Cosmofahmi.docx

import math import numpy as np import matplotlib import matplotlib.pyplot as plt

def cosmos_at_z(z, H0, w_r, w_m, w_v, n): # Some constants c = 299792.458 # speed of light in km/s HtoGyr = 977.8 # coefficient for converting 1/H to Gyr h = H0/100.0

# do a little calculation # w_r = 4.165E-5/(h*h) # includes 3 massless neutrino species, T CMB = 2.72528 w_k = 1 - w_m - w_r - w_v # calculate Omega curvature (1 - Omega(total)) az = 1.0/(1.0 + z) # scale factor of a given z

# calculate age of the universe at redshift z zage = 0.0 delta_a = az/n # step, delta_a for i in range(n): a = delta_a*(i + 0.5) _a = 1.0/a a_dot = math.sqrt(w_k + w_m*_a + w_r*_a*_a + w_v*a*a) zage = zage + 1.0/a_dot

zage = delta_a*zage # age of the universe at redshift z in units of 1/H0

# calculate time from z to now, and comoving radial distance

dtt = 0.0 # time from z to now in units of 1/H0 dcmr = 0.0 # r, comoving radial distance in units of c/H0 delta_a = (1.0 - az)/n # step, delta_a for i in range(n): a = az+delta_a*(i + 0.5) _a = 1.0/a a_dot = math.sqrt(w_k + w_m*_a + w_r*_a*_a + w_v*a*a) dtt = dtt + 1.0/a_dot dcmr = dcmr + 1.0/(a*a_dot)

dtt = delta_a*dtt dcmr = delta_a*dcmr # r = proper distance at the time observation, in units of c/H0 dpte = dcmr*az # proper distance at the time of emission, in units of c/H0 age = dtt + zage # age of the universe now in units of 1/H0

# calculate tangential comoving distance ratio = 1.0 x = math.sqrt(abs(w_k))*dcmr # x = r/R0 or R0 = r/x if x > 0.1: if w_k > 0: ratio = math.sinh(x)/x else: ratio = math.sin(x)/x else: y = x*x if w_k < 0: y = -y ratio = 1.0 + y/6.0 + y*y/120.0 # series expansion for sin(x) and sinh(x)

dcmt = ratio*dcmr # R0 * sin(r/R0) = r/x * sin(x) da = az*dcmt

dl = dcmt/az

# # human-readable zage_Gyr = HtoGyr/H0*zage age_Gyr = (HtoGyr/H0)*age dcmr_Mpc = (c/H0)*dcmr dtt_Gyr = (HtoGyr/H0)*dtt da_mpc = (c/H0)*da dl_mpc = (c/H0)*dl

print('For z, H0, Omega_M, Omega_Vacuum = ', z, H0, w_m, w_v) print('The age at redshift z was = '+ str(zage_Gyr) + ' Gyr') print('The comoving radial distance '+ str(dcmr_Mpc) + ' Mpc') print('The light travel time was '+ str(dtt_Gyr) + ' Gyr') print('It is now ' + str(age_Gyr) + ' Gyr since the Big Bang') print('DA = '+ str(da_mpc), ' Mpc') print('DL = ' + str(dl_mpc), ' Mpc')

return dcmr, dpte, da, dl, dtt, zage, age

def cosmos_at_z_array(z, H0, w_r, w_m, w_v, n): dcmrlist, dptelist, dalist, dllist, dttlist, zagelist, agelist = [], [], [], [], [], [], [] for zi in z: dcmr, dpte, da, dl, dtt, zage, age = cosmos_at_z(zi, H0, w_r, w_m, w_v, n) dcmrlist.append(dcmr) dptelist.append(dpte) dalist.append(da) dllist.append(dl) dttlist.append(dtt) zagelist.append(zage) agelist.append(age)

return dcmrlist, dptelist, dalist, dllist, dttlist, zagelist, agelist

def plot_proper_dist(): z = np.linspace(0.01, 1000, 1000) benchmark = cosmos_at_z_array(z, 70, 0.0, 0.3, 0.7, 1000) matter = cosmos_at_z_array(z, 70, 0.0, 1.0, 0.0, 1000) vacuum = cosmos_at_z_array(z, 70, 0.0, 0.0, 1.0, 1000)

# proper distance at the time of observation plt.plot(z, benchmark[0], 'r', label='Benchmark') plt.plot(z, matter[0], 'g', label='matter-only') plt.plot(z, vacuum[0], 'b', label=r'$\Lambda$-only') plt.xscale('log') plt.yscale('log') plt.xlabel(r'$z$', fontsize=20) plt.ylabel(r'$(H_{0}/c) d_{p}(t_{0})$', fontsize=20) plt.show() plt.savefig('fahmi2.png')

# proper distance at the time of emission plt.plot(z, benchmark[1], 'r', label='Benchmark') plt.plot(z, matter[1], 'g', label='matter-only') plt.plot(z, vacuum[1], 'b', label=r'$\Lambda$-only') plt.xscale('log') plt.yscale('log') plt.xlabel(r'$z$', fontsize=20) plt.ylabel(r'$(H_{0}/c) d_{p}(t_{e})$', fontsize=20) plt.show() plt.savefig('fahmi3.png')

if __name__ == "__main__": cosmos_at_z(1100, 67.74, 4.165E-5*10000/(67.74*67.74), 0.3089, 0.6911, 1000) plot_proper_dist()

ref: Ned Wright (www.astro.ucla.edu/~wright)