Late-time dark energy and Hubble tension

Abstract

Abstract We extend Einstein’s theory of general relativity by introducing stochastic elements in addition to the usual fields and apply it to explore late-time redshift. The stochastic perturbation of spacetime enforces an effective minimum length (ML) to give us a cosmological constant naturally derived from the diffusive nature of spacetime and a redshift driven by both the geometry of spacetime as well as its diffusive nature. In this new theory, “dark energy” is the manifestation of fundamental uncertainty caused by ML of spacetime. The new theory converges to the minimal Λ \Lambda CDM model in the era after the Big Bang, when the geometry dominates over the diffusive character of spacetime. However, as the Hubble parameter decreases in value over time, there is a period during which the diffusive effects play an increasingly important role. For later times, as the universe approaches its minimum total energy density, the resulting redshift obtains significant contributions from both the geometry, captured by the Hubble parameter “ H H ,” and spacetime diffusion, captured by a new parameter “ D D ,” the diffusive equivalent to H H . Hence, the new theory presented here is particularly important during the later times in which H H diminishes and becomes comparable to D D . The theory suggests that the Hubble tension might be relieved by the diffusive character of spacetime. In order to compare the early time Hubble parameter estimates to the late-time estimates, we must recognize the contribution diffusion makes to the redshift observations and further reformulate luminosity distance and its kinematic expression to account for the effects of diffusion in addition to geometry. We perform a simple analysis of Type Ia supernovae observations with distances calibrated using Cepheids to obtain estimates for the new diffusion parameter. Based on these results, the new theory places the universe well inside a vacuum-dominated regime with a small and diminishing diffusion parameter.