{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Supernova cosmology: theory, data, and simulations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Florent Leclercq
\n",
"Imperial Centre for Inference and Cosmology, Imperial College London
\n",
"florent.leclercq@polytechnique.org"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "Q7hbmwLTlYKY"
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "D1msUScsqHyE"
},
"source": [
"## Theory"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"id": "473xZW1Sl4Sn"
},
"outputs": [],
"source": [
"def mu(z,Omega_m,h):\n",
" return 25. - 5.*np.log10(h) + 5.*np.log10(D_L(z,Omega_m))\n",
"\n",
"def D_L(z,Omega_m):\n",
" return 3000.*(1+z)*(eta(1.,Omega_m) - eta(1/(1.+z),Omega_m))\n",
"\n",
"def eta(a,Omega_m):\n",
" s=((1.-Omega_m)/Omega_m)**(1/3.)\n",
" return 2*np.sqrt(s**3+1.) * (1/a**4 - 0.1540*s/a**3 + 0.4304*s**2/a**2 + 0.19097*s**3/a + 0.066941*s**4)**(-1/8.)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"id": "Srhk70X1mK0I"
},
"outputs": [],
"source": [
"zs=np.linspace(1e-3,2,100)\n",
"h=0.7\n",
"mus={}\n",
"for Omega_m in [0.2,0.3,0.4,0.5]:\n",
" mus[Omega_m]=mu(zs,Omega_m,h)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 516
},
"id": "TYUTBOgGnNKs",
"outputId": "bbcb7e6c-ce5d-46e8-8027-1cf16ea839ac"
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
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