A derived evolution of dark energy from cosmic inhomogeneity confronted with baryon acoustic oscillations and type Ia supernovae

Abstract

The volume dynamics of space is a framework in which the possibility that matter can be unevenly distributed enters the expansion dynamics directly. It yields a redshift-dependent effective Hubble constant and dark-energy density parameter from the Planck parameters alone. We derive the expansion history $H(z)$ that the framework implies and show that it is flat $\Lambda$CDM with the cosmological constant replaced by a dark-energy density that grows by 31 percent toward the present, with an effective equation of state $w(0) = -1.21$ approaching $-1$ at high redshift and a present-day age of 13.52 Gyr, 0.30 Gyr younger than in the homogeneous limit. We confront it with the DESI DR2 baryon acoustic oscillations and the Pantheon+ type Ia supernovae, with the Hubble constant, the sound horizon and the supernova absolute magnitude free, so that only the shape of $H(z)$ is tested. Relative to $\Lambda$CDM the prediction is disfavored by $\Delta\chi^2 = 65$ with one parameter fewer. A free matter density reduces this to $\Delta\chi^2 = 42$, because each probe alone accommodates the model only with incompatible matter densities (0.35 from the oscillations, 0.54 from the supernovae). Their combination bounds the heterogeneity amplitude to $\sigma_8<0.14$ at 95 percent confidence, against the Planck value 0.81 that enters the derivation; the best fit of the heterogeneous model is its homogeneous limit, flat $\Lambda$CDM. At the leading order in which it is currently evaluated, the heterogeneous contribution therefore cannot account for the Hubble tension, and it acts opposite to the evolution of dark energy that current distance data favor.