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@ny2292000
Created September 12, 2016 20:53
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Hypergeometrical Universe Theory"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "d395cbbb-ffde-4b9f-a2b5-acfeb8303524"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"14.43448806721477 lyr\n"
]
},
{
"data": {
"image/png": 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yOIXzzzcoSFKRDAuqCaNH54GLX/1qDgYPPwzt7fDpTxddmSSporAQESMj4sWI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\nw3qjreT5zHMW8HFF0e2o9ve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"text/plain": [
"<matplotlib.figure.Figure at 0x1049ef550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import matplotlib\n",
"import math\n",
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.optimize import fsolve\n",
"from scipy.stats import chisquare\n",
"from astropy.cosmology import Planck15\n",
"from astropy import constants, units\n",
"\n",
"def d_planck15(z):\n",
" R0 = (constants.c)/(Planck15.H0)\n",
" d_L = (Planck15.luminosity_distance(z))/R0.to(units.Mpc)\n",
" plt.plot(z, d_L)\n",
" R0=R0.to(units.lyr)/1e9\n",
" return R0,d_L\n",
"z = np.arange(0.0,1.5,0.01)\n",
"R0_GLY,d_L=d_planck15(z)\n",
"R0_GLY_CMB=R0_GLY\n",
"print(R0_GLY)\n",
"HubbleGRData=pd.DataFrame()\n",
"HubbleGRData['z']=z\n",
"HubbleGRData['d']=d_L\n",
"\n",
"# http://astronomy.swin.edu.au/cosmos/D/Distance+Modulus\n",
"SCPData = pd.ExcelFile('Data SupernovaLBLgov/SCPUnionData.xlsx').parse('Sheet2')\n",
"angle=math.pi/4\n",
"# First let's create a set of lambda-shifts\n",
"z = SCPData['redshift']"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "2ab0a58d-03c1-4ae3-8f04-6ed5d589ef69"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$13.580448 \\; \\mathrm{lyr}$"
],
"text/plain": [
"<Quantity 13.580447523237893 lyr>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"H0=72*units.km/units.s/units.mpc\n",
"H0_saved=H0\n",
"R0Diff=R0_GLY-(constants.c/H0).to(units.lyr)\n",
"R0_GLY=(constants.c/H0).to(units.lyr)\n",
"R0_GLY"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "30973531-10ee-4040-a257-e152ba339cd7"
}
},
"outputs": [],
"source": [
"H0=1\n",
"c=1\n",
"R0=1\n",
"def alphaZ(x):\n",
" alpha = math.pi/4 - math.asin(1/math.sqrt(2)/(1+x))\n",
" return alpha\n",
"\n",
"def d_HU_epoch(R0,z):\n",
" alpha = alphaZ(z)\n",
" d_HU=R0*(1- math.cos(alpha)+math.sin(alpha))\n",
" return d_HU"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "f630ab50-d910-4aa7-a57f-9fb5adf309e6"
}
},
"source": [
"The distance d_HU is the arc on the outter circumference. Later that distance will be converted on d_HU_corrected to reflect the point-to-point distance between our observation point and the position in the 4D Spatial manifold where the Supernova exploded.\n",
"\n",
"Remember that\n",
"\n",
"$$ \\frac {\\lambda_0}{\\lambda_{Obs}} = \\frac{1}{1+z} = \\sqrt2 sin(\\frac{\\pi}{4}-\\alpha))$$\n",
"\n",
"So\n",
" $$ \\alpha= \\frac{\\pi}{4}- asin(\\frac{1}{\\sqrt2(1+z)}) ) $$\n",
"\n",
"\n",
"so\n",
" \n",
" alpha = [math.pi/4 - math.asin(/math.sqrt(2)/(1+x)) for x in z]\n",
"\n",
"The scaling factor $$G_f = \\frac {R_0}{R(t)} = \\frac {1}{(cos(\\alpha)-sin(\\alpha))}$$\n",
"\n",
"The value of d', the actual distance is derived from the triangle law\n",
"\n",
"$$\\frac{sin(\\alpha)}{d'} = \\frac{sin(\\frac{3\\pi}{4})}{R_0} = \\frac{sin(\\frac{\\pi}{4} - \\alpha)}{R(t)}$$\n",
"\n",
"\n",
"$$ {d'}=\\sqrt2 R_0 sin(\\alpha)= \\sqrt2 R_0 sin(\\frac{\\pi}{4}-asin(\\frac{1}{\\sqrt2(1+z)})) $$\n",
"\n",
"The distance between Universe epochs is what is traversed at the speed of light c on our expanding hypersphere and that is given by:\n",
"\n",
"$$ d_{epoch}(t) = \\frac {R_0-R(t)}{R_0} = 1 - \\frac{1}{G_f}= 1-\\frac {R(t)}{R_0} =1- cos(\\alpha)+sin(\\alpha) $$\n",
"\n",
"This value is the one used on the predictions of the Hypergeometrical Universe. This is the distance travelled by a light entity traveling at the speed of light c, during the time the Universe took to reach our epoch. This is equivalent to the distance d on our epoch. This is the appropriate mapping since in the HU model, light travels at $\\sqrt2 c$ within a 4D spatial manifold."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "e8aef617-b3cf-4603-a565-d6dcb968ec80"
}
},
"outputs": [],
"source": [
"# All the light coming from supernovae maps initially to the cosmological region [0,pi/4]\n",
"# no modifications done to initial data\n",
"d_bar_measured= SCPData[\"d\"]/R0_GLY"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "2482d190-2878-44b4-a28f-1f5375d97d41"
}
},
"outputs": [],
"source": [
"# Consider two points separated by d_HU on the current epoch (current hyperspherical hypersurface)\n",
"\n",
"# First let's calculate the distance at the current Hypersphere. This distance will be projected into inner hyperspheres\n",
"# until a 45 degrees ray of light reaches the observer. That hypersphere will be defined by an R(t) and a d_HU_corrected.\n",
"# Simple geometry will be used to derive both.\n",
"\n",
"alpha = [math.pi/4 - math.asin(1/math.sqrt(2)/(1+x)) for x in z]\n",
"Gf=[1/(math.cos(x)-math.sin(x)) for x in alpha]\n",
"\n",
"# Calculate correction factors for measured distances\n",
"correctingFactors=[Gf[i]**1.5 for i in range(len(z))]\n",
"d_bar_measured_corrected=[d_bar_measured[i]/correctingFactors[i] for i in range(len(z))]\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true,
"nbpresent": {
"id": "20902759-f555-4e60-ac82-97cb66ed5eb7"
}
},
"outputs": [],
"source": [
"# the 4D Line_of_sight distance d_prime is easily calculated as:\n",
"d_prime_4DLineOfSight = [R0*math.sqrt(2)*math.sin(x) for x in alpha]\n",
"# This distance (line of sight) is not relevant since the actual trajectory of light goes from layer to layer at 45 \n",
"# degrees, thus traversing the same distance radially as tangentially. The distance traversed tangentially is equal \n",
"# to d_HU_corrected calculated by d_HU_epoch or distance to epoch.\n",
"# Notice that all distances are derived from z -> alpha -> d_HU_epoch = R0(1-cos(alpha)+sin(alpha))\n",
"# where R0 is always 1\n",
"d_HU_corrected= [d_HU_epoch(1,x) for x in z]"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "e1cf92b5-0ece-4503-bca2-a75356841cc0"
}
},
"outputs": [],
"source": [
"############################################\n",
"# Notice that all distances are derived from z -> alpha -> d = R0(1-cos(alpha)+sin(alpha))\n",
"# where R0 is always 1\n",
"upperlim=2-math.pi/4\n",
"bigz=[z*0.01 for z in range(2050)]\n",
"d_HU_big_corrected=pd.DataFrame()\n",
"\n",
"d_HU_big_corrected['z']=[z for z in bigz]\n",
"d_HU_big_corrected['d']= [d_HU_epoch(1,x) for x in bigz]\n",
"\n",
"d_HU_big_up_corrected=pd.DataFrame()\n",
"d_HU_big_up_corrected['z']=[z for z in bigz]\n",
"d_HU_big_up_corrected['d']=[2-x for x in d_HU_big_corrected.d]\n",
"ind= (d_HU_big_up_corrected.d<=upperlim) #& (d_HU_big_up_corrected.d>1) \n",
"d_HU_big_up_corrected['d']=[x for x in d_HU_big_corrected.d]\n",
"d_HU_big_up_corrected=d_HU_big_up_corrected[ind]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "c0414f56-f596-473b-b34b-3ec067adfbee"
}
},
"outputs": [
{
"data": {
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f42fqc6WUUipM0pqHwxjzlDFmALAbsI93280YM8AY87SLArPR5s2bmTt3rq9D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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1049cffd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"############################################\n",
"plt.semilogy(bigz,d_HU_big_corrected.d,'k-', label='1stQuad HU Hubble Law')\n",
"plt.semilogy(d_HU_big_up_corrected.z,d_HU_big_up_corrected.d,'r.', label='2ndQuad HU Hubble Law')\n",
"plt.semilogy(z,d_bar_measured_corrected,'k-', label='SCPData')\n",
"# plt.semilogy(z,d_prime_4DLineOfSight,'k+', label='4DLineOfSightDistance')\n",
"\n",
"\n",
"plt.xlabel('Relative Lambda Shift z')\n",
"plt.ylabel('Distance d as a Fraction of R0')\n",
"plt.title('HU Predictions - z vs Distance')\n",
"plt.grid(True)\n",
"\n",
"legend = plt.legend(loc='lower right', shadow=True, fontsize='small')\n",
"\n",
"# Put a nicer background color on the legend.\n",
"legend.get_frame().set_facecolor('#00FFCC')\n",
"\n",
"plt.ylim(0.01,1)\n",
"plt.xlim(0,10.55)\n",
"plt.savefig(\"img/vcDistanceBothQuad.png\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "73e372ac-d371-4e68-9c38-9e8efa5425c3"
}
},
"outputs": [
{
"data": {
"text/plain": [
"((2050,), (2050, 2))"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.shape(bigz),np.shape(d_HU_big_corrected)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "7281eea7-35a3-4544-8cf0-698613004dbd"
}
},
"outputs": [
{
"data": {
"image/png": 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ICxYssDo/NjbW+MVcrVo12rVrx7Rp05xuv+4J0a/rLI7u9+3bt5kwYYIx9l+v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"text/plain": [
"<matplotlib.figure.Figure at 0x115346780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"############################################\n",
"plt.semilogy(bigz,d_HU_big_corrected.d,'k-', label='1stQuad HU Hubble Law')\n",
"plt.semilogy(z,d_bar_measured_corrected,'k-', label='SCPData')\n",
"\n",
"plt.xlabel('Relative Lambda Shift z')\n",
"plt.ylabel('Distance d as a Fraction of R0')\n",
"plt.title('HU Predictions - z vs Distance')\n",
"plt.grid(True)\n",
"\n",
"legend = plt.legend(loc='lower right', shadow=True, fontsize='small')\n",
"\n",
"# Put a nicer background color on the legend.\n",
"legend.get_frame().set_facecolor('#00FFCC')\n",
"plt.ylim(0.01,1)\n",
"plt.xlim(0,1.5)\n",
"plt.savefig(\"img/vcDistancesmall.png\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "69f20c4d-fa6f-4fa7-857f-c151bb5f5eb8"
}
},
"outputs": [
{
"data": {
"text/plain": [
"0.71677745734501652"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(d_bar_measured_corrected)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "1da8d676-084d-4f6d-8b2c-0a3fac2d885e"
}
},
"outputs": [
{
"data": {
"image/png": 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HnRsugWPrQr1a0KGlPQV0WiOoUgl6ng/L/rTL1aoBvdrZ7dSvDQMvs4WRR9XKcO9/ICEB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\nD95XKP1PWkI9AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1155363c8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(HubbleGRData.z,HubbleGRData.d,'k:', label='Friedmann-Lemaitre Fitting')\n",
"plt.plot(z,d_bar_measured,'k+', label='SCPData')\n",
"plt.plot(z,d_HU_corrected,'k.', label='HU Hubble Law')\n",
"# Correcting Stellar Candles for Gravitational R(t) dependence\n",
"# The Absolute Luminosity should scale down with G ~ (R0/R(t))^(3/2)\n",
"\n",
"plt.plot(z,d_bar_measured_corrected,'k-', label='Normalized SCPData Epoch-Corrected')\n",
"\n",
"plt.xlabel('Relative Lambda Shift z')\n",
"plt.ylabel('Distance d as a Fraction of R0')\n",
"plt.title('z vs Distance vs')\n",
"plt.grid(True)\n",
"\n",
"legend = plt.legend(loc='upper left', shadow=True, fontsize='small')\n",
"\n",
"# Put a nicer background color on the legend.\n",
"legend.get_frame().set_facecolor('#00FFCC')\n",
"# plt.ylim(0,2.4)\n",
"plt.xlim(0,1.4)\n",
"plt.savefig(\"img/vcDistance.png\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "ffdfed9f-299d-4b9a-973a-7fb1f268f151"
}
},
"outputs": [
{
"data": {
"image/png": 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9fZcModDZRUh79zEYDIZUkXQkREROAf4HWEKkBBgBHA3UhWqd+/HHArcBkyI2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OCWW2xkZjDGbL0QKtteiVAeyN01r48AHAdwmYPjNQJwSoRXEMBYAPs0n02r+d5LInxHEMA7AL4B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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115883278>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"relativeD_Error=[d_bar_measured_corrected[i]/d_HU_corrected[i]-1 for i in range(len(d_HU_corrected))]\n",
"\n",
"plt.plot(z,relativeD_Error,'k-', label='Relative Distance Epoch-Corrected Error')\n",
"plt.xlabel('RedShift z')\n",
"plt.ylabel('Relative Error as a Fraction of distance')\n",
"plt.title('z vs Distance error')\n",
"plt.grid(True)\n",
"\n",
"legend = plt.legend(loc='upper left', shadow=True, fontsize='small')\n",
"\n",
"# Put a nicer background color on the legend.\n",
"legend.get_frame().set_facecolor('#00FFCC')\n",
"plt.ylim(-0.6,0.6)\n",
"plt.xlim(0,1.5)\n",
"plt.savefig(\"img/variance.png\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "f4e61a00-e880-46ee-b97b-cb49d0097aed"
}
},
"outputs": [
{
"data": {
"image/png": 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OOXFXmNjWTQGKhTDR2KMroUyKuy2MlNleXp6lM0pNTbX7XdztkF+4Y4eRI0fy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"text/plain": [
"<matplotlib.figure.Figure at 0x115db9b38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.semilogy(z,d_bar_measured_corrected,'k-', label='Epoch-Corrected Distance ')\n",
"plt.semilogy(z,d_HU_corrected,'k-', label='HU Distance Prediction')\n",
"\n",
"plt.xlabel('RedShift z')\n",
"plt.ylabel('Fractional Distance (fraction of R0)')\n",
"plt.title('z vs Distance for Supernova Survey Data')\n",
"plt.grid(True)\n",
"\n",
"legend = plt.legend(loc='lower right', shadow=True, fontsize='small')\n",
"\n",
"# Put a nicer background color on the legend.\n",
"legend.get_frame().set_facecolor('#00FFCC')\n",
"plt.ylim(0,1)\n",
"plt.xlim(0,1.4)\n",
"plt.savefig(\"img/comparison.png\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "6df3399a-0fec-4b24-bce0-615e9417be8d"
}
},
"outputs": [
{
"data": {
"text/plain": [
"Power_divergenceResult(statistic=-5691.7731294886398, pvalue=1.0)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chisquare(relativeD_Error)"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpresent": {
"id": "b6f0a862-9dba-4e55-a579-03582a868654"
}
},
"source": [
"The best fitting R0 for the Supernova dataset is for H0=72, that corresponds to R0=13.58. The best for CMB is R0=14.43, so there is a difference of 0.85 Billion Light Years difference between these two measurements!!!"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "0ccaefcc-2e69-4af9-a1cb-3900331454ee"
}
},
"outputs": [
{
"data": {
"text/plain": [
"Power_divergenceResult(statistic=2.6425406840687518, pvalue=1.0)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chisquare(d_HU_corrected, d_bar_measured_corrected)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"nbpresent": {
"id": "412d30ea-5fdf-41ba-9e97-50c9d2120b72"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"72.0 km / (mpc s) 13.580447523237893 lyr 14.43448806721477 lyr 0.8540405439768772 lyr\n"
]
}
],
"source": [
"print(H0_saved,R0_GLY,R0_GLY_CMB, R0Diff)"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [default]",
"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": "3.5.2"
},
"nbpresent": {
"slides": {
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