eg4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "https://github.com/astropy/astropy\n",
    "http://docs.astropy.org/en/stable/index.html\n",
    "Notes: \n",
    "    https://ned.ipac.caltech.edu/level5/Hogg/Hogg6.html\n",
    "    More than one notion of distance in cosmology. Angular diameter distance is one of them. It does not increase \n",
    "    indefinitely.\n",
    "\"\"\"\n",
    "from astropy import cosmology\n",
    "from matplotlib import pylab as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "cosmo = cosmology.default_cosmology.get()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FlatLambdaCDM(name=\"Planck15\", H0=67.7 km / (Mpc s), Om0=0.307, Tcmb0=2.725 K, Neff=3.05, m_nu=[0.   0.   0.06] eV, Ob0=0.0486)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosmo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$13.797617 \\; \\mathrm{Gyr}$"
      ],
      "text/plain": [
       "<Quantity 13.79761666 Gyr>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosmo.age(z=0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.7255 \\; \\mathrm{K}$"
      ],
      "text/plain": [
       "<Quantity 2.7255 K>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosmo.Tcmb(z=0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f4452502e48>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Pn/5Ku5SKeOoNATN7xszyzWxNnbY/mtkGM1ttZm+aWZzX3svMDpnZSu/rL3WeM8bMvjGzLDN72MysZd5S42zcU0p4qJGeoO0iAk1IiHH+iO7Mu+N0fn3+YNbtLuG8Rz7j1pdWsKuozN/lifhVQ3oCzwHTj2qbCwx1zg0HNgF31fnZFufcSO/r+jrtTwA/Afp5X0e/pl9tyjtAn6RowrVdRMCKCAvhRxMzWPjLM7jxjD58uHYPU+9fyG/eWauVRBK06v3Ec84tAoqOavvIOXd4o/cvgdQTvYaZpQCxzrkvnW9A9nngwsaV3DK2FJTSR9cHBIXYDuH84pyBLPj5GXx3dA/+/uUOTrtvAX94fz37Dlb6uzyRVtUcf/b+J/B+ne8zzGyFmS00s8leWw8gu84x2V5bm1BZXcuuojL6aOfQoNKtcwfu+d5w5t1xGtOHdmPWoq1Mvu8THpi7iZLyKn+XJ9IqmhQCZvbfQDXwgteUC6Q550YBdwAvmtlJ78FgZtea2VIzW1pQUNCUEhtkZ1EZtQ4ykhQCwahXYhQP/mAkH942hSn9E3l43mYm3/sJj32SxcEK3dlMAlujQ8DMrgbOAy73hnhwzlU45wq9x8uALUB/IIdvDxmlem3H5Jyb5ZzLdM5lJiUlNbbEBtu213ezkoxEDQcFs/7JMTx++Rjeu3kSmenx/PHDjUy57xOe+nSrNqiTgNWoEDCz6cAvgQucc2V12pPMLNR73BvfBPBW51wuUGJm47xVQVcCbze5+maytaAU8K0tFxnaozNPX30Kb9wwgcHdY/ndP9cz6d75PL4gi1L1DCTANGSJ6GxgMTDAzLLN7BrgUSAGmHvUUtApwGozWwm8BlzvnDs8qXwD8BSQha+HUHcewa+27T1IYnQEnTuG+7sUaUNGp8Xz92vG8tr14xnaozP3fbCRiffM588fb6a4THMGEhisrV89mZmZ6ZYuXdqi57j4r4txzvHq9RNa9DzSvq3atZ9HP8li7ro8YiLDuHJCOv85MYOE6Eh/lybyLWa2zDmX2ZBjtSgeX09AQ0FSnxE943jyykzm3DKZKQOSeHzBFibd+wm/e28d+SW6zkDapzB/F+BvB8qrKDhQoUlhabDB3WN57LLRZOUf4PFPtvDsF9t5fvEOvjemBz+e3Js+SfpdkvYj6HsC2/f65rXVE5CT1bdrDA/8YCTzf3YaF5+SyhvLc5j2wEJ+8vxSlu0oqv8FRNqAoO8JbC/0LQ/tldjJz5VIe5WeEMXvLhzGbdP68/wX23n+yx3MXZfHmPR4rpvSm2mDkgkJaVNbZYkcEfQ9gZ3eBmI94xUC0jSJ0ZHccfYAvrjzTH5z/mDySsq59u/LmPbgQmYv2amb20ibFPQhkL2vjISoCKIig75TJM2kU0QYV0/MYMHPT+eRS0fRKSKUu974hkn3zueBjzZqElnalKD/5NtVdIjULuoFSPMLCw3h/BHdOW94Cou3FPLM59t45JMsnli4he8MS+HqiRmM7Bnn7zIlyAV9COwsKmOE/kOUFmRmTOibyIS+iWzfe5C/Ld7Oq0uzeWvlbkalxfGjiRnMGNpN25iLXwT1b11NrWP3/kP0jO/o71IkSPRKjOLX5w9h8V2+eYN9Byu5ZfYKJt07n0fnb6awtMLfJUqQCeqeQG7xIaprHT01HCStLKZDOFdPzODK8b1YsCmfZz/fzp8+2sTD87I4d1g3Lh+XTmZ6PG3sBnwSgII6BLQySPwtJMQ4c2AyZw5MZnPeAV74aievL/MNFQ1IjuHycWlcOKoHsR20r5W0jKAeDsouOgRAzy4aDhL/65ccw28uGMJX/z2Ve783jMjwEP7n7bWM/f087nx9Nd9kF/u7RAlAQd0T2LWvjBCD7nEKAWk7OkWE8YNT0vjBKWmszt7PC1/u5K2VObz09S5GpHbm8rHpfGd4ipY1S7MI6p7ArqIyUjp31KoMabOGp8Zx7/eH89WvpvG/FwyhrLKGX76+mlN//zF3vr6aZTv20dZ3Apa2Laj/lNhZVKahIGkXOncM56oJvbhyfDrLduzjlaW7eGfVbl76ehd9kqK4OLMnF43uQdeYDv4uVdqZoA6B3fvLmdg30d9liDSYmZHZqwuZvbrwP+cPYc7qXF5Zuos/vL+B+z7cyBkDunJxZipnDOyqHq40SNCGQHVNLfkHyukep7+cpH2Kjgzj4lN6cvEpPdlSUMqrS7N5fXk2H6/PIzE6gotG9eC7o1MZlBLr71KlDQvaEMg7UEGtg5TOGg6S9q9PUjR3zhjIz8/uz8JNBbyydBfPfr6dJz/dxsBuMVw4qgczR3bX77v8m6ANgdz9vuWhKeoJSAAJCw1h6qBkpg5KpuhgJf9cvZs3V+Rwz/sbuPeDDYzvncCFo3owfWg3XXsgQANXB5nZM2aWb2Zr6rR1MbO5ZrbZ+zfeazcze9jMssxstZmNrvOcq7zjN5vZVc3/dhpud7FvJ8fu+stIAlSXqAiuGN+LN26YyIKfn85tU/uze/8hfvnaak753cfc+OJyPl6XR2V1rb9LFT9qaE/gOeBR4Pk6bXcC85xz95jZnd73/wXMAPp5X2OBJ4CxZtYF+DWQCThgmZm945zb1xxv5GSpJyDBpFdiFLdO68ctU/uyctd+3lqRw7urc/nn6lziO4UzY1gK5w1LYWzvBEJ1A5yg0qAQcM4tMrNeRzXPBE73Hv8NWIAvBGYCzzvf4uUvzSzOzFK8Y+c654oAzGwuMB2Y3aR30Ei5xeVER4apSyxBxcwYlRbPqLR4/t95g/l0cwFvrdjNWytyePGrnSRGRzJjaDfOG55CZq8uCoQg0JQ5gWTnXK73eA+Q7D3uAeyqc1y213a8dr/Yvf8QKZ3VC5DgFR4acmTfokOVNSzYmM97q3N5ddku/v7lDrrGRHLusBTOG57C6LR43SIzQDXLxLBzzplZs122aGbXAtcCpKWlNdfLfktucTkp2i5CBICOEaHMGJbCjGEplFVWM299Pv9cncvsJTt57ovtpHTuwLnDUjh3WAqjesYpEAJIU0Igz8xSnHO53nBPvteeA/Ssc1yq15bDv4aPDrcvONYLO+dmAbMAMjMzW+Sa+NziQwzprvXTIkfrFBHG+SO6c/6I7pRWVDNvfR7vrsrl74t38PRn20iOjeSswcmcM6Qb43on6KK0dq4pIfAOcBVwj/fv23XabzKzl/BNDBd7QfEhcPfhVUTA2cBdTTh/o1VU17C3tFJrpkXqER0ZxsyRPZg5sgcl5VXMW5/Hh2vyeH1ZDv/4ciexHcKYOiiZc4YkM6V/Ep0ignbVebvVoP/HzGw2vr/iE80sG98qn3uAV8zsGmAHcLF3+BzgXCALKAN+BOCcKzKz/wO+9o777eFJ4taWV+y7e5NWBok0XGyHcC4alcpFo1Ipr6ph0aYCPlybx7wNeby5IocO4SFM7pfEOUO6MW1QV+I6Rfi7ZGmAhq4OuvQ4P5p6jGMdcONxXucZ4JkGV9dCdhf7lofqGgGRxukQHsrZQ7px9pBuVNfUsmRbER+u3cNH6/KYuy6P0BBjbEYXpg1KZuqgrqQnRPm7ZDmOoOy77fEuFOum1UEiTRYWGsKEvolM6JvIby4Ywurs4iOB8Nv31vHb99bRJymKMwd25cyByWT2itc8QhsSlCGQV+ILgeTYSD9XIhJYzIwRPeMY0TOOX04fyM7CMuZvyGPehnz+9sUOnvx0GzEdwjitfxJnDuzK6QO60iVKw0b+FJQhkH+ggo7hoUTrzkwiLSotoRNXT8zg6okZlFZU89nmvXyyIZ/53jUJZjA6Ld7rJXRlYLcYzLT8tDUF5adg/oEKusZG6pdNpBVFR4YxfWg3pg/tRm2tY83uYuatz2f+hnz++OFG/vjhRpJiIpncL5HT+icxqW8iCdHqrbe04AyBknKSdQcmEb8JCTGGp8YxPDWO28/qT35JOQs2FbBoUwHzN+TzxvIczGBo985M6Z/IlH5JjE7XXEJLCM4QOFDBYF0oJtJmdI3twMWZPbk4syc1tY5vcopZ5IXCXxZu5bFPthAdGcb4PglM6ZfIlP5JWnHUTIIzBErKOX1Akr/LEJFjCA0xRvaMY2TPOG6Z2o+S8iq+yCpk0WZfKMxdlwdAekInJvRJZGLfBMb1TiBRQ0eNEnQhcLCimoOVNboht0g7Edsh/MhcgnOObXsPsmhTAZ9u3st7q3Yze8lOAAZ2i2F8nwQm9knk1N5dtENwAwVdCOQf8F0trOWhIu2PmdE7KZreSdFcPTGD6ppavskp5osthSzeUsiLX+3k2c+3E2IwLDWOiX0SmNAnkTHp8XSMCPV3+W1S8IWAd42AegIi7V9YaMiR+yPceEZfKqprWLFzP19k7eWLLYXMWrSVxxdsISI0hFFpcYzvk8DYjARGpcXRIVyhAEEYAnleT6CregIiAScyLJRxvX1zBHfgG/79ensRi7cU8sWWQv48bzPObSY81Lc66dSMLpya0YUx6fFBO3wUdCHwr56AQkAk0EVFhnH6AN+VyQDFh6pYvmMfX20rYsm2Qp5ctJUnFmwhxGBQSiynZnRhbEYXMnt1CZqJ5qALgYIDFUSEhdC5Y3Cmvkgw69wxnDMGduWMgb5QOFRZw4qd+1iyvYgl24qYvcQ3pwDQJymKUzMSODUjnsz0LqTGdwzIC0yDLgTyD1TQNUZXC4uI745qhze/A6is9k00L9lWxNfbi3hv9b9WHyXFRDImLZ7R6XGMSY9nSPfOATGvEIQhUK6hIBE5poiwEMakxzMmPZ6f0oeaWseGPSUs37mf5Tv2sXznPj5Yu8d3bGgIQ3rEesHge05ybPtbcBJ8IVBSQZ+kaH+XISLtQGiIMaR7Z4Z078wV49IB35Dy8p2+QFi+Yx/Pf7mDpz7bBkCPuI6+QEiLY3R6PAO7xRIR1ra3ugi6ENhbWsG43gn+LkNE2qmkmEjOGdKNc4Z0A3xDSOtyS1jm9RSWbi/i3VW7AV/PYkj3WEakxjGiZ2dGpMbRKyGKkJC2MxwdVCFQXVPLvrIqEqK1f7mINI+IsJAj21xcQwYAu/cfYvnOfazOLmblrv28snQXz32xHYCYDmGMSI1jeGpnRnjP8+cwUlCFQFFZJYC2pxWRFtU9riPd4zpy3vDuANTUOrLyS1m1az8rs/ezOns/sxZtpbrWAb4dDHy9hThGpMYxLLVzq61gbHQImNkA4OU6Tb2B/wHigJ8ABV77r5xzc7zn3AVcA9QAtzjnPmzs+RujsNQXAom6k5GItKLQEGNAtxgGdIvh4lN6AlBeVcO63BJW7drPql37WZ1dzEfe5ngAA5Jj+OC2yS2+krHRIeCc2wiMBDCzUCAHeBP4EfCgc+5PdY83s8HAJcAQoDvwsZn1d87VNLaGk3U4BNQTEBF/6xAeyui0eEanxR9pKy6rYnWOLxBKDlW1ylL25hoOmgpscc7tOEHRM4GXnHMVwDYzywJOBRY3Uw31Kjzo2zJCcwIi0hZ17hTO5H5JTO7XelvdN9fapUuA2XW+v8nMVpvZM2Z2OOZ6ALvqHJPttf0bM7vWzJaa2dKCgoJjHdIoe48MB6knICICzRACZhYBXAC86jU9AfTBN1SUC9x/sq/pnJvlnMt0zmUmJTVfIhaWVhAWYsR2DKr5cBGR42qOnsAMYLlzLg/AOZfnnKtxztUCT+Ib8gHfnEHPOs9L9dpaTdHBShKiI7RlhIiIpzlC4FLqDAWZWUqdn10ErPEevwNcYmaRZpYB9AOWNMP5G2xvaSUJGgoSETmiSeMiZhYFnAVcV6f5PjMbCThg++GfOefWmtkrwDqgGrixNVcGgW9iWJPCIiL/0qQQcM4dBBKOarviBMf/Hvh9U87ZFIWllaR36eSv04uItDlte2ejZlZYWqFrBERE6giaEDhUWcPByhoNB4mI1BE0IXD4QjFdIyAi8i/BEwJHtoxQT0BE5LDgCYEjW0aoJyAicljQhMDhLSMStIOoiMgRQRMC+w76QiBeISAickTwhEBZFeGhRlREqL9LERFpM4ImBPaXVRLXSfsGiYjUFTQhsK+skvhOrXO7NhGR9iKIQqCKuE6aDxARqStoQmC/egIiIv8maEJgX1kV8eoJiIh8S1CEgHPO1xPQ8lARkW/j0hpRAAAJ8UlEQVQJihA4WFlDVY3TcJCIyFGCIgQOXyimiWERkW8LjhAo864WVgiIiHxLkIRAFYCGg0REjtLkEDCz7Wb2jZmtNLOlXlsXM5trZpu9f+O9djOzh80sy8xWm9nopp6/IfaXaThIRORYmqsncIZzbqRzLtP7/k5gnnOuHzDP+x5gBtDP+7oWeKKZzn9CRzaPU09ARORbWmo4aCbwN+/x34AL67Q/73y+BOLMLKWFajji8HBQ544KARGRupojBBzwkZktM7NrvbZk51yu93gPkOw97gHsqvPcbK+tRe0vqyS2QxhhoUExBSIi0mBhzfAak5xzOWbWFZhrZhvq/tA558zMncwLemFyLUBaWlqTC9xXVqULxUREjqHJfxo753K8f/OBN4FTgbzDwzzev/ne4TlAzzpPT/Xajn7NWc65TOdcZlJSUlNLZJ+3jbSIiHxbk0LAzKLMLObwY+BsYA3wDnCVd9hVwNve43eAK71VQuOA4jrDRi1G20iLiBxbU4eDkoE3vRu1hAEvOuc+MLOvgVfM7BpgB3Cxd/wc4FwgCygDftTE8zfIvoNV9Osa0xqnEhFpV5oUAs65rcCIY7QXAlOP0e6AG5tyzsYoOVSllUEiIscQ8MtlamodByqqFQIiIscQ8CFQcsh3jUCsQkBE5N8EfgiU60IxEZHjCfgQKD7cE+jQHJdEiIgEloAPgZJD1YB6AiIixxLwIVCsOQERkeMK+BDQnICIyPEFfAgc7gkoBERE/l3Ah0DJoSpCQ4xOEaH+LkVEpM0J+BAo9q4W9ra2EBGROgI+BErKq7U8VETkOAI+BIq1b5CIyHEFfAiUHKrS8lARkeNQCIiIBLHAD4HyKmI7KARERI4loEPAOac5ARGREwjoEDhUVUNVjSO2o1YHiYgcS0CHgDaPExE5sYAOAW0ZISJyYo0OATPraWafmNk6M1trZrd67b8xsxwzW+l9nVvnOXeZWZaZbTSzc5rjDZzI4c3jNDEsInJsTRksrwZ+5pxbbmYxwDIzm+v97EHn3J/qHmxmg4FLgCFAd+BjM+vvnKtpQg0nVFymnoCIyIk0uifgnMt1zi33Hh8A1gM9TvCUmcBLzrkK59w2IAs4tbHnb4gjPQGFgIjIMTXLnICZ9QJGAV95TTeZ2Woze8bM4r22HsCuOk/L5jihYWbXmtlSM1taUFDQ6Lp0a0kRkRNrcgiYWTTwOnCbc64EeALoA4wEcoH7T/Y1nXOznHOZzrnMpKSkRtdWWu5bHRSjOQERkWNqUgiYWTi+AHjBOfcGgHMuzzlX45yrBZ7kX0M+OUDPOk9P9dpaTGlFNZFhIUSEBfQiKBGRRmvK6iADngbWO+ceqNOeUuewi4A13uN3gEvMLNLMMoB+wJLGnr8hSsqridFQkIjIcTXlE3IicAXwjZmt9Np+BVxqZiMBB2wHrgNwzq01s1eAdfhWFt3YkiuDwNcT0FCQiMjxNToEnHOfAce6XdecEzzn98DvG3vOk1VaXkV0pHoCIiLHE9CD5QfKqxUCIiInENAh4BsOUgiIiBxPQIfAgfJqohUCIiLHFdAhUFpRTYyGg0REjitgQ8A5p9VBIiL1CNgQOFRVQ02t03CQiMgJBGwIHN4yQquDRESOL2BDoOTIvkEKARGR4wnYECitUAiIiNQncEPgyHCQJoZFRI4ncEOgwncvAc0JiIgcX8CGgOYERETqF7AhUKoQEBGpV+CGgDcxHKXhIBGR4wrYEDhQXkXH8FDCQwP2LYqINFnAfkKWVmjzOBGR+gRsCBwo1+ZxIiL1CdgQ0L0ERETq1+ohYGbTzWyjmWWZ2Z0tdR7dS0BEpH6tGgJmFgo8BswABuO7Kf3gljhXqW4tKSJSr9buCZwKZDnntjrnKoGXgJktcSLdS0BEpH6tHQI9gF11vs/22ppdSXmVegIiIvVokxPDZnatmS01s6UFBQWNeo2pA7syPLVzM1cmIhJYWvtP5RygZ53vU722b3HOzQJmAWRmZrrGnOihS0Y15mkiIkGltXsCXwP9zCzDzCKAS4B3WrkGERHxtGpPwDlXbWY3AR8CocAzzrm1rVmDiIj8S6vPnDrn5gBzWvu8IiLy79rkxLCIiLQOhYCISBBTCIiIBDGFgIhIEFMIiIgEMXOuUdditRozKwB2NPLpicDeZizHnwLlvQTK+wC9l7YoUN4HNO29pDvnkhpyYJsPgaYws6XOuUx/19EcAuW9BMr7AL2XtihQ3ge03nvRcJCISBBTCIiIBLFAD4FZ/i6gGQXKewmU9wF6L21RoLwPaKX3EtBzAiIicmKB3hMQEZETCMgQaK2b2bc0M+tpZp+Y2TozW2tmt/q7pqYys1AzW2Fm7/m7lqYwszgze83MNpjZejMb7++aGsPMbvd+t9aY2Wwz6+DvmhrKzJ4xs3wzW1OnrYuZzTWzzd6/8f6ssaGO817+6P1+rTazN80sriXOHXAh0Jo3s28F1cDPnHODgXHAje34vRx2K7De30U0gz8DHzjnBgIjaIfvycx6ALcAmc65ofi2d7/Ev1WdlOeA6Ue13QnMc871A+Z537cHz/Hv72UuMNQ5NxzYBNzVEicOuBCgFW9m39Kcc7nOueXe4wP4Pmha5J7MrcHMUoHvAE/5u5amMLPOwBTgaQDnXKVzbr9/q2q0MKCjmYUBnYDdfq6nwZxzi4Cio5pnAn/zHv8NuLBVi2qkY70X59xHzrlq79sv8d2JsdkFYgi02s3sW5OZ9QJGAV/5t5ImeQj4JVDr70KaKAMoAJ71hraeMrMofxd1spxzOcCfgJ1ALlDsnPvIv1U1WbJzLtd7vAdI9mcxzeg/gfdb4oUDMQQCjplFA68DtznnSvxdT2OY2XlAvnNumb9raQZhwGjgCefcKOAg7WfY4QhvvHwmvlDrDkSZ2Q/9W1Xzcb6lj+1++aOZ/Te+oeEXWuL1AzEEGnQz+/bCzMLxBcALzrk3/F1PE0wELjCz7fiG6M40s3/4t6RGywaynXOHe2Wv4QuF9mYasM05V+CcqwLeACb4uaamyjOzFADv33w/19MkZnY1cB5wuWuh9fyBGAIBczN7MzN8487rnXMP+LuepnDO3eWcS3XO9cL3/8l851y7/KvTObcH2GVmA7ymqcA6P5bUWDuBcWbWyftdm0o7nOA+yjvAVd7jq4C3/VhLk5jZdHzDpxc458pa6jwBFwLeRMrhm9mvB15pxzeznwhcge+v5pXe17n+LkoAuBl4wcxWAyOBu/1cz0nzejKvAcuBb/B9HrSbK27NbDawGBhgZtlmdg1wD3CWmW3G19O5x581NtRx3sujQAww1/tv/y8tcm5dMSwiErwCricgIiINpxAQEQliCgERkSCmEBARCWIKARGRIKYQEBEJYgoBEZEgphAQEQli/x/OPqIUarK/QAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "#z_vals = np.concatenate(([0.], np.logspace(np.log(0.001),np.log(12.), 1000, base=np.exp(1))))\n",
    "z_vals = np.linspace(0.,12., 1000)\n",
    "ax.plot(z_vals, cosmo.angular_diameter_distance(z_vals))\n",
    "#ax.set_xscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$3000.7755 \\; \\mathrm{K}$"
      ],
      "text/plain": [
       "<Quantity 3000.7755 K>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosmo.Tcmb(z=1100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_temp, ax_temp = plt.subplots()\n",
    "z_vals_temp = np.linspace(0.,1100., 1000)\n",
    "ax_temp.plot(z_vals_temp, cosmo.Tcmb(z_vals_temp))\n",
    "ax_temp.set_yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}