add assignments

problem-set-4/.ipynb_checkpoints/Problem_Set_4_hints-checkpoint.ipynb

@@ -0,0 +1,116 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "from scipy.integrate import quad\n",
+    "\n",
+    "import numpy as np\n",
+    "\n",
+    "import PyCosmo"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'2.1.1'"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "PyCosmo.__version__"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 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"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "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=...)"
+   ]
+  }
+ ],
+ "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": "3.10.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}