IMspectra.ipynb

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   "source": [
    "Author: Alkistis Pourtsidou, ICG Portsmouth\n",
    "\n",
    "Using part of http://camb.readthedocs.io/en/latest/CAMBdemo.html \n",
    "\n",
    "To run this Jupyter notebook you need to have CAMB and the CAMB python package \n",
    "installed. In order to install the CAMB python package on your computer follow\n",
    "the instructions in http://camb.readthedocs.io/en/latest/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "%matplotlib inline\n",
    "import sys, platform, os\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import camb\n",
    "from camb import model, initialpower"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy\n",
    "from scipy.interpolate import interp1d\n",
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pi=np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "#plots settings\n",
    "font = {'size'   : 16, 'family':'STIXGeneral'}\n",
    "axislabelfontsize='x-large'\n",
    "plt.rc('font', **font)\n",
    "plt.rcParams['legend.fontsize']='medium'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "#Fiducial cosmological parameters\n",
    "c=3e5\n",
    "hubble=0.678\n",
    "omegab=0.022*pow(hubble,-2)\n",
    "omegac=0.119*pow(hubble,-2)\n",
    "om0=omegac+omegab\n",
    "H00=100*hubble\n",
    "Ass=2.14e-9\n",
    "nss = 0.968\n",
    "\n",
    "gamma=0.545"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Set up the fiducial cosmology\n",
    "pars = camb.CAMBparams()\n",
    "#Set cosmology\n",
    "pars.set_cosmology(H0=H00, ombh2=omegab*pow(hubble,2), omch2=omegac*pow(hubble,2),omk=0,mnu=0)\n",
    "pars.set_dark_energy() #LCDM (default)\n",
    "pars.InitPower.set_params(ns=nss, r=0, As=Ass)\n",
    "pars.set_for_lmax(2500, lens_potential_accuracy=0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#calculate results for these parameters\n",
    "results = camb.get_results(pars)\n",
    "#print pars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Get matter power spectrum at z=0: P(k,z=0)\n",
    "#Not non-linear corrections couples to smaller scales than you want\n",
    "pars.set_matter_power(redshifts=[0.], kmax=2.0)\n",
    "#Linear spectra\n",
    "pars.NonLinear = model.NonLinear_none\n",
    "results.calc_power_spectra(pars)\n",
    "kh, z, pk = results.get_matter_power_spectrum(minkh=1e-6, maxkh=2.0, npoints = 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Construct P(k,z=0) interpolating function, in units of Mpc (no h)\n",
    "Pkz0 = interp1d(kh*hubble, pk[0]/pow(hubble,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ztest = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Spatially flat Universe\n",
    "\n",
    "#Define E(z) = H(z)/H0\n",
    "def Ez(zc):\n",
    "    return np.sqrt(1-om0+om0*pow(1+zc,3))\n",
    "def Hz(zc):\n",
    "    return Ez(zc)*H00\n",
    "#Define the comoving distances\n",
    "def drdz(zp):\n",
    "    return (c/H00)/Ez(zp)\n",
    "def rcom(zc):\n",
    "    return scipy.integrate.romberg(drdz,0,zc)\n",
    "def DA(zc):\n",
    "    return rcom(zc)/(1+zc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Define the growth function in LCDM\n",
    "def fg(zz):\n",
    "    omz=om0*pow(1+zz,3)/pow(Ez(zz),2)\n",
    "    return pow(omz,gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Get the growth factor \n",
    "def Dg_dz(zz):\n",
    "    return -fg(zz)/(1+zz)\n",
    "\n",
    "def Dgz(zc):\n",
    "    ans = scipy.integrate.romberg(Dg_dz, 0.0, zc)\n",
    "    return np.exp(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#fiducial bHI from Bull et al 2015\n",
    "def bHI(zc):\n",
    "    return 0.67+0.18*zc+0.05*pow(zc,2)\n",
    "\n",
    "#fiducial OmHI Mario's fit\n",
    "def OmHI(zc):\n",
    "    return 0.00048+0.00039*zc-0.000065*pow(zc,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Construct matter P(k,z), no RSD\n",
    "def Pkz(kk,zc):    \n",
    "    return pow(Dgz(zc),2)*Pkz0(kk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#mean brightness temperature in [mK] Mario's fit from Bull et al 2015\n",
    "def Tb(zc):\n",
    "    return 0.0559+0.2324*zc-0.024*pow(zc,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Construct P_HI(k,z)\n",
    "def PHI(kk,zc):\n",
    "    return pow(Tb(zc),2)*pow(bHI(zc),2)*Pkz(kk,zc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "kminn=1e-3\n",
    "kmaxx=0.2\n",
    "\n",
    "k1 = np.linspace(kminn,kmaxx,400)\n",
    "\n",
    "plin = [PHI(k,ztest) for k in k1]\n",
    "\n",
    "plt.loglog(k1,plin,color='blue')\n",
    "\n",
    "plt.xlim(kminn,kmaxx)\n",
    "#plt.ylim(1e2,5e5)\n",
    "\n",
    "plt.xlabel(\"$k \\, \\mathrm{[Mpc^{-1}]}$\")\n",
    "plt.ylabel(\"$P_{\\, \\mathrm{HI}}(k) \\, \\mathrm{[mK^2 Mpc^3]}$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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