Observing evolution from steady state

Abstract

The time-translation symmetry of the conformal FLRW frame $\bar{g}=a^{-2}g$ allows reinterpretation of cosmological observation in the static space of a stationary universe, where constant matter density ${\bar{\rho }}_{\text{m}}={\rho }_{\text{m0}}$ induces constant curvature $R_0^{-2}$. A hyperbolic de Sitter solution arises from equipartition of the kinetic energy of recessional and peculiar components of the gravitational field, corresponding to a total density $24R_0^{-2}$ of twice the scalar curvature. This predicts a matter density ${\Omega }_{\text{m}}=\frac{1}{24}$, or a Hubble constant $h=\sqrt{24{\rho }_{\text{m0}}}\approx 0.72$, in agreement with distance-ladder estimates. Projecting the equilibrium state onto the $\Lambda \text{CDM}$ model returns $\hat{h}=\frac{4}{3}\sqrt{12{\rho }_{\text{m0}}}\approx 0.68$ and exact densities ${\hat{\Omega }}_{\text{m}}=1-{\hat{\Omega }}_{\Lambda }=[\text{sinh}(\frac{4}{3}\text{asinh}(1){)}^2+1{]}^{-1}=\mathrm{0.3179...}$, within confidence limits of Planck 2018 results.

5 pages