Caption: The evolution of the cosmic quantities for the Λ-CDM model: cosmic scale factor a(t), cosmic temperature (in electron-volts (eV): 1 eV ≅ 10**4 K), and cosmic LTE hydrogen ionization (assuming pure atomic hydrogen gas).

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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 (inflation end 10**(-32) s ? -- 51.7(8) kyr).

Features:

1. The cosmic quantities were calculated with the fiducial values:
   1. Hubble constant fiducial value 70 (km/s)/Mpc
   2. 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).
   3. 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).
   4. 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

   5. 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.

2. 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.

3. 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