
        "| 0.51 | 1276 | 19 |\n",
        "| 0.61 | 1370 | 26 |\n",
        "\n",
        "This data can be plotted in the following manner:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1XXTje8ltZdt",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "outputId": "4c51c9c3-7448-443d-8af6-e99dce4cebce"
      },
      "source": [
        "z_bao = np.array([0.38, 0.51, 0.61])\n",
        "dang_bao = np.array([1081., 1276., 1370.])\n",
        "err_dang_bao = np.array([15., 19., 26.])\n",
        "errorbar(z_bao, dang_bao, yerr=err_dang_bao, fmt='bo', label='SDSS Data DR12 [https://arxiv.org/abs/1607.03155]')\n",
        "xlabel('z')\n",
        "ylabel('$D_A(z)~[Mpc]$')\n",
        "legend(loc='upper left')"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fe6a8926f80>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e7zwRnfCtgeB"
      },
      "source": [
        "**Question 6:** Overplot the theoretical models for three sets of cosmological parameters:\n",
        "\n",
        "\n",
        "1.   $\\Lambda$CDM with h=0.7, $\\Omega_m$=0.3, $\\Omega_\\Lambda$=0.7 (and $w$=-1)\n",
        "2.   The so-called \"open\" model with h=0.7, $\\Omega_m$=0.3, $\\Omega_\\Lambda$=0.0 (and $w$=-1)\n",
        "3.   The so-called \"flat\" model with $\\Lambda$CDM with h=0.7, $\\Omega_m$=1.0, $\\Omega_\\Lambda$=0. (and $w$=-1)\n",
        "\n",
        "[NB: Model 3 is called \"flat\" in the sense \"flat with no $\\Lambda$\" as you all =have noticed that $\\Lambda$CDM is also flat.]\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pIs16pP_tjGb"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TChSUlyDtjmk"
      },
      "source": [
        "You should notice here that $\\Lambda$CDM works much better, but you can also remark that changing the Hubble-Lemaître constant to other values (around 0.6 - 0.65) in the two other models gives predictions that are in quite good agreement with the data. This shows an inherent degeneracy between cosmological parameters that can only be lifted by combining different cosmological probes (BAO as here, type Ia supernovae and the CMB). You will work on this durng the \"Semaine d'Intégration\"."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MbdJmaeBpAy4"
      },
      "source": [
        "## Calculating the age of the Universe\n",
        "Similarly to the distance calculation, one can calculate the time elapsed since a given redshift (we have used variable changes similar as above):\n",
        "$$t(z) = \\int_t^{t0} dt' = \\int_0^z \\frac{dz'}{(1+z')H(z')}$$\n",
        "\n",
        "Calculating this integral from 0 to infinity gives the age of the Universe for a given cosmological model. You may implement your own calculation of the age of the Universe or use the function available in the cosmolib library:\n",
        "age [Gyr] = cs.lookback(z, cosmo)\n",
        "\n",
        "where z can be just a value or an numpy array of redshifts and cosmo is a dictionary given in the following manner:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6dLxRWQsol8N"
      },
      "source": [
        "cosmo_lcdm = {'h':0.7, 'omega_M_0':0.3, 'omega_lambda_0':0.7, 'w0':-1.}"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wS-zMQAGrBwF"
      },
      "source": [
        "Let's calculate the age of the Universe when the redshift was 0.1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dQGAjFGcpE0C",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3cccd46c-ed4f-495f-e6e3-400bb51b8ace"
      },
      "source": [
        "print(cs.lookback(0.1, cosmo_lcdm))"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.3015743503698538\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pQo0yAbyrHq4"
      },
      "source": [
        "And let's calculate an array with ages of the Universe at various redshifts:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IdsxU5i4rGcM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2fb3a1d-64a8-436a-92db-be8235de88ba"
      },
      "source": [
        "zvalues = np.array([0.1, 1, 10])\n",
        "print(cs.lookback(zvalues, cosmo_lcdm))"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1.30157435  7.71697782 13.0038611 ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3wEFpPturfuJ"
      },
      "source": [
        "***Question 7:*** In the next cell, calculate the time elapsed between today and 1000 redshifts logarithmically spaced between $10^{-4}$ and $10^4$ for the standard $\\Lambda CDM$ cosmology and represent it as a function of redshift."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dijhCcaprTDP"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7H4ldqfhrrft"
      },
      "source": [
        "***Question 8:*** You should see that beyond $z=10$ the elapsed time reaches its maximum, the age of the Universe whose value is therefore the maximum of this array. You are expected to print it in the following cell:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-vw3ahGzritW"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Elpv2vNRryRD"
      },
      "source": [
        "You will now calculate this age as a function of cosmological parameters, for this you will need to perform loops and use two-dimensional arrays.\n",
        "\n",
        "***Question 9:*** Calculate the age of Universe as a function of the matter density (30 or 100 values between 0 and 1) and the Cosmological Constant density (30 or 100 values between 0 and 1.5). For each couple of values, you will calculate the age of the Universe and fill a 2D-array. You will then represent this age using a color 2D plot using the matplotlib function *imshow()*. Do not forget to add correct axes, title and labels on the axes. You will also add a color-bar next to the image by calling the *colorbar()* function just after your 2D plot."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pQLDFbTUrxZL"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H_ZkMfobsMKL"
      },
      "source": [
        "***Question 10:*** You are now requested to redo the same plot adding:\n",
        "- contours for various integer values of the age of the Universe (bettween 0 and 20 GYr). You should use both the *contour()* and the *contourf()* functions from matplotlib that allow you to respectively plot and fill the contours with colors. Note that these to function expect 2d arrays as x,y coordinates for the values to display, so you will have to build 2d arrays from your x and y 1d arrays using the function *np.meshgrid()*\n",
        "- an additional contour (different color) for the star HE1523-0901 whose age has been measured to be 13.2 Gyr\n",
        "- A star at the coordinates corresponding to $\\Lambda CDM$ cosmology ($\\Omega_m=0.3$, $\\Omega_\\Lambda=0.7$)\n",
        "- A dot in a given color for the open Univserse with no $\\Lambda$  ($\\Omega_m=0.3$, $\\Omega_\\Lambda=0$)\n",
        "- A dot in another color for the flat no $\\Lambda$ ($\\Omega_m=1$, $\\Omega_\\Lambda=0$)\n",
        "\n",
        "And of course pout all these into a legend. \n",
        "\n",
        "In order to do the contours\n",
        "\n",
        "At the end, you should get the following plot which look like it could be published in a paper...  ![ageUniverse](http://www.apc.univ-paris7.fr/Downloads/cosmobs/JCH/CentraleSupelec/age.png)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "40OdJld6r5Q3"
      },
      "source": [
        "### Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_TJyqh72uAPB"
      },
      "source": [
        "End of TD1"
      ]
    }
  ]
}