{ "cells": [ { "cell_type": "markdown", "id": "cloudy-liver", "metadata": {}, "source": [ "# Graphs\n", "\n", "This SageMath notebook plots numerical calculations for the paper *A theory of the dark matter*.\n", "\n", "The section numbering follows the paper. Equation numbers refer to equations in the paper." ] }, { "cell_type": "markdown", "id": "digital-target", "metadata": {}, "source": [ "## Preamble" ] }, { "cell_type": "code", "execution_count": 1, "id": "gentle-public", "metadata": {}, "outputs": [], "source": [ "%display latex\n", "LE = lambda latex_string: LatexExpr(latex_string);" ] }, { "cell_type": "code", "execution_count": 2, "id": "secondary-constitutional", "metadata": {}, "outputs": [], "source": [ "from mpmath import mp\n", "from mpmath import mpf,mpc\n", "import sage.libs.mpmath.all as a\n", "mp.pretty = True\n", "mp.dps=400\n", "#\n", "binary_precision=mp.prec\n", "Reals = RealField(binary_precision+10)\n", "RealNumber = Reals\n", "myR = Reals" ] }, { "cell_type": "code", "execution_count": 3, "id": "novel-small", "metadata": {}, "outputs": [], "source": [ "lambdaH = var('lambdaH',latex_name=r\"\\lambda_H\")\n", "gsq = var('gsq',latex_name=r\"g^2\")\n", "K_EW = var('K_EW',latex_name=r\"K_{\\mathrm{EW}}\")\n", "ahat_EW = var('ahat_EW',latex_name=r\"\\hat a_{\\mathrm{EW}}\")\n", "m = var('m')\n", "#m = var('m',latex_name=r\"k^2\")\n", "K = var('K')\n", "EoverK = var('EoverK',latex_name=r\"\\frac{E}{K}\")\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "charged-torture", "metadata": {}, "outputs": [], "source": [ "lambdaH_val = 0.5080829235055462\n", "gsq_val= 0.4262847210445738\n", "K_EW_val = myR(mp.ellipk(mpf(1/2)))\n", "ahat_EW_val = myR(sqrt(6*pi)/(4*K_EW_val))" ] }, { "cell_type": "code", "execution_count": 5, "id": "separated-mason", "metadata": {}, "outputs": [], "source": [ "Kdot = K*(EoverK/(1-m) -1)/2\n", "EoverKdot = EoverK -1/2 -EoverK^2/(2*(1-m))\n", "def dot(fn):\n", " return m*fn.derivative(m) + Kdot*fn.derivative(K) + EoverKdot*fn.derivative(EoverK)" ] }, { "cell_type": "code", "execution_count": 6, "id": "measured-advancement", "metadata": {}, "outputs": [], "source": [ "#\n", "latex_name={}\n", "latex_name['alpha'] = r\"\\alpha\"\n", "latex_name['bsq'] = r\"\\langle b^2\\rangle\"\n", "latex_name['musq'] = r\"\\mu^2\"\n", "latex_name['ECGF'] = r\"E_{\\mathrm{EW}}\"\n", "latex_name['ahatsq'] = r\"\\hat a^2\"\n", "latex_name['rhohat'] = r\"\\hat \\rho\"\n", "latex_name['ahat'] = r\"\\hat a\"\n", "latex_name['phat'] = r\"\\hat p\"\n", "latex_name['ahat_norm'] = r\"\\frac{\\hat a}{\\hat a_{\\mathrm{EW}}}\"\n", "latex_name['phisq_norm'] = r\"\\frac{(\\phi^\\dagger\\phi)_0}{v^2/2}\"\n", "latex_name['w'] = r\"w\"\n", "for vstr,form in latex_name.items():\n", " var(vstr,latex_name=latex_name[vstr])\n", "#" ] }, { "cell_type": "code", "execution_count": 7, "id": "viral-syria", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\alpha \\phantom{\\verb!x!}\\verb|=| 2^{\\frac{1}{3}} \\left(\\frac{{\\left({\\frac{E}{K}} {\\left(2 \\, m - 1\\right)} - m + 1\\right)} K}{{K_{\\mathrm{EW}}}}\\right)^{\\frac{1}{3}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\alpha \\phantom{\\verb!x!}\\verb|=| 2^{\\frac{1}{3}} \\left(\\frac{{\\left({\\frac{E}{K}} {\\left(2 \\, m - 1\\right)} - m + 1\\right)} K}{{K_{\\mathrm{EW}}}}\\right)^{\\frac{1}{3}}$$" ], "text/plain": [ "\\alpha ' = ' 2^(1/3)*((EoverK*(2*m - 1) - m + 1)*K/K_EW)^(1/3)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\langle b^2\\rangle \\phantom{\\verb!x!}\\verb|=| \\frac{{\\frac{E}{K}} + m - 1}{{\\alpha}^{2}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\langle b^2\\rangle \\phantom{\\verb!x!}\\verb|=| \\frac{{\\frac{E}{K}} + m - 1}{{\\alpha}^{2}}$$" ], "text/plain": [ "\\langle b^2\\rangle ' = ' (EoverK + m - 1)/alpha^2" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mu^2 \\phantom{\\verb!x!}\\verb|=| -\\frac{2 \\, m - 1}{{\\alpha}^{2}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mu^2 \\phantom{\\verb!x!}\\verb|=| -\\frac{2 \\, m - 1}{{\\alpha}^{2}}$$" ], "text/plain": [ "\\mu^2 ' = ' -(2*m - 1)/alpha^2" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}E_{\\mathrm{EW}} \\phantom{\\verb!x!}\\verb|=| -\\frac{{\\left(m - 1\\right)} m}{2 \\, {\\alpha}^{4}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}E_{\\mathrm{EW}} \\phantom{\\verb!x!}\\verb|=| -\\frac{{\\left(m - 1\\right)} m}{2 \\, {\\alpha}^{4}}$$" ], "text/plain": [ "E_{\\mathrm{EW}} ' = ' -1/2*(m - 1)*m/alpha^4" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat a^2 \\phantom{\\verb!x!}\\verb|=| \\frac{4 \\, {\\lambda_H}^{2} {\\mu^2}}{{g^2}} + \\frac{3}{2} \\, {\\langle b^2\\rangle}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat a^2 \\phantom{\\verb!x!}\\verb|=| \\frac{4 \\, {\\lambda_H}^{2} {\\mu^2}}{{g^2}} + \\frac{3}{2} \\, {\\langle b^2\\rangle}$$" ], "text/plain": [ "\\hat a^2 ' = ' 4*lambdaH^2*musq/gsq + 3/2*bsq" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat \\rho \\phantom{\\verb!x!}\\verb|=| \\frac{3 \\, {\\left(\\frac{32 \\, {E_{\\mathrm{EW}}}}{{g^2}} + \\frac{3 \\, {\\langle b^2\\rangle}^{2}}{{\\lambda_H}^{2}}\\right)}}{32 \\, {\\hat a^2}^{2}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat \\rho \\phantom{\\verb!x!}\\verb|=| \\frac{3 \\, {\\left(\\frac{32 \\, {E_{\\mathrm{EW}}}}{{g^2}} + \\frac{3 \\, {\\langle b^2\\rangle}^{2}}{{\\lambda_H}^{2}}\\right)}}{32 \\, {\\hat a^2}^{2}}$$" ], "text/plain": [ "\\hat \\rho ' = ' 3/32*(32*ECGF/gsq + 3*bsq^2/lambdaH^2)/ahatsq^2" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat p \\phantom{\\verb!x!}\\verb|=| -\\frac{\\frac{32 \\, {\\left({\\langle b^2\\rangle} {\\mu^2} - {E_{\\mathrm{EW}}}\\right)}}{{g^2}} + \\frac{9 \\, {\\langle b^2\\rangle}^{2}}{{\\lambda_H}^{2}}}{32 \\, {\\hat a^2}^{2}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat p \\phantom{\\verb!x!}\\verb|=| -\\frac{\\frac{32 \\, {\\left({\\langle b^2\\rangle} {\\mu^2} - {E_{\\mathrm{EW}}}\\right)}}{{g^2}} + \\frac{9 \\, {\\langle b^2\\rangle}^{2}}{{\\lambda_H}^{2}}}{32 \\, {\\hat a^2}^{2}}$$" ], "text/plain": [ "\\hat p ' = ' -1/32*(32*(bsq*musq - ECGF)/gsq + 9*bsq^2/lambdaH^2)/ahatsq^2" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}w \\phantom{\\verb!x!}\\verb|=| \\frac{{\\hat p}}{{\\hat \\rho}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}w \\phantom{\\verb!x!}\\verb|=| \\frac{{\\hat p}}{{\\hat \\rho}}$$" ], "text/plain": [ "w ' = ' phat/rhohat" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat a \\phantom{\\verb!x!}\\verb|=| \\sqrt{{\\hat a^2}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\hat a \\phantom{\\verb!x!}\\verb|=| \\sqrt{{\\hat a^2}}$$" ], "text/plain": [ "\\hat a ' = ' sqrt(ahatsq)" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\hat a}{\\hat a_{\\mathrm{EW}}} \\phantom{\\verb!x!}\\verb|=| \\frac{{\\hat a}}{{\\hat a_{\\mathrm{EW}}}}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\hat a}{\\hat a_{\\mathrm{EW}}} \\phantom{\\verb!x!}\\verb|=| \\frac{{\\hat a}}{{\\hat a_{\\mathrm{EW}}}}$$" ], "text/plain": [ "\\frac{\\hat a}{\\hat a_{\\mathrm{EW}}} ' = ' ahat/ahat_EW" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] }, { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{(\\phi^\\dagger\\phi)_0}{v^2/2} \\phantom{\\verb!x!}\\verb|=| -\\frac{3 \\, {\\langle b^2\\rangle}}{2 \\, {\\hat a^2}} + 1\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{(\\phi^\\dagger\\phi)_0}{v^2/2} \\phantom{\\verb!x!}\\verb|=| -\\frac{3 \\, {\\langle b^2\\rangle}}{2 \\, {\\hat a^2}} + 1$$" ], "text/plain": [ "\\frac{(\\phi^\\dagger\\phi)_0}{v^2/2} ' = ' -3/2*bsq/ahatsq + 1" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] } ], "source": [ "formula={}\n", "formula['alpha'] = ((K/K_EW)*2*(1-m+(2*m-1)*EoverK))^(1/3)\n", "formula['bsq'] = (m-1+EoverK)/alpha^2\n", "formula['musq'] = (1-2*m)/alpha^2\n", "formula['ECGF'] = (m*(1-m)/2)/alpha^4\n", "formula['ahatsq'] = 3*bsq/2 + (4*lambdaH^2/gsq)*musq\n", "formula['rhohat'] = ((3/gsq)*ECGF+(9/(32*lambdaH^2))*bsq^2)/ahatsq^2\n", "formula['phat'] = ((1/gsq)*(ECGF-musq*bsq)-(9/(32*lambdaH^2))*bsq^2)/ahatsq^2\n", "formula['w'] = phat/rhohat\n", "formula['ahat'] = (ahatsq)^(1/2)\n", "formula['ahat_norm'] = ahat/ahat_EW\n", "formula['phisq_norm'] = 1 - (3/2)*bsq/ahatsq\n", "for vstr,form in formula.items():\n", " pretty_print(LE(latex_name[vstr]),' = ', formula[vstr], hold= True)\n", " print('\\n')" ] }, { "cell_type": "code", "execution_count": 8, "id": "gross-civilization", "metadata": {}, "outputs": [], "source": [ "alpha = ((K/K_EW)*2*(1-m+(2*m-1)*EoverK))^(1/3)\n", "bsq = (m-1+EoverK)/alpha^2\n", "musq = (1-2*m)/alpha^2\n", "ECGF = (m*(1-m)/2)/alpha^4\n", "ahatsq = 3*bsq/2 + (4*lambdaH^2/gsq)*musq\n", "rhohat = ((3/gsq)*ECGF+(9/(32*lambdaH^2))*bsq^2)/ahatsq^2\n", "phat = ((1/gsq)*(ECGF-bsq*musq)-(9/(32*lambdaH^2))*bsq^2)/ahatsq^2\n", "w = phat/rhohat\n", "ahat = (ahatsq)^(1/2)\n", "ahat_norm = ahat/ahat_EW\n", "phisq_norm = 1 - (3/2)*bsq/ahatsq" ] }, { "cell_type": "code", "execution_count": 9, "id": "aggregate-illness", "metadata": {}, "outputs": [], "source": [ "def paramsub(vstr):\n", " temp = eval(vstr).subs(lambdaH=lambdaH_val,gsq=gsq_val,ahat_EW=ahat_EW_val,K_EW=K_EW_val)\n", " return temp" ] }, { "cell_type": "code", "execution_count": 10, "id": "killing-principal", "metadata": {}, "outputs": [], "source": [ "#\n", "alphan = paramsub('alpha')\n", "bsqn = paramsub('bsq')\n", "musqn = paramsub('musq')\n", "ECGFn = paramsub('ECGF')\n", "ahatsqn = paramsub('ahatsq')\n", "rhohatn = paramsub('rhohat')\n", "phatn = paramsub('phat')\n", "wn = paramsub('w')\n", "ahatn = paramsub('ahat')\n", "ahat_normn = paramsub('ahat_norm')\n", "phisq_normn = paramsub('phisq_norm')" ] }, { "cell_type": "code", "execution_count": 11, "id": "loose-tomorrow", "metadata": {}, "outputs": [], "source": [ "def msub(v,m_val):\n", " # v is one of the physical variables, m is a Sage real\n", "# m_mpf = mpf(m_val)\n", " m_R = myR(m_val)\n", " K_val = myR(elliptic_kc(m_R))\n", " E_val = myR(elliptic_ec(m_R))\n", " EoverK_val = E_val/K_val\n", "# print(RDF(m_R),RDF(EoverK_val-1), RDF(E_val-K_val),RDF(K_val-myR(pi)/2))\n", " temp = v.subs({EoverK:EoverK_val,m:m_R,K:K_val})\n", " return myR(temp)\n", "def fn(v):\n", " return lambda marg: msub(v,marg)" ] }, { "cell_type": "code", "execution_count": 12, "id": "adjacent-internet", "metadata": {}, "outputs": [], "source": [ "t = var('t')\n", "ahat_t = lambda t: fn(ahat_normn)(10^(-t)/2)\n", "w_t = lambda t: fn(wn)(10^(-t)/2)\n", "phisq_t = lambda t: fn(phisq_normn)(10^(-t)/2)\n", "#\n", "plt1 = parametric_plot([ahat_t ,w_t],(t,0,56),scale=\"semilogx\")\n", "plt2 = parametric_plot([ahat_t,phisq_t],(t,0,56),scale=\"semilogx\")" ] }, { "cell_type": "code", "execution_count": 13, "id": "otherwise-edwards", "metadata": {}, "outputs": [], "source": [ "anorm=var('anorm')\n", "coeff_low = ahat_EW_val^4 * gsq_val/(lambdaH_val^2)\n", "w_low = lambda anorm: -1+4/(3+anorm^4*coeff_low)\n", "plt3=plot(w_low,(anorm,1e-2,1),scale='semilogx')" ] }, { "cell_type": "code", "execution_count": 14, "id": "prospective-chuck", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 9 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt=plt1+plt2+plt3\n", "# +line([(1e-2,1),(100,1)],linestyle=\":\")\\\n", "plt = plt\\\n", "+text(r\"$w_{\\mathrm{CGF}}$\",(6e1,.1),fontsize=16,color='black')\\\n", "+text(r\"$\\frac{\\phi^\\dagger\\phi}{v^2/2}$\",(5e1,.75),fontsize=16,color='black')\\\n", "+text(r\"the Standard Model epoch\",(10^3,-.3),fontsize=16,color='black',\\\n", " horizontal_alignment='left',fontweight=300)\\\n", "+text(r\"$a_0$\",(4.54e18,-.14),fontsize=16,color='black')\\\n", "+text(r\"$a_{\\mathrm{EW}}$\",(1,-.14),fontsize=16,color='black')\n", "#plt.set_aspect_ratio(1)\n", "plt.set_axes_range(xmin=10^(-2),xmax=10^(22),ymin=0)\n", "plt = plt+ arrow((.1,-.2),(10^21,-.2),width=1,arrowsize=2,color='black')\n", "plt.axes_labels([r\"$\\frac{a}{a_{\\mathrm{EW}}}$\",\"\"])\n", "plt.axes_labels_size(2)\n", "#plt.axes_labels([\"\",\"\"])\n", "show(plt,title=\"Figure 1\",\\\n", " ticks=[[10^(-2),1,10^2,10^4,10^6,10^8,10^(10),10^(12),10^(14),10^(16),10^(18),RDF(1.0e20)],[0,1/2,1]],\\\n", " tick_formatter='latex')\n", "plt.save('plots/SMepoch.pdf',dpi=600,\\\n", " ticks=[[10^(-2),1,10^2,10^4,10^6,10^8,10^(10),10^(12),10^(14),10^(16),10^(18),RDF(1.0e20)],[0,1/2,1]],\\\n", " tick_formatter='latex')" ] }, { "cell_type": "markdown", "id": "designing-yemen", "metadata": {}, "source": [ "### 4.3 $a$ as a function of $k^2$\n", "\n", "Figure 1 showing that $a$ increases monotonically from $a_{\\mathrm{EW}}$ to $\\infty$ as $k^2$ decreases from $\\frac12$ to 0." ] }, { "cell_type": "code", "execution_count": 15, "id": "spiritual-landscape", "metadata": {}, "outputs": [], "source": [ "y=-(dot(ahatsq)/ahatsq)\n", "yn = paramsub('y')" ] }, { "cell_type": "code", "execution_count": 16, "id": "animated-locator", "metadata": {}, "outputs": [], "source": [ "plt=plot(fn(yn),m,1e-8,0.5)" ] }, { "cell_type": "code", "execution_count": 17, "id": "sharp-secret", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.set_axes_range(ymin=0)\n", "plt.set_aspect_ratio(0.1)\n", "plt.axes_labels([r\"$k^2$\",r\"$-\\frac{d \\ln a}{d\\ln k}$\"])\n", "plt.axes_labels_size(2)\n", "show(plt,title=\"Figure 2a\")\n", "plt.save('plots/aofkmonotonic.pdf',dpi=600)" ] }, { "cell_type": "code", "execution_count": 18, "id": "static-postcard", "metadata": {}, "outputs": [], "source": [ "plt = parametric_plot([fn(ahat_normn),m],(m,1e-5,0.5),scale=\"loglog\")" ] }, { "cell_type": "code", "execution_count": 19, "id": "assumed-biology", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.set_aspect_ratio(0.5)\n", "plt.set_axes_range(xmin=1,xmax=100,ymax=0.5)\n", "plt.axes_labels([r\"$\\frac{a}{a_{\\mathrm{EW}}} $\",r\"$k^2$\"])\n", "plt.axes_labels_size(2)\n", "plt.show(title=\"Figure 2b\")\n", "plt.save('plots/ksqofa.pdf',dpi=600)" ] }, { "cell_type": "markdown", "id": "unnecessary-gravity", "metadata": {}, "source": [ "### 5.2 w_CGF=0\n", "\n", "Figure 2 shows $w_{\\mathrm{CGF}}$ and the progress of the electroweak transition in the first 2 ten-folds of expansion after $a_{\\mathrm{EW}}$." ] }, { "cell_type": "code", "execution_count": 20, "id": "minimal-property", "metadata": {}, "outputs": [], "source": [ "plt1 = parametric_plot([fn(ahat_normn),fn(wn)],(m,1e-6,0.5),scale=\"semilogx\")\n", "plt2 = parametric_plot([fn(ahat_normn),fn(phisq_normn)],(m,1e-6,0.5),scale=\"semilogx\")" ] }, { "cell_type": "code", "execution_count": 21, "id": "certain-dubai", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt=plt1+plt2\\\n", "+line([(1,1),(100,1)],linestyle=\":\")\\\n", "+text(r\"$w_{\\mathrm{CGF}}$\",(2.2,.2),fontsize=16,color='black')\\\n", "+text(r\"$\\frac{(\\phi^\\dagger\\phi)_0}{v^2/2}$\",(2.8,.7),fontsize=16,color='black')\n", "plt.set_aspect_ratio(1)\n", "plt.set_axes_range(xmin=1,xmax=100)\n", "plt.axes_labels([r\"$\\frac{a}{a_{\\mathrm{EW}}}$\",\"\"])\n", "plt.axes_labels_size(2)\n", "show(plt,title=\"Figure 3\")\n", "plt.save('plots/wandphisq.pdf',dpi=600)" ] }, { "cell_type": "markdown", "id": "electrical-seafood", "metadata": {}, "source": [ "### 5.4 CGF equation of state" ] }, { "cell_type": "code", "execution_count": 22, "id": "macro-castle", "metadata": {}, "outputs": [], "source": [ "y=(dot(rhohat)/rhohat)\n", "yn = paramsub('y')" ] }, { "cell_type": "code", "execution_count": 23, "id": "eligible-programming", "metadata": {}, "outputs": [], "source": [ "plt=plot(fn(yn),m,1e-8,0.5)" ] }, { "cell_type": "code", "execution_count": 24, "id": "genetic-preference", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.set_axes_range(ymin=0)\n", "plt.set_aspect_ratio(0.05)\n", "plt.axes_labels([r\"$k^2$\",r\"$\\frac{d \\ln \\hat\\rho_{CGF}}{d\\ln k}$\"])\n", "plt.axes_labels_size(2)\n", "show(plt,title=\"Figure 4\")\n", "plt.save('plots/rhoofkmonotonic.pdf',dpi=600)" ] }, { "cell_type": "markdown", "id": "victorian-amsterdam", "metadata": {}, "source": [ "### 5.5 Adiabatic condition for $a\\ge a_{\\mathrm{EW}}$\n", "\n", "Figure 4 showing a bound on the ratio of time scales, verifying the adiabatic condition." ] }, { "cell_type": "code", "execution_count": 25, "id": "promotional-apparel", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\mathrm{gH}}=\\frac{t_{\\mathrm{grav}}^2}{t_{\\mathrm{Higgs}}^2}= 2.6387686437244608 \\times 10^{-33} \\qquad r_{\\mathrm{HH}}=\\frac{t_{\\mathrm{Higgs}}^2}{t_{\\mathrm{Hubble}}^2}= 1.3207956122976951 \\times 10^{-88} \\qquad \\Omega_\\Lambda= 0.685\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\mathrm{gH}}=\\frac{t_{\\mathrm{grav}}^2}{t_{\\mathrm{Higgs}}^2}= 2.6387686437244608 \\times 10^{-33} \\qquad r_{\\mathrm{HH}}=\\frac{t_{\\mathrm{Higgs}}^2}{t_{\\mathrm{Hubble}}^2}= 1.3207956122976951 \\times 10^{-88} \\qquad \\Omega_\\Lambda= 0.685$$" ], "text/plain": [ "r_{\\mathrm{gH}}=\\frac{t_{\\mathrm{grav}}^2}{t_{\\mathrm{Higgs}}^2}= 2.6387686437244608e-33 \\qquad r_{\\mathrm{HH}}=\\frac{t_{\\mathrm{Higgs}}^2}{t_{\\mathrm{Hubble}}^2}= 1.3207956122976951e-88 \\qquad \\Omega_\\Lambda= 0.685" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_gH= 2.6387686437244608e-33\n", "r_HH= 1.3207956122976951e-88\n", "Omega_Lambda = 0.685\n", "pretty_print(LE(r\"r_{\\mathrm{gH}}=\\frac{t_{\\mathrm{grav}}^2}{t_{\\mathrm{Higgs}}^2}=\"),\\\n", " RDF(r_gH),LE(r\"\\qquad r_{\\mathrm{HH}}=\\frac{t_{\\mathrm{Higgs}}^2}{t_{\\mathrm{Hubble}}^2}=\"),RDF(r_HH),\\\n", " LE(r\"\\qquad \\Omega_\\Lambda=\"),RDF(Omega_Lambda))" ] }, { "cell_type": "code", "execution_count": 26, "id": "utility-importance", "metadata": {}, "outputs": [], "source": [ "bound = 4*K*alpha*sqrt(r_gH*ahatsq*rhohat/3 + r_HH*Omega_Lambda*ahatsq)\n", "boundn = paramsub('bound')" ] }, { "cell_type": "code", "execution_count": 27, "id": "monthly-reserve", "metadata": {}, "outputs": [], "source": [ "plt= parametric_plot((fn(ahat_normn),fn(boundn)),(m,5e-7,0.5),scale=\"loglog\")" ] }, { "cell_type": "code", "execution_count": 28, "id": "million-glance", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.set_aspect_ratio(.5)\n", "plt.set_axes_range(ymax=1e-15,ymin=1e-19)\n", "plt.axes_labels([r\"$\\frac{a}{a_{\\mathrm{EW}}} $\",r\"$y$\"])\n", "plt.axes_labels_size(2)\n", "show(plt,title=\"Figure 5\")\n", "plt.save('plots/adiabaticbound.pdf',dpi=600)" ] }, { "cell_type": "markdown", "id": "downtown-housing", "metadata": {}, "source": [ "### 6.4 Temperature after $a_{\\mathrm{EW}}$" ] }, { "cell_type": "markdown", "id": "narrow-tolerance", "metadata": {}, "source": [ "CGF temperature $\\qquad k_{\\mathrm{B}} T_{\\mathrm{CGF}} = \\frac{\\hbar}{4 K' \\alpha a}= \\frac{m_{\\mathrm{Higgs}}}{4 K' \\alpha \\hat a}$" ] }, { "cell_type": "markdown", "id": "painful-sterling", "metadata": {}, "source": [ "redshifted to the present $\\qquad k_{\\mathrm{B}} T_{\\mathrm{rs}}=\\frac{a}{a_0} k_B T_{\\mathrm{CGF}} = \\frac{m_{\\mathrm{Higgs}}}{4 K' \\alpha \\hat a_0}$" ] }, { "cell_type": "markdown", "id": "blond-construction", "metadata": {}, "source": [ "use numbers from the Arithmetic notebook and from above" ] }, { "cell_type": "code", "execution_count": 29, "id": "super-column", "metadata": {}, "outputs": [], "source": [ "T_CMB = mpf(2.7255) # K\n", "K_EW_mpf = mp.ellipk(1/2)\n", "m_Higgs_mpf= mpf(125.1) # GeV\n", "kB_mpf = mpf(8.61733326214518e-14) # GeV/K\n", "ahat0_mpf = mpf(2.6592893046343716e18) # s\n", "ahat_EW_mpf = mpf(0.5854143283037644) # s\n", "lambda_mpf = mpf(lambdaH_val)\n", "gsq_mpf = mpf(gsq_val) # g^2" ] }, { "cell_type": "markdown", "id": "broad-tiffany", "metadata": {}, "source": [ "define functions in mpmath" ] }, { "cell_type": "code", "execution_count": 30, "id": "little-homework", "metadata": {}, "outputs": [], "source": [ "def kT_CGF(ma):\n", " m=mpf(ma)\n", " K = mp.ellipk(m)\n", " Kp = mp.ellipk(1-m)\n", " E = mp.ellipe(m) \n", " EoverK = E/K\n", " alpha = mp.power( (K/K_EW_mpf)*2*(1-m+(2*m-1)*EoverK) ,1/3)\n", " ahatsq = ((3/2)*(m-1+EoverK)+(4*lambda_mpf^2/gsq_mpf)*(1-2*m))/alpha^2\n", " ahat = mp.sqrt(ahatsq)\n", " return m_Higgs_mpf/(4*Kp*alpha*ahat)\n", "def T_rs(ma):\n", " m=mpf(ma)\n", " K = mp.ellipk(m)\n", " Kp = mp.ellipk(1-m)\n", " E = mp.ellipe(m) \n", " EoverK = E/K\n", " alpha = mp.power( (K/K_EW_mpf)*2*(1-m+(2*m-1)*EoverK) ,1/3)\n", " return m_Higgs_mpf/(4*Kp*alpha*ahat0_mpf*kB_mpf)\n", "def ahat_over_ahat0_mp(ma):\n", " m=mpf(ma)\n", " K = mp.ellipk(m)\n", " E = mp.ellipe(m) \n", " EoverK = E/K\n", " alpha = mp.power( (K/K_EW_mpf)*2*(1-m+(2*m-1)*EoverK) ,1/3)\n", " ahatsq = ((3/2)*(m-1+EoverK)+(4*lambda_mpf^2/gsq_mpf)*(1-2*m))/alpha^2\n", " ahat = mp.sqrt(ahatsq)\n", " return ahat/ahat_EW_mpf\n" ] }, { "cell_type": "code", "execution_count": 31, "id": "sunset-publication", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt=parametric_plot((ahat_over_ahat0_mp,kT_CGF),(m,1e-21,0.5),scale=\"semilogx\")\n", "plt.set_aspect_ratio(.1)\n", "plt.set_axes_range(ymin=0,ymax=30,xmin=1,xmax=1e7)\n", "yaxis_label = Graphics()+text(r\"$ k_\\mathrm{B} T_{\\mathrm{CGF}}$\",(-0.15,0.80),axis_coords=True,fontsize=12,color='black')\n", "yaxis_label += text(r\"$ (\\mathrm{GeV})$\",(-0.15,0.70),axis_coords=True,fontsize=11,color='black')\n", "xaxis_label = Graphics()+text(r\"$\\frac{a}{a_{\\mathrm{EW}}} $\",(1.05,-0.04),axis_coords=True,fontsize=18,color='black')\n", "plt2 = plt+yaxis_label+xaxis_label\n", "plt.axes_labels_size(2)\n", "show(plt2,title=\"Figure 6\",figsize=[8,20],ymax=30,xmin=1)\n", "plt2.save('plots/kT_after_a_EW.pdf',figsize=[8,20],ymax=30,xmin=1,dpi=600)" ] }, { "cell_type": "markdown", "id": "furnished-software", "metadata": {}, "source": [ "Solve $T_{\\mathrm{rs}}(k^2) = T_{\\mathrm{CMB}}$" ] }, { "cell_type": "code", "execution_count": 32, "id": "united-dominican", "metadata": {}, "outputs": [], "source": [ "m_dc=mp.findroot(lambda ma: T_rs(ma)-T_CMB,1e-17,solver='anewton')\n", "T_rs_dc=T_rs(m_dc)\n", "ahatnorm_dc = ahat_over_ahat0_mp(m_dc)\n", "kT_dc = kT_CGF(m_dc)" ] }, { "cell_type": "code", "execution_count": 33, "id": "fifteen-capital", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}k^2 = 5.1168 \\times 10^{-18} \\qquad \\frac{a}{a_0} k_B T_{\\mathrm{CGF}} = 2.7255 \\,\\mathrm{K} \\qquad \\frac{a}{a_0} = 1.1305 \\times 10^{6} \\qquad k_B T_{\\mathrm{CGF}} = 0.94371 \\,\\mathrm{GeV}\\]" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k^2 = 5.1168 \\times 10^{-18} \\qquad \\frac{a}{a_0} k_B T_{\\mathrm{CGF}} = 2.7255 \\,\\mathrm{K} \\qquad \\frac{a}{a_0} = 1.1305 \\times 10^{6} \\qquad k_B T_{\\mathrm{CGF}} = 0.94371 \\,\\mathrm{GeV}$$" ], "text/plain": [ "k^2 = 5.1168e-18 \\qquad \\frac{a}{a_0} k_B T_{\\mathrm{CGF}} = 2.7255 \\,\\mathrm{K} \\qquad \\frac{a}{a_0} = 1.1305e6 \\qquad k_B T_{\\mathrm{CGF}} = 0.94371 \\,\\mathrm{GeV}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pretty_print(\\\n", " LE(r\"k^2 = \"), RDF(m_dc).n(prec=20),\\\n", " LE(r\"\\qquad \\frac{a}{a_0} k_B T_{\\mathrm{CGF}} = \"),RDF(T_rs_dc).n(prec=20),LE(r\"\\,\\mathrm{K}\"),\\\n", " LE(r\"\\qquad \\frac{a}{a_0} = \"),RDF(ahatnorm_dc).n(prec=20),\\\n", " LE(r\"\\qquad k_B T_{\\mathrm{CGF}} = \"),RDF(kT_dc).n(prec=20),LE(r\"\\,\\mathrm{GeV}\"))\n" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.4", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.5" } }, "nbformat": 4, "nbformat_minor": 5 }