cosmological-probes-exercises/problem-set-4/Problem_Set_4_hints.ipynb
2023-10-25 18:16:03 +02:00

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"%matplotlib inline\n",
"\n",
"from scipy.integrate import quad\n",
"\n",
"import numpy as np\n",
"\n",
"import PyCosmo"
]
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"data": {
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"'2.1.1'"
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"PyCosmo.__version__"
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"# 1. Wavenumber at equality\n",
"1. Assume that around equality the dominant components are matter and radiation. Use the first Friedmann equation i.e.: \n",
"\n",
"\t\\begin{equation}\n",
"\tH^2 = H_0^2[\\sum_i \\Omega_i a^{-3(1+w)}],\n",
"\t\\end{equation}\n",
" \n",
" to calculate $a_{eq}$, $H(a_{eq})$ and therefore $k_{eq}$.\n",
" \n",
" How might you identify $k_{eq}$ in a cosmological observable? Can you make a plot which includes this scale using PyCosmo? Do yout think this has been observed in data?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. Growth factor\n",
"\n",
"Here compute the growth factor for various cosmologies. The basic command in PyCosmo is shown below"
]
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"cell_type": "code",
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{
"ename": "SyntaxError",
"evalue": "invalid syntax (4003919975.py, line 4)",
"output_type": "error",
"traceback": [
"\u001b[0;36m Cell \u001b[0;32mIn[10], line 4\u001b[0;36m\u001b[0m\n\u001b[0;31m Cosmo.set(h=0.7, omega_b=, omega_m=)\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
]
}
],
"source": [
"# Define the Cosmology\n",
"Cosmo = PyCosmo.build()\n",
"#TODO: Set the parameters accordingly\n",
"Cosmo.set(h=0.7, omega_b=, omega_m=)\n",
"\n",
"# Function to calculate the growth factor\n",
"# uses the scaling parameter as input\n",
"growth_factor = Cosmo.lin_pert.growth_a(a=...)"
]
}
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