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Age_by_redshift.png (580 × 455 pixels, file size: 45 KB, MIME type: image/png)
Summary
DescriptionAge by redshift.png |
English: The age of the universe since the Big Bang in millions of years for astronomical objects of redshift z=5 through z=20, demarcated by the furthest observation at present, galaxy JADES-GS-z13-0. Please see also S.V. Pilipenko (2013-21) "Paper-and-pencil cosmological calculator" arxiv:1303.5961, for the Fortran-90 code upon which the Python code below for this chart was based. |
Date | |
Source | Own work |
Author | Sandizer |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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Python source code
# Thanks to ChatGPT-4 and the Fortran-90 code from arxiv:1303.5961,
# https://code.google.com/archive/p/cosmonom/downloads
# here's how to get the age of the universe from redshift in Python:
from scipy.special import hyp2f1 # hypergeometric function 2F1 is in integral solution
import matplotlib.pyplot as plt
# Cosmological parameters from the Fortran params.f90 header
#H0 = 67.15 # Hubble constant in km/s/Mpc (or, 73.5: the "crisis in cosmology")
H0 = 69.32 # from Explainxkcd for 2853: Redshift; seems a consensus compromise
#OL = 0.683 # Cosmological constant for dark energy density, Omega_Lambda or _vac
#Om = 0.317 # Density parameter for matter, Omega_mass
Om = 0.286 # From https://arxiv.org/pdf/1406.1718.pdf page 8
OL = 1.0 - Om - 0.4165/(H0**2) # flat curvature, from https://www.astro.ucla.edu/~wright/CC.python
# (on https://www.astro.ucla.edu/~wright/CosmoCalc.html which see)
#print(f"{OL=:.3F}") # 0.714
# Age of universe at redshift z as a closed-form solution to its integral definition,
def age_at_z(z): # ...which is 27 times faster than the original numeric integration
hypergeom = hyp2f1(0.5, 0.5, 1.5, -OL / (Om * (z + 1)**3))
return (2/3) * hypergeom / (Om**0.5 * (z + 1)**1.5) * (977.8 / H0) # 977.8 for Gyr
# Current age of the universe at redshift 0 in Gyr
age0 = age_at_z(0) # 13.78
# Function to calculate the look-back time at redshift z in Gyr
def zt(z): # from the function name in the Fortran cosmonom.f90 code
return age0 - age_at_z(z)
rs = [z * 20 / 299 for z in range(300)] # redshifts 0 to 20 in 300 steps
lb = [zt(z) for z in rs] # look_back_times
fo = 13.2 # furthest observation at present
#print(age_at_z(fo)) # 0.3285
rs = [z * 15 / 299 + 5 for z in range(300)] # redshifts 5 to 20 in 300 steps
ages = [age_at_z(z) * 1000 for z in rs] # Gyr to million years
plt.plot([x for x in rs if x<fo], [y for x,y in zip(rs,ages) if x<fo], color='red')
plt.plot([x for x in rs if x>fo], [y for x,y in zip(rs,ages) if x>fo], color='darkred')
plt.text(13.2, 650, 'Furthest observation as of 2023:\n' +
'the metal-poor JADES-GS-z13-0 galaxy\nat z=13.2: age 329 Myr', ha='center')
plt.title('Age of Universe by Redshift')
plt.xlabel('z: (observed λ - expected λ) / expected λ')
plt.ylabel('Million Years')
plt.xticks(range(5, 21))
plt.yticks(range(0, 1300, 100))
plt.grid(True, color='lightgray')
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['top'].set_visible(False)
plt.savefig('age_by_redshift.png', bbox_inches='tight')
#plt.show() # https://i.ibb.co/C537rxJ/age-by-redshift.png
Captions
The age of the universe for observations by their redshift
Items portrayed in this file
depicts
redshift
age of the universe
Big Bang
creator
some value
author name string: Sandizer
Wikimedia username: Sandizer
copyright status
copyrighted, dedicated to the public domain by copyright holder
copyright license
Creative Commons CC0 License
inception
14 November 2023
media type
image/png
source of file
original creation by uploader
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 01:06, 15 November 2023 | ![]() | 580 × 455 (45 KB) | Sandizer | Uploaded own work with UploadWizard |
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If the file has been modified from its original state, some details may not fully reflect the modified file.
Software used | |
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Horizontal resolution | 39.37 dpc |
Vertical resolution | 39.37 dpc |
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