Homogeneity and isotropy reduce gravitational expansion to two balances.
Key knowledge
For a homogeneous isotropic perfect-fluid universe, H = ȧ/a, H² = 8πGρ_tot/3 − kc²/a² and ä/a = −4πG(ρ_tot + 3p_tot/c²)/3, with ρ_tot a mass-equivalent density.
Cosmic proper time, scale factor a > 0 in length units and normalized k = −1,0,+1.
Total density and pressure include any vacuum component; no additional Λ term is added here. Local inhomogeneity and quantum regimes require other treatment.
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For a homogeneous isotropic perfect-fluid universe, H = ȧ/a, H² = 8πGρ_tot/3 − kc²/a² and ä/a = −4πG(ρ_tot + 3p_tot/c²)/3, with ρ_tot a mass-equivalent density.
Homogeneous isotropic perfect-fluid specialization; vacuum included in total density/pressure here rather than double-counted as an extra term.
In an FLRW expansion model, light emitted and observed by comoving observers is stretched by the ratio of their scale factors. A spectral redshift therefore connects emission epoch to expansion history. Local peculiar motion and gravitational effects can also contribute to an observed redshift.
Matter, curvature and energy determine the chosen expansion history.
In an expanding FLRW model with present scale factor one, the line-of-sight comoving distance is D_C=c∫₀ᶻ dz′/H(z′), and the lookback time is t_L=∫₀ᶻ dz′/[(1+z′)H(z′)]. Spatial curvature converts D_C to transverse comoving distance D_M through a sine, identity or hyperbolic sine. These definitions refer to different geometric or temporal observables.
For small sub-Hubble-scale perturbations of pressureless matter in a homogeneous expanding background, the Newtonian growing-density model obeys δ̈+2Hδ̇−4πGρ̄_mδ=0. Gravity drives growth while expansion affects it through H. In an Einstein–de Sitter matter-only flat model, independent solutions are δ∝a and δ∝a⁻³ᐟ²; a general background requires its own growth solution.
The consistent background expansion and density determine the growth coefficients.
In hot Big-Bang nucleosynthesis, neutron–proton conversion initially approaches chemical equilibrium. As its interaction rate Γ becomes too slow relative to expansion H, equilibrium tracking fails. Free neutrons subsequently decay until incorporated into nuclei. Deuterium formation is delayed by photodissociation from the high-energy photon tail; having k_BT below its binding energy alone is insufficient when photons greatly outnumber baryons. Once the bottleneck eases, a reaction network assembles light nuclei; later dilution and cooling limit further processing.
The cosmological background supplies the expansion rate.
For an independently conserved homogeneous component with constant equation-of-state w, density scales with a as a^-3(1+w). Here density is mass-equivalent density, so pressure appears divided by c², matching the Ark's existing Friedmann convention.
Conceptual association supported by the recorded research scope; this relation does not assert a proven derivation or mandatory prerequisite.