Distance Calculations Example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate cosmological distances with CCL\n",
    "In this example, we will calculate various cosmological distances for an example cosmology."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab as plt\n",
    "import pyccl as ccl\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set up a Cosmology object\n",
    "`Cosmology` objects contain the parameters and metadata needed as inputs to most functions. Each `Cosmology` object has a set of cosmological parameters attached to it. In this example, we will only use the parameters of a vanilla LCDM model, but simple extensions (like curvature, neutrino mass, and w0/wa) are also supported.\n",
    "\n",
    "`Cosmology` objects also contain precomputed data (e.g. splines) to help speed-up certain calculations. As such, `Cosmology` objects are supposed to be immutable; you should create a new `Cosmology` object when you want to change the values of any cosmological parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "cosmo = ccl.Cosmology(Omega_c=0.27, Omega_b=0.045, h=0.67, A_s=2.1e-9, n_s=0.96)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<pyccl.cosmology.Cosmology>\n",
      "\tA_s     = 2.1e-09\n",
      "\tNeff    = 3.044\n",
      "\tOmega_b = 0.045\n",
      "\tOmega_c = 0.27\n",
      "\th       = 0.67\n",
      "\tn_s     = 0.96\n",
      "\textra_parameters =\n",
      "\t\temu = {'neutrinos': 'strict'}\n",
      "\tHASH_ACCURACY_PARAMS = 0xa0af9c5b75d6de86\n"
     ]
    }
   ],
   "source": [
    "print(cosmo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameter values can be accessed from the `Cosmology` object contains, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.27\n"
     ]
    }
   ],
   "source": [
    "print(cosmo['Omega_c'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nan\n"
     ]
    }
   ],
   "source": [
    "print(cosmo['sigma8'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice $\\sigma_8$ is nan here because it has not yet been computed. Instead, the normalization of the power spectrum was defined via $A_s$ above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Cosmological Distances\n",
    "\n",
    "With a cosmology in hand, we can begin performing some calculations. We can start with the most basic measure, the comoving radial distance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1962.9390685778556"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = 0.5 \n",
    "ccl.comoving_radial_distance(cosmo, 1/(1+z)) # Mpc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that all distance function calls require scale factors, not redshifts. This function can take a `numpy` array of values as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0.        ,  436.6985067 ,  851.3944111 , 1243.78925379,\n",
       "       1614.09910482, 1962.93906858, 2291.20721282, 2599.98198852,\n",
       "       2890.43959663, 3163.79072723])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zs = np.arange(0, 1, 0.1)\n",
    "ccl.comoving_radial_distance(cosmo, 1/(1+zs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CCL also supports calculation of the comoving angular distance. In flat spacetime (like the cosmology we have here) it is the same as  the radial distance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1962.9390685778556"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ccl.comoving_angular_distance(cosmo, 1/(1+z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we create a cosmology with curvature, we'll get a different result. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Radial Dist. = 1992.53 Mpc \t Angular Dist. = 1999.12 Mpc\n"
     ]
    }
   ],
   "source": [
    "curved_cosmo = ccl.Cosmology(Omega_k = 0.1, Omega_c=0.17, Omega_b=0.045, h=0.67, A_s=2.1e-9, n_s=0.96)\n",
    "\n",
    "chi_rad  = ccl.comoving_radial_distance(curved_cosmo, 1/(1+z))\n",
    "chi_curved = ccl.comoving_angular_distance(curved_cosmo, 1/(1+z))\n",
    "\n",
    "print ('Radial Dist. = %.2f Mpc \\t Angular Dist. = %.2f Mpc'%(chi_rad, chi_curved))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CCL explictly supports the calculation of the luminosity distance and the distance modulus too:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Luminosity Dist = 2944.41 Mpc \t Distance Modulus = 42.34 \n"
     ]
    }
   ],
   "source": [
    "chi_lum = ccl.luminosity_distance(cosmo, 1/(1+z))\n",
    "DM = ccl.distance_modulus(cosmo, 1/(1+z))\n",
    "print('Luminosity Dist = %.2f Mpc \\t Distance Modulus = %.2f ' % (chi_lum, DM))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, CCL supports an inverse operation, which calculates the scale factor for a given comoving distance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6666639215879805"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ccl.scale_factor_of_chi(cosmo, 1962.96)"
   ]
  }
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