- The cosmic quantities were calculated with the fiducial values:
- Hubble constant fiducial value 70 (km/s)/Mpc
- Ω_matter = 0.3: i.e., the density parameter Ω due to matter: both baryonic matter and dark matter. This is just a round number. Note Planck 2018, p. 14,15 Plik Ω_matter = 0.3153(73).
- Ω_Λ = 0.7: i.e., the density parameter Ω due to the cosmological constant Λ or equivalently dark energy. Note Planck 2018, p. 15 Plik Ω_Λ = 0.6847(73).
- Ω_radiation = 9.0606*10**(-5):
i.e., the
density parameter Ω
due to the
cosmic background radiation (CBR)
plus cosmic neutrinos
which were extreme relativistic particles,
and so acted like
electromagnetic radiation (EMR)
during the
radiation era
(cosmic time ∼ 0--178.5 kyr).
The value is from
Cahill (2017, p. 3,5 based
on
cosmic microwave background temperature T = 2.72548(57) K (Fixsen 2009).
**UNDER CONSTRUCTION BELOW** - The number density
hydrogen atoms
is 1.898*10**(-7) 1/cm**3.
This is a fiducial value
derived from the assuming the
critical density = 3H_0**2/(8πG) = (9.20387*10**(-27))*h_70**2 kg/m**3 = (1.35989*10**11)*h_70**2 M_☉/Mpc**3
with fiducial value h_70=1
(which close to most universal density estimates: e.g.,
Wikipedia: Λ-CDM model: Parameters),
Planck 2018, p. 14,15 Plik Ω_baryonic matter = 0.02237/(H_0/100),
and cosmic mass fraction
of hydrogen 0.75.

- The cosmic scale factor a(t).
was calculated using nearly exact
a(t) formula
for the Λ-CDM model given by
Galanti & Roncadelli 2021.
Their formula is exact for the
a "radiation"-matter universe and a matter-Λ universe.
The two exact branches are joined in the
"radiation"-Λ equality time 0.5899 Gyr
where both radiation and Λ
make nearly negligible to the
mass-energy
content of the observable universe.
- The
radiation era
(cosmic time ∼ 0--178.5 kyr) is when
"radiation" (i.e., photons plus all other
extreme relativistic particles) dominates
the mass-energy
evolution of the observable universe.
The time zero for radiation era
is formally the
Big Bang singularity and is really as early
as we believe we can extrapolate known cosmology.
The end of the
radiation era
is here chosen
**NOT**be "radiation"-matter equality time

Caption: The evolution of the cosmic quantities for the Λ-CDM model: cosmic scale factor a(t), cosmic background radiation (CBR) temperature, cosmic LTE hydrogen ionization (assuming pure atomic hydrogen gas.

You need to click on the image to see it in its entirety.

The cosmic time of evolution is from well after the Big Bang nucleosynthesis (cosmic time ∼ 10--1200 s ≅ 0.17--20 m) and starting well into the radiation era (cosmic time ∼ 0--178.5 kyr).

Features:

Image link: Itself.

Local file: local link: cosmic_scale_factor_lambda_cdm.html.

File: Cosmology file: cosmic_scale_factor_lambda_cdm.html.