{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fa7ba993",
   "metadata": {},
   "source": [
    "# Gravitational wave production"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f719b13",
   "metadata": {},
   "source": [
    "## Importing the modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3bee1551",
   "metadata": {},
   "outputs": [],
   "source": [
    "#start by importing the controller and manipulate modules\n",
    "from analytical.controller import *\n",
    "from numerical.manipulate import *\n",
    "#reimport numpy (though it is pulled by numerical) for smarter syntax highlighting in vscode\n",
    "import numpy as np\n",
    "#import matplotlib too\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4579b931",
   "metadata": {},
   "source": [
    "## The Standard Model, reproducing the results of [2004.11392](https://arxiv.org/abs/2004.11392)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3369f4a6",
   "metadata": {},
   "source": [
    "The relevant part of the config file is as follows\n",
    "```ini\n",
    "[Model]\n",
    "modelpath = /Users/jacopo/NextCloud/AUTOTHERM/autotherm/analytical/models/symmetric_grav.fr\n",
    "# Symbol for the Lagrangian in the model file\n",
    "lagrangian = Ltot\n",
    "# \"Name\" of the particle whose production rate must be computed\n",
    "produced = T[1]\n",
    "# List of the particles in the thermal bath (or leave empty for SM assumption)\n",
    "# Unused for now, but still required.\n",
    "assumptions = Element[ht,Reals], Element[kappa,Reals]\n",
    "replacements =\n",
    "includeSM = yes\n",
    "noneq = kappa\n",
    "flavorexpand = \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "18a6bc76",
   "metadata": {},
   "outputs": [],
   "source": [
    "GWdict=analytical_pipeline(\"../../MyModels/grav/grav.cfg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "2a7ab001",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "- statistics: (1, -1, -1):  $$6 \\vert h_t\\vert^2 \\kappa^{2} s + \\frac{2 \\kappa^{2} \\left(t^{2} + u^{2}\\right) \\left(5 g_{1}^{2} + 9 g_{2}^{2} + 24 g_{3}^{2}\\right)}{s}$$\n",
       "- statistics: (-1, -1, 1):  $$- 6 \\vert h_t\\vert^2 \\kappa^{2} t - \\frac{2 \\kappa^{2} \\left(s^{2} + u^{2}\\right) \\left(5 g_{1}^{2} + 9 g_{2}^{2} + 24 g_{3}^{2}\\right)}{t}$$\n",
       "- statistics: (-1, 1, -1):  $$- 6 \\vert h_t\\vert^2 \\kappa^{2} u - \\frac{2 \\kappa^{2} \\left(s^{2} + t^{2}\\right) \\left(5 g_{1}^{2} + 9 g_{2}^{2} + 24 g_{3}^{2}\\right)}{u}$$\n",
       "- statistics: (1, 1, 1):  $$\\frac{\\kappa^{2} \\left(g_{1}^{2} + 15 g_{2}^{2} + 48 g_{3}^{2}\\right) \\left(s^{2} + t^{2} + u^{2}\\right)^{2}}{4 s t u}$$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import display, Markdown\n",
    "out=\"\"\n",
    "s = sympy.Symbol(\"s\")\n",
    "t = sympy.Symbol(\"t\")\n",
    "u = sympy.Symbol(\"u\")\n",
    "g1 = sympy.Symbol(\"g1\")\n",
    "g2 = sympy.Symbol(\"g2\")\n",
    "g3 = sympy.Symbol(\"g3\")\n",
    "ht = sympy.Symbol(\"ht\")\n",
    "kappa=sympy.Symbol(\"kappa\")\n",
    "for key, item, in GWdict[0].items():\n",
    "    sitem=sympy.simplify(sympy.sympify(item).subs(2*t*u,(s*s-t*t-u*u)))\n",
    "    sitemsubst= sitem\n",
    "    sitemsubstcollect=0\n",
    "    for exprtemp in sympy.factor(sitemsubst.expand().as_independent(ht)).subs(t+u,-s)\\\n",
    "        .subs(2*t*t+2*t*u,2*t*t+(s*s-t*t-u*u)).subs(t*t+2*t*u,t*t+(s*s-t*t-u*u)).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2):\n",
    "        sitemsubstcollect += exprtemp.simplify()\n",
    "        # beautify the output\n",
    "    out+=f\"- statistics: {key}:  $${sympy.latex(sitemsubstcollect).replace('ht^{2}',r'\\vert h_t\\vert^2')}$$\\n\"\n",
    "    # display(sympy.pprint(sitem))\n",
    "display(Markdown(out))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9e3fde99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{T^{3} \\kappa^{2} \\left(11 g_{1}^{2} \\log{\\left(\\frac{24 k^{2}}{11 T^{2} g_{1}^{2}} \\right)} + 33 g_{2}^{2} \\log{\\left(\\frac{24 k^{2}}{11 T^{2} g_{2}^{2}} \\right)} + 96 g_{3}^{2} \\log{\\left(\\frac{2 k^{2}}{T^{2} g_{3}^{2}} \\right)}\\right)}{192 \\pi}$"
      ],
      "text/plain": [
       "T**3*kappa**2*(11*g1**2*log(24*k**2/(11*T**2*g1**2)) + 33*g2**2*log(24*k**2/(11*T**2*g2**2)) + 96*g3**2*log(2*k**2/(T**2*g3**2)))/(192*pi)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GW=NumRate(*GWdict,2)\n",
    "GW.get_leadlog()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcd52177",
   "metadata": {},
   "source": [
    "make the masses explicit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "79fd6851",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{T \\kappa^{2} \\left(m_{D1}^2 \\log{\\left(\\frac{4 k^{2}}{m_{D1}^2} \\right)} + 3 m_{D2}^2 \\log{\\left(\\frac{4 k^{2}}{m_{D2}^2} \\right)} + 8 m_{D3}^2 \\log{\\left(\\frac{4 k^{2}}{m_{D3}^2} \\right)}\\right)}{32 \\pi}$"
      ],
      "text/plain": [
       "T*kappa**2*(m_{D1}^2*log(4*k**2/m_{D1}^2) + 3*m_{D2}^2*log(4*k**2/m_{D2}^2) + 8*m_{D3}^2*log(4*k**2/m_{D3}^2))/(32*pi)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md1 = sympy.Symbol(\"m_{D1}^2\")\n",
    "md2 = sympy.Symbol(\"m_{D2}^2\")\n",
    "md3 = sympy.Symbol(\"m_{D3}^2\")\n",
    "T = sympy.S(\"T\")\n",
    "GW.get_leadlog().subs(g1*g1,6*md1/(11*T**2)).subs(g2*g2,6*md2/(11*T**2)).subs(g3*g3,md3/(2*T**2)).simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01107a85",
   "metadata": {},
   "source": [
    "Illustration plot at a very high temperature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fb4e6e69",
   "metadata": {},
   "outputs": [],
   "source": [
    "k=numpy.logspace(numpy.log10(0.1),numpy.log10(12.),100)\n",
    "GWtestrate = GW.rate(k,numpy.sqrt(32*numpy.pi),(numpy.sqrt(0.172942),numpy.sqrt(0.255890),numpy.sqrt(0.235984),\\\n",
    "                                                numpy.sqrt(0.152066)),0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6cde1a44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(1, -1, -1): [0,\n",
       "  -12*ht**2*kappa**2,\n",
       "  kappa**2*(20*g1**2 + 36*g2**2 + 96*g3**2),\n",
       "  0],\n",
       " (-1, -1, 1): [kappa**2*(20*g1**2 + 36*g2**2 + 96*g3**2),\n",
       "  kappa**2*(10*g1**2 + 18*g2**2 + 48*g3**2 + 6*ht**2),\n",
       "  0,\n",
       "  kappa**2*(20*g1**2 + 36*g2**2 + 96*g3**2)],\n",
       " (-1, 1, -1): [0,\n",
       "  kappa**2*(10*g1**2 + 18*g2**2 + 48*g3**2 - 6*ht**2),\n",
       "  0,\n",
       "  kappa**2*(-10*g1**2 - 18*g2**2 - 48*g3**2 - 6*ht**2)],\n",
       " (1, 1, 1): [kappa**2*(-g1**2 - 15*g2**2 - 48*g3**2),\n",
       "  0,\n",
       "  kappa**2*(-g1**2 - 15*g2**2 - 48*g3**2),\n",
       "  0]}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GW.get_coeffs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "45a7e90e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['ytick.right'] = True \n",
    "plt.rcParams['ytick.labelright'] = False \n",
    "plt.rcParams['ytick.left'] = plt.rcParams['ytick.labelleft'] = True\n",
    "plt.rcParams[\"xtick.top\"] =  True\n",
    "plt.rcParams['xtick.direction']='in'\n",
    "plt.rcParams['ytick.direction']='in'\n",
    "plt.plot(k,GWtestrate[1],\"r--\",label=\"strict LO\")\n",
    "plt.plot(k,GWtestrate[2],\"b:\",label=\"subtracted\")\n",
    "plt.plot(k,GWtestrate[3],\"k\",label=\"tuned\")\n",
    "plt.xlim(0,12)\n",
    "plt.ylim(-5,25)\n",
    "plt.xlabel(\"k/T\")\n",
    "plt.ylabel(r\"$\\Gamma_{GW} m_\\mathrm{Pl}^2/T^3$\")\n",
    "plt.title(\"$T=10^{18}$ GeV\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f99fccb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(k,10**(2.*18)/((1.2209*10**19)**2)*GWtestrate[1],\"r--\",label=\"strict LO\")\n",
    "plt.plot(k,10**(2.*18)/((1.2209*10**19)**2)*GWtestrate[2],\"b:\",label=\"subtracted\")\n",
    "plt.plot(k,10**(2.*18)/((1.2209*10**19)**2)*GWtestrate[3],\"k\",label=\"tuned\")\n",
    "plt.xlim(0,12)\n",
    "#plt.ylim(-5,25)\n",
    "plt.xlabel(\"k/T\")\n",
    "plt.ylabel(r\"$\\Gamma_{GW}/T$\")\n",
    "plt.title(\"$T=10^{18}$ GeV\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4c08ebc",
   "metadata": {},
   "source": [
    "## SMASH, reproducing the results of [2011.04731](https://arxiv.org/abs/2011.04731)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06905656",
   "metadata": {},
   "source": [
    "The configuration file is altogether similar to the one above, but points to `analytical/models/SMASH_gravity.fr`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecb7bb43",
   "metadata": {},
   "outputs": [],
   "source": [
    "smashGW=analytical_pipeline(\"../../MyModels/smashgrav/smashgrav.cfg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "64c31bc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "- statistics: (1, -1, -1):  $$3 \\kappa^{2} s \\left(2 \\vert h_t\\vert^2 + \\vert y_Q\\vert^{2}\\right) + \\frac{2 \\kappa^{2} \\left(t^{2} + u^{2}\\right) \\left(16 g_{1}^{2} + 27 g_{2}^{2} + 84 g_{3}^{2}\\right)}{3 s}$$\n",
       "- statistics: (-1, -1, 1):  $$- 3 \\kappa^{2} t \\left(2 \\vert h_t\\vert^2 + \\vert y_Q\\vert^{2}\\right) - \\frac{2 \\kappa^{2} \\left(s^{2} + u^{2}\\right) \\left(16 g_{1}^{2} + 27 g_{2}^{2} + 84 g_{3}^{2}\\right)}{3 t}$$\n",
       "- statistics: (-1, 1, -1):  $$- 3 \\kappa^{2} u \\left(2 \\vert h_t\\vert^2 + \\vert y_Q\\vert^{2}\\right) - \\frac{2 \\kappa^{2} \\left(s^{2} + t^{2}\\right) \\left(16 g_{1}^{2} + 27 g_{2}^{2} + 84 g_{3}^{2}\\right)}{3 u}$$\n",
       "- statistics: (1, 1, 1):  $$\\frac{\\kappa^{2} \\left(g_{1}^{2} + 15 g_{2}^{2} + 48 g_{3}^{2}\\right) \\left(s^{2} + t^{2} + u^{2}\\right)^{2}}{4 s t u}$$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import display, Markdown\n",
    "out=\"\"\n",
    "s = sympy.Symbol(\"s\")\n",
    "t = sympy.Symbol(\"t\")\n",
    "u = sympy.Symbol(\"u\")\n",
    "yq=sympy.S('yq')\n",
    "for key, item, in smashGW[0].items():\n",
    "    sitem=sympy.simplify(sympy.sympify(item).subs(2*t*u,(s*s-t*t-u*u)))\n",
    "    sitemsubst= sitem\n",
    "    sitemsubstcollect=0\n",
    "    for exprtemp in sympy.factor(sitemsubst.expand().as_independent(ht,yq)).subs(t+u,-s)\\\n",
    "        .subs(2*t*t+2*t*u,2*t*t+(s*s-t*t-u*u)).subs(t*t+2*t*u,t*t+(s*s-t*t-u*u)).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2):\n",
    "        sitemsubstcollect += exprtemp.simplify()\n",
    "        # again, beautify output\n",
    "    out+=f\"- statistics: {key}:  $${sympy.latex(sitemsubstcollect).replace('ht^{2}',r'\\vert h_t\\vert^2').replace('yq',r'\\vert y_Q\\vert')}$$\\n\"\n",
    "    # display(sympy.pprint(sitem))\n",
    "display(Markdown(out))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e308484",
   "metadata": {},
   "source": [
    "If we subtract off the SM contribution we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "5320cf87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "- statistics: (1, -1, -1): $$3 \\kappa^{2} s \\,\\vert y_Q\\vert^{2} + \\frac{2 \\kappa^{2} \\left(g_{1}^{2} + 12 g_{3}^{2}\\right) \\left(t^{2} + u^{2}\\right)}{3 s}$$\n",
       "- statistics: (-1, -1, 1): $$- 3 \\kappa^{2} t \\,\\vert y_Q\\vert^{2} - \\frac{2 \\kappa^{2} \\left(g_{1}^{2} + 12 g_{3}^{2}\\right) \\left(s^{2} + u^{2}\\right)}{3 t}$$\n",
       "- statistics: (-1, 1, -1): $$- 3 \\kappa^{2} u \\,\\vert y_Q\\vert^{2} - \\frac{2 \\kappa^{2} \\left(g_{1}^{2} + 12 g_{3}^{2}\\right) \\left(s^{2} + t^{2}\\right)}{3 u}$$\n",
       "- statistics: (1, 1, 1): $$0$$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "out=\"\"\n",
    "s = sympy.Symbol(\"s\")\n",
    "t = sympy.Symbol(\"t\")\n",
    "u = sympy.Symbol(\"u\")\n",
    "for key, item, in smashGW[0].items():\n",
    "    sitem=sympy.sympify(item).subs(2*t*u,(s*s-t*t-u*u)).simplify()\n",
    "    sitemSM=sympy.sympify(GWdict[0][key]).subs(2*t*u,(s*s-t*t-u*u)).simplify()\n",
    "    diff=sympy.simplify((sitem-sitemSM))\n",
    "    diffcollect=0\n",
    "    for exprtemp in sympy.factor(diff.expand().as_independent(ht,yq)).subs(t+u,-s)\\\n",
    "        .subs(2*t*t+2*t*u,2*t*t+(s*s-t*t-u*u)).subs(t*t+2*t*u,t*t+(s*s-t*t-u*u)).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2):\n",
    "        diffcollect += exprtemp.simplify()\n",
    "    out+=f\"- statistics: {key}: $${sympy.latex(diffcollect).replace('yq',r'\\,\\vert y_Q\\vert')}$$\\n\"\n",
    "    # display(sympy.pprint(sitem))\n",
    "display(Markdown(out))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71e10eb8",
   "metadata": {},
   "source": [
    "The contribution from the BSM Yukawa $y_Q$ agrees with that of [2011.04731](https://arxiv.org/abs/2011.04731). Its contribution through U(1) and SU(3) interactions also agrees"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "142114ce",
   "metadata": {},
   "source": [
    "The thermal masses agree with [2011.04731](https://arxiv.org/abs/2011.04731)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6ecb1876",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('(35*g1^2)/18', '(11*g2^2)/6', '(13*g3^2)/6')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smashGW[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1e3ed04",
   "metadata": {},
   "source": [
    "and the leading-log term has the usual form in terms of the masses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "1600ca31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{T \\kappa^{2} \\left(m_{D1}^2 \\log{\\left(\\frac{4 k^{2}}{m_{D1}^2} \\right)} + 3 m_{D2}^2 \\log{\\left(\\frac{4 k^{2}}{m_{D2}^2} \\right)} + 8 m_{D3}^2 \\log{\\left(\\frac{4 k^{2}}{m_{D3}^2} \\right)}\\right)}{32 \\pi}$"
      ],
      "text/plain": [
       "T*kappa**2*(m_{D1}^2*log(4*k**2/m_{D1}^2) + 3*m_{D2}^2*log(4*k**2/m_{D2}^2) + 8*m_{D3}^2*log(4*k**2/m_{D3}^2))/(32*pi)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smashGWrate=NumRate(*smashGW,2)\n",
    "smashGWrate.get_leadlog().subs(g1*g1,18*md1/(35*T**2)).subs(g2*g2,6*md2/(11*T**2)).subs(g3*g3,6*md3/(13*T**2)).simplify()"
   ]
  }
 ],
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