ScaleFactorvsTimeLCDM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f45b3231-5329-49b7-a745-81f043e7dc20",
   "metadata": {},
   "source": [
    "# Lookback time (scale factor vs cosmic time movie)\n",
    "Florent Leclercq<br/>\n",
    "Institut d'Astrophysique de Paris<br/>\n",
    "17 July 2023"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "235a7ffa-51ed-4399-89e6-b9151181d905",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "%matplotlib widget\n",
    "plt.rcParams.update({'lines.linewidth': 2})\n",
    "plt.rcParams.update({'text.usetex': True})\n",
    "plt.rcParams.update({'text.latex.preamble': r\"\\usepackage{amsmath}\\usepackage{upgreek}\"})\n",
    "plt.rcParams.update({'font.family': 'serif'})\n",
    "plt.rcParams.update({'font.size': 10})\n",
    "plt.rcParams.update({'figure.max_open_warning': 20})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5af5eca8-195e-4729-8b28-7eab3d2ca2b4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from LookbackTimeLib import *\n",
    "Npast = int(Nframes*(-tmin)/(tmax-2*tmin))\n",
    "\n",
    "# find the time of dark energy domination\n",
    "aDE=fsolve(lambda a : w0waCDM4.Om(a2z(1.))*a**(-3) - w0waCDM4.Ode(a2z(1.)), 1.)[0]\n",
    "tDE=-w0waCDM4.lookback_time(a2z(aDE)).value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "be059f18-d134-4397-b759-9a501cc4bd49",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class movie:\n",
    "    def __init__(self, t, a1=None, a2=None, a3=None, a4=None):\n",
    "        self.fig, self.ax = plt.subplots(1,1, figsize=(6,4))\n",
    "        self.steps = len(t)\n",
    "        self.a1, self.a2, self.a3, self.a4 = a1, a2, a3, a4\n",
    "\n",
    "    def show(self):\n",
    "        self.fig.show()\n",
    "    \n",
    "    # Initialization function\n",
    "    def init(self):\n",
    "        ax = self.ax\n",
    "        a1, a2, a3, a4 = self.a1, self.a2, self.a3, self.a4\n",
    "        frame = 0\n",
    "        Nstart = 0\n",
    "        ax.set_xlim([tmin-1.,tmax])\n",
    "        ax.set_ylim([0.,3.])\n",
    "        self.band1 = ax.fill_between([tmin-1.,tDE],[0.,0.],[3.,3.], color=\"C0\", alpha=0.)\n",
    "        self.band2 = ax.fill_between([tDE,tmax],[0.,0.],[3.,3.], color=\"C7\", alpha=0.)\n",
    "        if a1 is not None:\n",
    "            self.plot1, = ax.plot(t[Nstart:frame], (a1*acrit1)[Nstart:frame], color=\"C1\")\n",
    "            self.hline, = ax.plot([tcrit1-5,tcrit1+5], [acrit1,acrit1], ls=\"None\", color=\"black\")\n",
    "        else:\n",
    "            self.plot1, self.hline = None, None\n",
    "        if a2 is not None:\n",
    "            self.plot2, = ax.plot(t[Nstart:frame], (a2*acrit1)[Nstart:frame], color=\"C3\")\n",
    "        else:\n",
    "            self.plot2 = None\n",
    "        if a3 is not None:\n",
    "            self.plot3, = ax.plot(t[Nstart:frame], (a3*acrit1)[Nstart:frame], color=\"C4\")\n",
    "        else:\n",
    "            self.plot3 = None\n",
    "        if a4 is not None:\n",
    "            self.plot4, = ax.plot(t[Nstart:frame], (a4*acrit1)[Nstart:frame], color=\"C9\")\n",
    "        else:\n",
    "            self.plot4 = None\n",
    "        return self.plot1, self.hline, self.plot2, self.plot3, self.plot4, self.band1, self.band2, \n",
    "    \n",
    "    # Update function\n",
    "    def update(self, frame):\n",
    "        a1, a2, a3, a4 = self.a1, self.a2, self.a3, self.a4\n",
    "        Nstart = Npast if frame>Npast else 0\n",
    "        \n",
    "        if frame>Npast:\n",
    "            self.band1.set_alpha(0.25)\n",
    "        if frame>Npast and t[frame]>tDE:\n",
    "            self.band2.set_alpha(0.25)\n",
    "        \n",
    "        if a1 is not None:\n",
    "            self.plot1.set_data(t[Nstart:frame], (a1*acrit1)[Nstart:frame])\n",
    "            if t[frame]>tcrit1:\n",
    "                self.hline.set_linestyle(\":\")\n",
    "        if a2 is not None:\n",
    "            self.plot2.set_data(t[Nstart:frame], (a2*acrit1)[Nstart:frame])\n",
    "        if a3 is not None:\n",
    "            self.plot3.set_data(t[Nstart:frame], (a3*acrit1)[Nstart:frame])\n",
    "        if a4 is not None:\n",
    "            self.plot4.set_data(t[Nstart:frame], (a4*acrit1)[Nstart:frame])\n",
    "        return self.plot1, self.hline, self.plot2, self.plot3, self.plot4, self.band1, self.band2, \n",
    "        \n",
    "    # Create the animation\n",
    "    def animate(self):\n",
    "        animation = FuncAnimation(self.fig, self.update, frames=len(t), init_func=self.init, blit=False)\n",
    "        return animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "64f724b5-a83d-4f6b-8c1e-903b3b233c29",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i=200\n",
    "frame = movie(t, a1=None, a2=None, a3=None, a4=a4)\n",
    "frame.init();\n",
    "frame.update(i);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "60a35b37-cc7d-411f-a55d-865719c351e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e50cc709540644d4b19c90d8e9010dd8",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "this_movie = movie(t, a1=None, a2=None, a3=None, a4=a4)\n",
    "animation = this_movie.animate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "27ff3961-a1ae-40f8-8bd7-bf9c9c32db4c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "animation.save(\"output/ScaleFactorvsTimeLCDM.mp4\", dpi=300, fps=48)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "910b8667-5201-4e75-9604-a8cb34965b40",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}