User guides/Advanced/Gaussian_bump/Gaussian bump potential 1- background plots and power spectrum.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian bump potential 1 - background plots and power spectrum\n",
    "\n",
    "This is the first in a series of notebooks which will run importance sampling for the Gaussian bump potential. It is commended the reading is familair with\n",
    "- [Importance sampling](https://arxiv.org/abs/2206.11234).\n",
    "- How to simulate the linear Sasaki-Mukhanov mode equation in inflation. \n",
    "- The [PyFPT user guides](https://github.com/Jacks0nJ/PyFPT/tree/main/User%20guides).\n",
    "\n",
    "These Notebooks are simply meant to make all of the 2D results reproducible and are minimal in details.\n",
    "\n",
    "In this notebook the background dynamics will be simulated and the power spectrum found.\n",
    "\n",
    "Throughout natural units with $c = 8\\pi M_{\\rm PL} = \\hbar =1$ are used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import mystyle\n",
    "plt.style.use(mystyle.paper_style)\n",
    "\n",
    "from scipy.interpolate import CubicSpline\n",
    "from scipy.integrate import odeint\n",
    "from scipy.integrate import RK45\n",
    "from scipy.optimize import root\n",
    "from scipy.integrate import quad\n",
    "from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes \n",
    "from mpl_toolkits.axes_grid1.inset_locator import mark_inset\n",
    "from timeit import default_timer as timer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The potential\n",
    "This is the [Gaussian bump potential](https://arxiv.org/abs/1911.00057)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def potential(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction = (phi**2)/(m_squared + phi**2)\n",
    "    return V_0*fraction*(1 + K*expo)\n",
    "\n",
    "def potential_functional_form(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction = (phi**2)/(m_squared + phi**2)\n",
    "    return fraction*(1 + K*expo)\n",
    "\n",
    "def potential_dif(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction1 = (phi**2)/(m_squared + phi**2)\n",
    "    fraction2 = (phi)/(m_squared + phi**2) - (phi**3)/((m_squared + phi**2)**2)\n",
    "    \n",
    "    term1 = 2*V_0*fraction2*(1 + K*expo)\n",
    "    term2 = V_0*fraction1*(-K*expo*(phi-phi_0)/(sigma_tilde**2))\n",
    "    return term1 + term2\n",
    "\n",
    "# I tested this against an interpolation of my previous derivative\n",
    "def potential_ddif(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    square_brackets = 1 + K*expo\n",
    "    overall_factor = 2*V_0/(m_squared + phi**2)\n",
    "    \n",
    "    term1 = -2*potential_dif(phi)*phi/(m_squared + phi**2)\n",
    "    term2 = overall_factor*(1 - 3*(phi**2)/(m_squared + phi**2) + 2*(phi**4)/((m_squared + phi**2)**2))*\\\n",
    "        (1 + K*expo)\n",
    "    term3 = overall_factor*(phi - (phi**3)/(m_squared + phi**2))*(-K*(phi-phi_0)*expo/(sigma_tilde**2))\n",
    "    term4 = -overall_factor*0.5*phi*K*(3*phi - 2*phi_0)*expo/(sigma_tilde**2)\n",
    "    term5 = overall_factor*0.5*K*expo*(phi*(phi-phi_0)/(sigma_tilde**2))**2\n",
    "    \n",
    "    return term1 + term2 + term3 + term4 + term5\n",
    "\n",
    "def V_prime_by_V(phi):\n",
    "    expo = np.exp(-0.5*((phi-phi_0)/sigma_tilde)**2)\n",
    "    fraction3 = 1/phi - (phi)/(m_squared + phi**2)\n",
    "    fraction4 = -(phi-phi_0)/(sigma_tilde**2)\n",
    "    \n",
    "    term1 = 2*fraction3\n",
    "    term2 = fraction4*K*expo/(1 + K*expo)\n",
    "    return term1 + term2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameters are shown such that the power spectrum peaks at $5 \\times 10^{-3}$ in the astroid mass gap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 1.17*(10**-3)  # This needs all 3 sig fig\n",
    "cmb_power = 2*10**-9\n",
    "cmb_phi = 3.0\n",
    "phi_0 = 2.18812\n",
    "m = 0.5\n",
    "m_squared = m**2\n",
    "sigma_tilde = 1.59*(10**-2)\n",
    "\n",
    "V_0 = 12*(np.pi**2)*(cmb_power/potential_functional_form(cmb_phi))*(V_prime_by_V(cmb_phi)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x700 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x520 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi_values = np.linspace(0.1, 3.5, 1000)\n",
    "V_values = potential(phi_values)\n",
    "\n",
    "small_phi = 3*sigma_tilde\n",
    "fig = plt.figure(figsize = [8., 7.])\n",
    "ax = plt.axes()\n",
    "ax.plot(phi_values, V_values)\n",
    "axins = zoomed_inset_axes(ax, 20, loc=7) # zoom = 2\n",
    "axins.plot(phi_values, V_values)\n",
    "axins.set_xlim(phi_0 - small_phi, phi_0 + small_phi)\n",
    "axins.set_ylim(0.999*potential(phi_0 - small_phi), 1.001*potential(phi_0 + small_phi))\n",
    "mark_inset(ax, axins, loc1=2, loc2=4, fc=\"none\", ec=\"0.5\")\n",
    "plt.draw()\n",
    "ax.set_xlabel(r\"$\\phi$\")\n",
    "ax.set_ylabel(r\"$V(\\phi)$\")\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Background simulation\n",
    "Let's simulate background dynamics starting on CMB scales until the end of inflation using a Runge-Kutta 45 method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def klien_gordon(N, vec):\n",
    "    phi, pi = vec\n",
    "    dpi_by_dN = -(3 - 0.5*pi**2)*(pi + V_prime_by_V(phi))\n",
    "    return [pi, dpi_by_dN]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use slow roll at NLO to set the initial conditions with maximum accuracy.\n",
    "\n",
    "We need second derivative of the potential, where I will do it numerically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi_values = np.linspace(0.1, 3.5, 1000)\n",
    "V_dif_values = potential_dif(phi_values)\n",
    "V_dif_interpolation = CubicSpline(phi_values, V_dif_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hubble_param_LO_1(phi):\n",
    "    return 0.5*(potential_dif(phi)/potential(phi))**2\n",
    "\n",
    "def hubble_param_LO_2(phi):\n",
    "    return 2*( (potential_dif(phi)/potential(phi))**2\\\n",
    "              - V_dif_interpolation(phi, 1)/potential(phi) )\n",
    "\n",
    "def hubble_param_NLO_1(phi):\n",
    "    return hubble_param_LO_1(phi)*(1 - hubble_param_LO_2(phi)/3)\n",
    "\n",
    "def dpi_by_dN_NLO(phi):\n",
    "    return -(2*hubble_param_NLO_1(phi))**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now simulate the background"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi_in_start = cmb_phi\n",
    "dpi_by_dN_in_start  = dpi_by_dN_NLO(phi_in_start)\n",
    "initial_state = [phi_in_start , dpi_by_dN_in_start]\n",
    "\n",
    "# Step through the simulations\n",
    "N_values = []\n",
    "phi_values = []\n",
    "phi_diff_values = []\n",
    "solution_background = RK45(klien_gordon, 0, initial_state, 57, rtol=10**-12, atol=10**-15)\n",
    "\n",
    "\n",
    "# Step through the simulations\n",
    "while solution_background.status != 'finished':\n",
    "    solution_background.step()\n",
    "    N_values.append(solution_background.t)\n",
    "    phi_values.append(solution_background.y[0])\n",
    "    phi_diff_values.append(solution_background.y[1])\n",
    "\n",
    "N_values = np.array(N_values)\n",
    "phi_values = np.array(phi_values)\n",
    "phi_diff_values = np.array(phi_diff_values)\n",
    "\n",
    "sol = np.zeros((len(N_values), 2))\n",
    "sol[:, 0] = phi_values\n",
    "sol[:, 1] = phi_diff_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have the general sim, now let's find when it should end and re-simulate, ending at that value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hubble_param_1_func(dpi_by_dN):\n",
    "    return (dpi_by_dN**2)/2 \n",
    "\n",
    "def hubble_func(phi, pi):\n",
    "    H_squared = 2*potential(phi)/(6-pi**2)\n",
    "    return H_squared**0.5\n",
    "\n",
    "def hubble_param_2_func(phi, pi):\n",
    "    epsilon_H = hubble_param_1_func(pi)\n",
    "    V_prime_by_V_value =  V_prime_by_V(phi)\n",
    "    return 2*epsilon_H - V_prime_by_V_value*(6-pi**2)/pi - 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nu_sqaured_func(N):\n",
    "    epsilon2 = epsilon2_interpolation(N, 0)\n",
    "    epsilon1 = epsilon1_interpolation(N, 0)\n",
    "    epsilon2_derivative = epsilon2_interpolation(N, 1)\n",
    "    return 9/4 - epsilon1 + (3/2)*epsilon2 - (1/2)*epsilon1*epsilon2 + (epsilon2**2)/4\\\n",
    "        + epsilon2_derivative/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "hubble_param_values = np.array([hubble_func(sol[i, 0], sol[i, 1]) for i in range(len(sol[:, 0]))])\n",
    "epsilon1_values = np.array([hubble_param_1_func(dpi_by_dN) for dpi_by_dN in sol[:, 1]])\n",
    "epsilon2_values = np.array([hubble_param_2_func(sol[i, 0], sol[i, 1]) for i in range(len(sol[:, 0]))])\n",
    "\n",
    "# interpolation\n",
    "hubble_param_interpolation = CubicSpline(N_values, hubble_param_values)\n",
    "epsilon1_interpolation = CubicSpline(N_values, epsilon1_values)\n",
    "epsilon2_interpolation = CubicSpline(N_values, epsilon2_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2688430896289513"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "epsilon1_values[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this simulated ended after inflation ended. Let's use it to find when inflation actually ended, and then re-simulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N end\n",
      "56.8826959159262\n",
      "phi end\n",
      "0.35826387061478066\n"
     ]
    }
   ],
   "source": [
    "from scipy.interpolate import interp1d\n",
    "N_interpolate = interp1d(epsilon1_values, N_values)\n",
    "N_end = N_interpolate(1)\n",
    "print(\"N end\")\n",
    "print(N_end)\n",
    "phi_interpolate = interp1d(epsilon1_values, phi_values)\n",
    "phi_end = phi_interpolate(1)\n",
    "print(\"phi end\")\n",
    "print(phi_end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's resimulate up to this point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step through the simulations\n",
    "N_values = []\n",
    "phi_values = []\n",
    "phi_diff_values = []\n",
    "solution_background = RK45(klien_gordon, 0, initial_state, N_end, rtol=10**-12, atol=10**-15)\n",
    "\n",
    "\n",
    "# Step through the simulations\n",
    "while solution_background.status != 'finished':\n",
    "    solution_background.step()\n",
    "    N_values.append(solution_background.t)\n",
    "    phi_values.append(solution_background.y[0])\n",
    "    phi_diff_values.append(solution_background.y[1])\n",
    "\n",
    "N_values = np.array(N_values)\n",
    "phi_values = np.array(phi_values)\n",
    "phi_diff_values = np.array(phi_diff_values)\n",
    "\n",
    "sol = np.zeros((len(N_values), 2))\n",
    "sol[:, 0] = phi_values\n",
    "sol[:, 1] = phi_diff_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "phi end\n",
      "0.3582680276468886\n"
     ]
    }
   ],
   "source": [
    "print(\"phi end\")\n",
    "phi_end = phi_values[-1]\n",
    "print(phi_end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's interpolate over these new values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "hubble_param_values = np.array([hubble_func(sol[i, 0], sol[i, 1]) for i in range(len(sol[:, 0]))])\n",
    "epsilon1_values = np.array([hubble_param_1_func(dpi_by_dN) for dpi_by_dN in sol[:, 1]])\n",
    "epsilon2_values = np.array([hubble_param_2_func(sol[i, 0], sol[i, 1]) for i in range(len(sol[:, 0]))])\n",
    "\n",
    "# interpolation\n",
    "hubble_param_interpolation = CubicSpline(N_values, hubble_param_values)\n",
    "epsilon1_interpolation = CubicSpline(N_values, epsilon1_values)\n",
    "epsilon2_interpolation = CubicSpline(N_values, epsilon2_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "nu_squared_values = np.array([nu_sqaured_func(N_values[i]) for i in range(len(N_values))])\n",
    "\n",
    "nu_squared_interpolation = CubicSpline(N_values, nu_squared_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_for_plotting_logic = (N_values>25) & (N_values<N_end-4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot what the Hubble flow parameters and $\\nu^2$ is doing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x520 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x520 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epsilon_H_values = np.array([hubble_param_1_func(dpi_by_dN) for dpi_by_dN in sol[:, 1]])\n",
    "\n",
    "plt.plot(N_values[N_for_plotting_logic], np.log10(epsilon_H_values[N_for_plotting_logic]),\n",
    "         label=r\"$\\log_{10}{(\\epsilon_{1})}$\")\n",
    "plt.plot(N_values[N_for_plotting_logic], epsilon2_values[N_for_plotting_logic], label=r\"$\\epsilon_{2}$\")\n",
    "plt.plot(N_values[N_for_plotting_logic], nu_squared_values[N_for_plotting_logic], label=r\"$\\nu^2$\")\n",
    "plt.xlabel(r\"$N$\")\n",
    "plt.ylim(top=8)\n",
    "plt.legend(ncol=2)\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While there is clearly a period of ultra-slow roll, what is its precise duration? Let's find out using standard root-finding techniques and interpolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def root_finding_epsilon2(N_guess, epsilon2_chosen=-3):\n",
    "    def epsilon2_value_diff(N_epsilon2_time):\n",
    "        return epsilon2_interpolation(N_epsilon2_time) - epsilon2_chosen\n",
    "    sol_epsilon2_time = root(epsilon2_value_diff, N_guess)\n",
    "    N_epsilon2_time = sol_epsilon2_time.x\n",
    "    return float(N_epsilon2_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ultra-slow roll started at\n",
      "29.84178346243688\n",
      "and ended at\n",
      "32.25059795813168\n"
     ]
    }
   ],
   "source": [
    "N_usr_start_guess = N_values[epsilon2_values<-3][0]\n",
    "N_usr_end_guess = N_values[epsilon2_values<-3][-1]\n",
    "\n",
    "N_usr_start = root_finding_epsilon2(N_usr_start_guess)\n",
    "N_usr_end = root_finding_epsilon2(N_usr_end_guess)\n",
    "\n",
    "print(\"Ultra-slow roll started at\")\n",
    "print(N_usr_start)\n",
    "print(\"and ended at\")\n",
    "print(N_usr_end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now let's save this "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_dict = {}\n",
    "data_dict[\"N\"] = N_values\n",
    "data_dict[\"phi\"] = phi_values\n",
    "data_dict[\"phi_N_diff\"] = phi_diff_values\n",
    "data_dict[\"H\"] = hubble_param_values\n",
    "data_dict[\"epsilon1\"] = epsilon1_values\n",
    "data_dict[\"epsilon2\"] = epsilon2_values\n",
    "data_dict[\"nu_squared\"] = nu_squared_values\n",
    "\n",
    "data_pandas = pd.DataFrame(data_dict)\n",
    "\n",
    "data_pandas.to_csv(\"gaussian_bump_dynamics_dynamics\"+\".csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mode simulation\n",
    "\n",
    "To find the power spectrum, we need to be able to simulare a linear mode from deep inside the horizon until Hubble-crossing until the end of inflation. Below are the required functions for the comoving curvature perturbation $\\mathcal{R}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def R_initial_condition_BD_with_phase(k, a_0, H_0, epsilon1_0, epsilon2_0, comoving_time):\n",
    "    phase = np.exp(complex(0, -k*comoving_time))\n",
    "    R0 = complex(np.divide(1, 2*a_0*(epsilon1_0*k)**0.5), 0)*phase\n",
    "    R_derivative_0 = -complex(1 + 0.5*epsilon2_0, k/(a_0*H_0))*R0\n",
    "    return R0, R_derivative_0 \n",
    "\n",
    "def R_mode_equation(N, vec):\n",
    "    R, d_R_by_dN = vec\n",
    "    epsilon1 = epsilon1_interpolation(N)\n",
    "    epsilon2 = epsilon2_interpolation(N)\n",
    "    aH = aH_interpolation(N)\n",
    "    d2_R_by_dN2 = -complex(3 - epsilon1 + epsilon2, 0)*d_R_by_dN - R*(k/(aH))**2\n",
    "    return [d_R_by_dN, d2_R_by_dN2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def comoving_time_func(N_interest, N_end):\n",
    "    def comoving_time_integrand(N):\n",
    "        aH = aH_interpolation(N)\n",
    "        return 1/aH\n",
    "    comoving_time_value, _ = quad(comoving_time_integrand, N_end, N_interest, limit=1000)\n",
    "    return comoving_time_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_cg_time(k, sigma, N_exit):\n",
    "    def exit_time_func(N_rc_exit):\n",
    "        return k - sigma*aH_interpolation(N_rc_exit)\n",
    "    N_guess = N_exit + np.log(sigma**-1)\n",
    "    sol_rc_time = root(exit_time_func, N_guess)\n",
    "    N_rc_exit = sol_rc_time.x\n",
    "    return float(N_rc_exit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_mode_sim(N_exit):\n",
    "\n",
    "    N_time_to_horizon = 6.\n",
    "    N_starting = N_exit - N_time_to_horizon\n",
    "\n",
    "    H_0 = hubble_param_interpolation(N_starting)\n",
    "    epsilon1_0 = epsilon1_interpolation(N_starting)\n",
    "    epsilon2_0 = epsilon2_interpolation(N_starting)\n",
    "    a_0 = a_interpolation(N_starting)\n",
    "\n",
    "    k = aH_interpolation(N_exit)\n",
    "\n",
    "    comoving_time_0 = comoving_time_func(N_starting, N_end)\n",
    "\n",
    "    N_values_R_sim = []\n",
    "    R_values = []\n",
    "    R_diff_values = []\n",
    "\n",
    "    R_0, d_R_by_dN_0 = R_initial_condition_BD_with_phase(k, a_0, H_0, epsilon1_0, epsilon2_0, comoving_time_0)\n",
    "    initial_state_R = [R_0, d_R_by_dN_0]\n",
    "    solution_R = RK45(R_mode_equation, N_starting, initial_state_R, N_end, rtol=10**-11, atol=10**-14)\n",
    "\n",
    "    # Only need to do 1 simulation\n",
    "    while solution_R.status != 'finished':\n",
    "        solution_R.step()\n",
    "        N_values_R_sim.append(solution_R.t)\n",
    "        R_values.append(solution_R.y[0])\n",
    "        R_diff_values.append(solution_R.y[1])\n",
    "    N_values_R_sim = np.array(N_values_R_sim)\n",
    "    R_values = np.array(R_values)\n",
    "    R_diff_values = np.array(R_diff_values)\n",
    "    return N_values_R_sim, R_values, R_diff_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's test it for a mode near the CMB scale to make sure it has the correct overall amplitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Overall scale factor\n",
    "a_in = 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Need to normalise the scale factor, this is so reasonable numbers are always used in the numerics.\n",
    "# If an an overall normalisation is done, then errors can occur from needing to store very large or small\n",
    "# numbers.\n",
    "\n",
    "N_exit = 7\n",
    "aH_interpolation = CubicSpline(N_values, hubble_param_values*a_in*np.exp(N_values-N_exit))\n",
    "a_interpolation = CubicSpline(N_values, a_in*np.exp(N_values-N_exit))\n",
    "\n",
    "k = aH_interpolation(N_exit)\n",
    "\n",
    "N_values_R_sim, R_values, R_diff_values = run_mode_sim(N_exit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_rescaled_values = R_values*(k**3/(2*np.pi**2))**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5944606528160838e-09"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(R_rescaled_values[-1])**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x520 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x520 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(N_values_R_sim-N_exit, np.abs(R_rescaled_values))\n",
    "plt.yscale(\"log\")\n",
    "plt.xlim(left=-6, right=4)\n",
    "plt.ylabel(r\"$|\\mathcal{R}| (k^3/2\\pi^2)^{1/2}$\")\n",
    "plt.xlabel(r\"$N - N_{\\rm exit}$\")\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correct!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Power spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To obtain the power spectrum, we need to run many such mode simulations. This is done with the code. Only the value at certian $\\sigma$ values and the end of inflation is kept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "Taken 3.942743946099654 so far\n",
      "50\n",
      "Taken 190.11771151900757 so far\n",
      "100\n",
      "Taken 375.9592401260743 so far\n",
      "150\n",
      "Taken 562.1504127900116 so far\n",
      "200\n",
      "Taken 746.8883698619902 so far\n",
      "250\n",
      "Taken 934.4148605500814 so far\n",
      "300\n",
      "Taken 1122.8168407930061 so far\n",
      "350\n",
      "Taken 1313.4340012359899 so far\n",
      "400\n",
      "Taken 1507.4999519620324 so far\n",
      "450\n",
      "Taken 1704.7447338360362 so far\n",
      "500\n",
      "Taken 1898.726762150065 so far\n",
      "550\n",
      "Taken 2093.7291814390337 so far\n"
     ]
    }
   ],
   "source": [
    "from scipy.integrate import RK45\n",
    "from timeit import default_timer as timer\n",
    "# Define the when the modes left and find their scale\n",
    "# Define the time when the different modes are coarse-grained\n",
    "\n",
    "sigma_values = np.array([1.0, 0.5, 0.1, 0.01])\n",
    "N_time_to_horizon = 6.\n",
    "\n",
    "# Remember to give time for super horizon evolution\n",
    "N_modes = np.linspace(N_usr_start-9, N_usr_start+11, 600)\n",
    "\n",
    "k_raw_values = np.zeros(len(N_modes))\n",
    "\n",
    "R_at_sigma_values = np.zeros((len(sigma_values), len(N_modes)), dtype=\"complex\")\n",
    "R_diff_at_sigma_values = np.zeros((len(sigma_values), len(N_modes)), dtype=\"complex\")\n",
    "R_end_values = np.zeros(len(N_modes), dtype=\"complex\")\n",
    "\n",
    "start_time = timer()\n",
    "\n",
    "for i in range(len(N_modes)):\n",
    "    N_exit = N_modes[i]\n",
    "    aH_interpolation = CubicSpline(N_values, hubble_param_values*a_in*np.exp(N_values-N_exit))\n",
    "    a_interpolation = CubicSpline(N_values, a_in*np.exp(N_values-N_exit))\n",
    "\n",
    "    k = aH_interpolation(N_exit)\n",
    "\n",
    "    N_values_R_sim, R_values, R_diff_values = run_mode_sim(N_exit)\n",
    "\n",
    "    R_interp = interp1d(N_values_R_sim, R_values)\n",
    "    R_diff_interp = interp1d(N_values_R_sim, R_diff_values)\n",
    "\n",
    "    for j in range(len(sigma_values)):\n",
    "        sigma = sigma_values[j]\n",
    "        N_cg = find_cg_time(k, sigma, N_exit)\n",
    "        R_cg = R_interp(N_cg)\n",
    "        R_diff_cg = R_diff_interp(N_cg)\n",
    "\n",
    "        R_at_sigma_values[j, i] = R_cg\n",
    "        R_diff_at_sigma_values[j, i] = R_diff_cg\n",
    "\n",
    "    # Storing\n",
    "    k_raw_values[i] = k\n",
    "    R_end_values[i] = R_values[-1]\n",
    "\n",
    "    if (i%50)==0:\n",
    "        end_time = timer()\n",
    "        print(i)\n",
    "        print(\"Taken \"+str(end_time-start_time)+\" so far\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's ca use these to find the power spectrum.\n",
    "\n",
    "**It is important to store each $k$ value seperately, as each one has a different scale factor normalisation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def power_spectrum_func(k, R):\n",
    "    return (np.abs(R)**2)*(k**3)/(2*np.pi**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's save these values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "data_dict = {}\n",
    "data_dict[\"N exit\"] = N_modes\n",
    "data_dict[\"k\"] = k_raw_values\n",
    "data_dict[\"R end\"] = R_end_values\n",
    "for j in range(len(sigma_values)):\n",
    "    data_dict[\"R at sigma \"+str(sigma_values[j])] = R_at_sigma_values[j,:]\n",
    "    data_dict[\"R diff at sigma \"+str(sigma_values[j])] = R_diff_at_sigma_values[j,:]\n",
    "\n",
    "data_pandas = pd.DataFrame(data_dict)\n",
    "\n",
    "data_pandas.to_csv(\"gaussian_bump_range_of_R_values_at_different_sigma\"+\".csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's load this data back in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_values = np.array([1.0, 0.5, 0.1, 0.01])\n",
    "\n",
    "matching_data = pd.read_csv(\"gaussian_bump_range_of_R_values_at_different_sigma\"+\".csv\", index_col=0)\n",
    "\n",
    "N_modes = np.array(matching_data[\"N exit\"])\n",
    "k_raw_values = np.array(matching_data[\"k\"])\n",
    "R_end_values = np.array(matching_data[\"R end\"],  dtype=np.complex64)\n",
    "\n",
    "\n",
    "R_at_sigma_values = np.zeros((len(sigma_values), len(N_modes)), dtype=\"complex\")\n",
    "R_diff_at_sigma_values = np.zeros((len(sigma_values), len(N_modes)), dtype=\"complex\")\n",
    "\n",
    "for j in range(len(sigma_values)):\n",
    "    R_at_sigma_values[j, :] = matching_data[\"R at sigma \"+str(sigma_values[j])]\n",
    "    R_diff_at_sigma_values[j, :] = matching_data[\"R diff at sigma \"+str(sigma_values[j])]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's also test it is giving me the correct final form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "power_spectrum = power_spectrum_func(k_raw_values, R_end_values)\n",
    "power_spectrum_at_sigma_001_new = power_spectrum_func(k_raw_values, R_at_sigma_values[-1, :])\n",
    "\n",
    "aH_interpolation = CubicSpline(N_values, hubble_param_values*a_in*np.exp(N_values-N_usr_start))\n",
    "a_interpolation = CubicSpline(N_values, a_in*np.exp(N_values-N_usr_start))\n",
    "\n",
    "k_usr_start = aH_interpolation(N_usr_start)\n",
    "k_usr_end = aH_interpolation(N_usr_end)\n",
    "\n",
    "k_values_normalised = aH_interpolation(N_modes)/k_usr_start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x520 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x520 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(k_values_normalised, power_spectrum)\n",
    "plt.yscale(\"log\")\n",
    "plt.xscale(\"log\")\n",
    "plt.ylabel(r\"$\\mathcal{P}_{\\mathcal{R}}(k)$\")\n",
    "plt.xlabel(r\"$k/k_{\\rm T}$\")\n",
    "plt.show()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}