-
Notifications
You must be signed in to change notification settings - Fork 0
/
cosmic.py
187 lines (160 loc) · 6.44 KB
/
cosmic.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
# ========== Cosmic ==========
import os.path
import matplotlib.pyplot as plt
import matplotlib.ticker as tck
import numpy as np
import PySimpleGUI as sg
from scipy.integrate import quad
N = 10**6 # step size
c = 299792.458 # speed of light [km/s]
# ========== Cosmological Functions ==========
def H(a):
"""
Hubble Parameter in terms of the scale factor
Args:
a [float]: The scale factor, a(t)
"""
E_a = np.sqrt(Omega_m*(a)**(-1) + Omega_r*a**(-2) + Omega_l*a**(-1-3*w_l) + Omega_k)
return hubble_time / E_a
def H_z(z):
"""
Hubble Parameter in terms of the redshift
Args:
z [float]: The redshift, z
"""
E_z = np.sqrt(Omega_m*(1+z)**(3) + Omega_r*(1+z)**(4) + Omega_l*(1+z)**(3+3*w_l) + Omega_k*(1+z)**2)
return hubble_dis / E_z
def S_k(r):
"""
Transverse comoving distance, given in terms of the comoving distance, r.
Args:
r [float]: The comoving distance
"""
if Omega_k < 0:
return (hubble_dis / np.sqrt(abs(Omega_k))) * np.sin((np.sqrt(abs(Omega_k)) * r) / hubble_dis)
elif Omega_k == 0:
return r
elif Omega_k > 0:
return (hubble_dis / np.sqrt(Omega_k)) * np.sinh((np.sqrt(Omega_k) * r) / hubble_dis)
def distancePlotter():
"""
Plotting distances
"""
dz = 10**(-5) # differential redshift element
z_values = np.arange(0, 14, dz)
comoving_dist_points = []
angular_dist_points = []
luminosity_dist_points = []
dis_point = 0
for z in z_values:
dis_point += H_z(z) * dz
comoving_dist_points.append(dis_point)
angular_dist_points.append(S_k(dis_point) / (1 + z))
luminosity_dist_points.append(S_k(dis_point) * (1 + z))
# Plotting Options
fig, ax0 = plt.subplots()
ax0.plot(z_values, comoving_dist_points, 'r')
# Setting Limits
ax0.set_xlim(0, 14)
# Setting Labels
ax0.set_xlabel('$z$')
ax0.set_ylabel('$\chi$ (Mpc)')
ax0.set_title('Comoving Distance vs Redshift')
# Minor Ticks
ax0.yaxis.set_ticks_position('both')
ax0.xaxis.set_ticks_position('both')
ax0.yaxis.set_minor_locator(tck.AutoMinorLocator())
# Tick Options
ax0.tick_params(which='major', width=1, size=7, direction='in')
ax0.tick_params(which='minor', width=0.6, size=4, direction='in')
plt.show()
fig, ax1 = plt.subplots()
ax1.plot(z_values, angular_dist_points, 'b')
# Setting Limits
ax1.set_xlim(0, 14)
# Setting Labels
ax1.set_xlabel('$z$')
ax1.set_ylabel('$d_A$ (Mpc)')
ax1.set_title('Angular Diameter Distance vs Redshift')
# Minor Ticks
ax1.yaxis.set_ticks_position('both')
ax1.xaxis.set_ticks_position('both')
ax1.yaxis.set_minor_locator(tck.AutoMinorLocator())
# Tick Options
ax1.tick_params(which='major', width=1, size=7, direction='in')
ax1.tick_params(which='minor', width=0.6, size=4, direction='in')
plt.show()
fig, ax2 = plt.subplots()
plt.plot(z_values, luminosity_dist_points, 'g')
# Setting Limits
ax2.set_xlim(0, 14)
# Setting Labels
ax2.set_xlabel('$z$')
ax2.set_ylabel('$d_L$ (Mpc)')
ax2.set_title('Luminosity Distance vs Redshift')
# Minor Ticks
ax2.yaxis.set_ticks_position('both')
ax2.xaxis.set_ticks_position('both')
ax2.yaxis.set_minor_locator(tck.AutoMinorLocator())
# Tick Options
ax2.tick_params(which='major', width=1, size=7, direction='in')
ax2.tick_params(which='minor', width=0.6, size=4, direction='in')
plt.show()
# ========== GUI ==========
# PySimpleGUI Theme Option
sg.change_look_and_feel('SandyBeach')
layout_input = [
[sg.Frame(layout=[
[sg.Image(os.path.normpath('res/h0.png')),
sg.InputText(default_text='67.36', font=('Tahoma', 12))],
[sg.Image(os.path.normpath('res/omega_matter.png')),
sg.InputText(default_text='0.3369', font=('Tahoma', 12))],
[sg.Image(os.path.normpath('res/omega_lambda.png')),
sg.InputText(default_text='0.6847', font=('Tahoma', 12))],
[sg.Image(os.path.normpath('res/omega_radiation.png')),
sg.InputText(default_text='0.00009', font=('Tahoma', 12))],
[sg.Image(os.path.normpath('res/z.png')),
sg.InputText(default_text='3', font=('Tahoma', 12))],
[sg.Image(os.path.normpath('res/w_lambda.png')),
sg.InputText(default_text='-1', font=('Tahoma', 12))]],
title='Cosmological Parameters', font=('Georgia', 14))],
[sg.Submit(button_color='blue'),
sg.Exit(button_color='red')]
]
window_input = sg.Window('Cosmic', layout_input)
event, values = window_input.read()
while True:
if event == sg.WIN_CLOSED or event == 'Exit':
break
if event == 'Submit':
H_0, Omega_m, Omega_l, Omega_r, z, w_l = [float(values[i]) for i in range(1, 13, 2)]
# derived parameters
hubble_time = (((1 / H_0) * (3.086e+19)) / (3.154e+7)) / 10**9 # in Gyr
a_emit = 1 / (1 + z)
Omega_k = 1 - (Omega_m + Omega_l + Omega_r)
q_0 = Omega_r + (Omega_m / 2) - Omega_l
hubble_dis = c / H_0 # in Mpc
# calculated parameters
age_of_universe = quad(H, 10**(-16), 1)[0]
age_of_universe_at_z = age_of_universe - quad(H, a_emit, 1)[0]
lookback_time = age_of_universe - age_of_universe_at_z
comoving_distance = quad(H_z, 0, z)[0]
luminosity_distance = (1 + z) * S_k(comoving_distance)
angular_distance = S_k(comoving_distance) / (1 + z)
# plotting distances
distancePlotter()
layout_output = [
[sg.Frame(layout=[
[sg.Text('Age of The Universe Today: {:.4f} Gyr'.format(age_of_universe), font=('Tahoma', 12))],
[sg.Text('Age of The Universe at Redshift {}: {:.4f} Gyr'.format(z, age_of_universe_at_z), font=('Tahoma', 12))],
[sg.Text('Lookback Time: {:.4f} Gyr'.format(lookback_time), font=('Tahoma', 12))],
[sg.Text('Comoving Distance at Redshift {}: {:.4f} Mpc'.format(z, comoving_distance), font=('Tahoma', 12))],
[sg.Text('Angular Diameter Distance at Redshift {}: {:.4f} Mpc'.format(z, angular_distance), font=('Tahoma', 12))],
[sg.Text('Luminosity Distance at Redshift {}: {:.4f} Mpc'.format(z, luminosity_distance),
font=('Tahoma', 12))]], title='Results', font=('Georgia', 14))
]
]
window_output = sg.Window('Cosmic', layout_output)
event, values = window_output.read()
if event == sg.WIN_CLOSED:
window_output.close()