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@icarob-eng
Created November 29, 2023 23:49
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Integrações sobre a equação de Friedmann para diversos modelos cosmológicos.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "4Lhaq0LvVq1E"
},
"source": [
"# Integração da equação de Friedmann\n",
"\n",
"A equação de Friedmann pode ser escrita na forma:\n",
"\n",
"$$\\frac{H^2}{H_0^2} = \\Omega_{r0} a^{-4} + \\Omega_{m0} a^{-3} + \\Omega_{k0} a^{-2} + \\Omega_{\\Lambda 0}$$\n",
"\n",
"Onde $\\Omega_k = 1 - \\Omega_0$ é o parâmetro de densidade da curvatura.\n",
"\n",
"Com algumas manipulações, obtemos:\n",
"\n",
"$$H_0 t = \\int_0^a\\frac{da}{\\sqrt{\\Omega_{r0} a^{-2} + \\Omega_{m0} a^{-1} + \\Omega_{k0} + \\Omega_{\\Lambda 0} a^2}} \\tag 1$$\n",
"\n",
"Que é a equação que queremos resolver, para $a$, onde $a(t_0) = 0$. No entanto, esta integral não possui solução analítica. Podemos reescreve-la na forma\n",
"$$H_0 t = \\int_0^a f(a) da$$\n",
"\n",
"Assim, resolvendo a integral, obtemos uma expressão numérica para\n",
"$$H_0 t \\approx F(a) \\tag 2$$\n",
"\n",
"O que pode facilmente gerar\n",
"$$F^{-1} (H_0 t) \\approx a$$\n",
"\n",
"## Criando a função de Friedman\n",
"Vamos definir a função $f$, criando os símbolos e constantes no `sympy`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "GnbVaMbqSa0c"
},
"outputs": [],
"source": [
"import sympy as sy\n",
"from scipy import integrate\n",
"from scipy import interpolate\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"\n",
"sy.init_printing()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "5ZaZeCjrUz-Z"
},
"outputs": [],
"source": [
"a, t, h0, or0, om0, ok0, oL0 = sy.symbols('a t H_0 \\Omega_{r0} \\Omega_{m0} \\Omega_{k0} \\Omega_{\\Lambda0}')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69
},
"id": "S_oZ9JZyFtG7",
"outputId": "20099eb2-7722-47ff-f709-78f1ed015cfd"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" 1 \n",
"─────────────────────────────────────────────────────────────────────\n",
" ________________________________________________________________\n",
" ╱ 2 \\Omega_{m0} \\Omega_{r0} \n",
" ╱ \\Omega_{\\Lambda0}⋅a + \\Omega_{k0} + ─────────── + ─────────── \n",
" ╱ a 2 \n",
"╲╱ a "
],
"text/latex": "$\\displaystyle \\frac{1}{\\sqrt{\\Omega_{\\Lambda0} a^{2} + \\Omega_{k0} + \\frac{\\Omega_{m0}}{a} + \\frac{\\Omega_{r0}}{a^{2}}}}$"
},
"metadata": {},
"execution_count": 3
}
],
"source": [
"f = 1 / sy.sqrt(or0 * a**-2 + om0 * a**-1 + ok0 + oL0 * a**2)\n",
"f"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 80
},
"id": "Zs1XHhReG_VZ",
"outputId": "7315d334-4ad6-4cf5-c4c6-44872db01469"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"a \n",
"⌠ \n",
"⎮ 1 \n",
"⎮ ───────────────────────────────────────────────────────────────────── da\n",
"⎮ ________________________________________________________________ \n",
"⎮ ╱ 2 \\Omega_{m0} \\Omega_{r0} \n",
"⎮ ╱ \\Omega_{\\Lambda0}⋅a + \\Omega_{k0} + ─────────── + ─────────── \n",
"⎮ ╱ a 2 \n",
"⎮ ╲╱ a \n",
"⌡ \n",
"0 "
],
"text/latex": "$\\displaystyle \\int\\limits_{0}^{a} \\frac{1}{\\sqrt{\\Omega_{\\Lambda0} a^{2} + \\Omega_{k0} + \\frac{\\Omega_{m0}}{a} + \\frac{\\Omega_{r0}}{a^{2}}}}\\, da$"
},
"metadata": {},
"execution_count": 4
}
],
"source": [
"F = sy.integrate(f, (a, 0, a))\n",
"F"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Nx681uoVOOdh"
},
"source": [
"Agora basta definir os parâmetros cosmolôgicos:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69
},
"id": "EUkGFcBBHNSZ",
"outputId": "f23cf1d4-f810-471d-92e5-60ee1a085fc1"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" 1.19530032950583 \n",
"────────────────────────────────────────────────────\n",
" _______________________________________________\n",
" ╱ 2 0.428622863315026 0.000120014401728207 \n",
" ╱ a + ───────────────── + ──────────────────── \n",
" ╱ a 2 \n",
"╲╱ a "
],
"text/latex": "$\\displaystyle \\frac{1.19530032950583}{\\sqrt{a^{2} + \\frac{0.428622863315026}{a} + \\frac{0.000120014401728207}{a^{2}}}}$"
},
"metadata": {},
"execution_count": 5
}
],
"source": [
"params = {\n",
" or0: 8.4e-5,\n",
" om0: 0.3,\n",
" oL0: 0.7 - 8.4e-5,\n",
" ok0: 0\n",
"}\n",
"f.subs(params)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "AFrXSDdNKrOP"
},
"outputs": [],
"source": [
"fa = sy.lambdify(a, f.subs(params))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "v1sf6UpRMvaR"
},
"source": [
"## Integração numérica\n",
"\n",
"O próximo passo é integrar numericamente $f$ de $0$ a $a$, com $a \\in [0, 10]$."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "QE_y5tqZNKXf"
},
"outputs": [],
"source": [
"a_range = np.geomspace(2e-9, 1, 5000)\n",
"\n",
"F_lambda = lambda a: integrate.quad(fa, 1e-10, a)\n",
"# integral de f(a) de aprox 0 -> a\n",
"\n",
"F_range = np.array(list(map(F_lambda, a_range)))[:, 0]\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "UWBavZotStPJ"
},
"source": [
"Como $H_0 t = F(a)$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 477
},
"id": "PRcV7cinQMaI",
"outputId": "cfefc751-1377-48af-93d4-7f07d4d2c9e2"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"plt.clf()\n",
"plt.title('Evolução do parâmetro de escala')\n",
"plt.xlabel('$a$')\n",
"plt.ylabel('$H_0 t$')\n",
"plt.plot(a_range, F_range)\n",
"plt.xscale(\"log\")\n",
"plt.yscale(\"log\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 491
},
"id": "ON_9s22VU5z6",
"outputId": "1eae411d-ba4b-463b-c707-e47f16ee2dda"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7de098617a00>]"
]
},
"metadata": {},
"execution_count": 9
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"plt.clf()\n",
"plt.title('Evolução do parâmetro de escala')\n",
"plt.xlabel('$a$')\n",
"plt.ylabel('$H_0 t$')\n",
"plt.plot(a_range, F_range)"
]
},
{
"cell_type": "markdown",
"source": [
"### Cálculo da idade do universo\n",
"\n",
"Podemos reescrever a integral $(1)$ de modo a achar a idade do universo, $t_0$.\n",
"\n",
"$$H_0 t_0 = \\int_{a_i}^{a_0}\\frac{da}{\\sqrt{\\Omega_{r0} a^{-2} + \\Omega_{m0} a^{-1} + \\Omega_{k0} + \\Omega_{\\Lambda 0} a^2}} \\tag 2$$\n",
"\n",
"Para um $a_i$ suficientemente pequeno ($\\approx 10^{-3}$) já é o suficiente para determindar a idade do universo. Depois podemos reescreve-la em termos da constante de Hubble.\n",
"\n",
"A integração numérica de $(3)$ resulta numa expressão na forma\n",
"$$t_0 = \\frac{F(a_0) - F(a_i)}{H_0}$$\n",
"\n",
"Mas, como vemos pela expressão $(2)$,\n",
"$$0 \\approx F(a_0)$$\n",
"Assim,\n",
"\n",
"$$t_0 \\approx - \\frac{F(a_i)}{H_0}$$"
],
"metadata": {
"id": "2VecF_cv1rCO"
}
},
{
"cell_type": "code",
"source": [
"Fa_i = integrate.quad(fa, 1, 1e-3)[0]\n",
"Fa_i"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 37
},
"id": "abaUaBa31qX8",
"outputId": "42c4bac0-577f-40c3-a470-fc7b99bf5ab8"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-0.9636960961510956"
],
"text/latex": "$\\displaystyle -0.963696096151096$"
},
"metadata": {},
"execution_count": 10
}
]
},
{
"cell_type": "code",
"source": [
"t_0 = lambda h: - Fa_i / (100 * h) * \\\n",
" (3.17e-8 * 3.036e19) * 1e-9\n",
"# conversão giga para anos"
],
"metadata": {
"id": "bG7ng4uX6hGt"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"t_0(h=0.68)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 37
},
"id": "yb0j1lE56vop",
"outputId": "ca10564d-660a-4d64-9272-8f62d6f6317b"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"13.639304224837769"
],
"text/latex": "$\\displaystyle 13.6393042248378$"
},
"metadata": {},
"execution_count": 12
}
]
},
{
"cell_type": "markdown",
"source": [
"### Identificando fazes do universo\n",
"\n",
"Podemos derivar a função logarítmica usando `interpolate.InterpolatedUnivariateSpline` e assim descobrir as épocas na história do universo."
],
"metadata": {
"id": "XCyYL1PguZUW"
}
},
{
"cell_type": "code",
"source": [
"log_a = interpolate.InterpolatedUnivariateSpline(\n",
" np.log10(F_range),\n",
" np.log10(a_range),\n",
" k=4\n",
" )\n",
"\n",
"d_log_a = log_a.derivative()\n",
"\n",
"d_log_a_range = np.array([d_log_a(F) for F in np.log10(F_range)])"
],
"metadata": {
"id": "h3kkxMSXuw81"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"plt.clf()\n",
"plt.title('Derivada do parâmetro de escala')\n",
"plt.xlabel('$log (a\\')$')\n",
"plt.ylabel('$log (H_0 t)$')\n",
"plt.plot(d_log_a_range, np.log10(F_range))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 495
},
"id": "-enycDhbwnfg",
"outputId": "7e918249-2add-4663-8bd2-ef6be6f32c6c"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7de09869d000>]"
]
},
"metadata": {},
"execution_count": 14
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zdcpICLlr_uG"
},
"source": [
"## Outros modelos\n",
"\n",
"Podemos generalizar o processo mostrado com uma função com os parâmetros de densidade."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "5IZKxdxosK6P"
},
"outputs": [],
"source": [
"def cosmic_models(in_a_range, params_list):\n",
" plt.clf()\n",
" plt.title('Evolução do parâmetro de escala')\n",
" plt.xlabel('$a$')\n",
" plt.ylabel('$H_0 t$')\n",
"\n",
" for in_params in params_list:\n",
" in_params.update({ok0: 1 - sum(in_params.values())})\n",
" # define o parâmtro de curvatura\n",
"\n",
" fa = sy.lambdify(a, f.subs(in_params))\n",
"\n",
" F_lambda = lambda a: integrate.quad(fa, 1e-5, a)\n",
" # integral de f(a) de aprox 0 -> a\n",
"\n",
" F_range = np.array(list(map(F_lambda, in_a_range)))\n",
"\n",
" plt.plot(in_a_range, F_range[:,0])\n",
"\n",
" plt.legend([f'Curva {i}' for i in range(len(params_list))])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 588
},
"id": "Guo8bu872jw8",
"outputId": "ca7ed465-f09b-4cd7-86a7-565e17c2ea19"
},
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"<lambdifygenerated-4>:2: RuntimeWarning: invalid value encountered in sqrt\n",
" return 0.953462589245592/sqrt(-0.090909090909091 + a**(-1.0))\n",
"<ipython-input-15-e9c3face3404>:13: IntegrationWarning: The occurrence of roundoff error is detected, which prevents \n",
" the requested tolerance from being achieved. The error may be \n",
" underestimated.\n",
" F_lambda = lambda a: integrate.quad(fa, 1e-5, a)\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"# matéria e curvatura\n",
"\n",
"cosmic_models(\n",
" np.geomspace(3e-10, 40, 5000),\n",
" [\n",
" {\n",
" or0: 0,\n",
" om0: 0.9,\n",
" oL0: 0,\n",
" },\n",
" {\n",
" or0: 0,\n",
" om0: 1,\n",
" oL0: 0,\n",
" },\n",
" {\n",
" or0: 0,\n",
" om0: 1.1,\n",
" oL0: 0,\n",
" },\n",
" ]\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 627
},
"id": "DJDZ8JlfLSw4",
"outputId": "59fdd607-93cc-4ced-dfa3-4bfeb5271d4d"
},
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"<lambdifygenerated-7>:2: RuntimeWarning: invalid value encountered in sqrt\n",
" return 1/sqrt(-1 + 2/a)\n",
"<ipython-input-15-e9c3face3404>:13: IntegrationWarning: The occurrence of roundoff error is detected, which prevents \n",
" the requested tolerance from being achieved. The error may be \n",
" underestimated.\n",
" F_lambda = lambda a: integrate.quad(fa, 1e-5, a)\n",
"<lambdifygenerated-8>:2: RuntimeWarning: invalid value encountered in sqrt\n",
" return 1/sqrt(-3 + 4/a)\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"# matéria e curvatura, fora do livro\n",
"\n",
"cosmic_models(\n",
" np.geomspace(3e-10, 4, 5000),\n",
" [\n",
" {\n",
" or0: 0,\n",
" om0: 1,\n",
" oL0: 0\n",
" },\n",
" {\n",
" or0: 0,\n",
" om0: 1.1,\n",
" oL0: 0\n",
" },\n",
" {\n",
" or0: 0,\n",
" om0: 2,\n",
" oL0: 0\n",
" },\n",
" {\n",
" or0: 0,\n",
" om0: 4,\n",
" oL0: 0\n",
" },\n",
" ]\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 627
},
"id": "jFYrxYfyukok",
"outputId": "8f93a25e-4f4d-4cf2-8df5-9a211a805708"
},
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"<lambdifygenerated-30>:2: RuntimeWarning: invalid value encountered in sqrt\n",
" return 0.74535599249993/sqrt(a**2 - 0.611111111111111 + 0.166666666666667/a)\n",
"<ipython-input-15-e9c3face3404>:13: IntegrationWarning: The occurrence of roundoff error is detected, which prevents \n",
" the requested tolerance from being achieved. The error may be \n",
" underestimated.\n",
" F_lambda = lambda a: integrate.quad(fa, 1e-5, a)\n",
"<lambdifygenerated-32>:2: RuntimeWarning: invalid value encountered in sqrt\n",
" return 0.845154254728517/sqrt(-0.5*a**2 + 1 + 0.214285714285714/a)\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"# matéria e lambda\n",
"\n",
"cosmic_models(\n",
" np.geomspace(3e-10, 2, 5000),\n",
" [\n",
" { # 0: Loitering Universe\n",
" or0: 0,\n",
" om0: 0.3,\n",
" oL0: 1.7134\n",
" },\n",
" { # 1: Big Bounce\n",
" or0: 0,\n",
" om0: 0.3,\n",
" oL0: 1.8\n",
" },\n",
" { # 2: Big Chill\n",
" or0: 0,\n",
" om0: 0.3,\n",
" oL0: 0.7\n",
" },\n",
" { # 3: Big Crunch\n",
" or0: 0,\n",
" om0: 0.3,\n",
" oL0: -0.7\n",
" },\n",
" ]\n",
")"
]
}
],
"metadata": {
"colab": {
"provenance": []
},
"kernelspec": {
"display_name": "Python 3",
"name": "python3"
},
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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