Tests of standard cosmology in Hořava gravity, Bayesian evidence for a closed universe, and the Hubble tension

Abstract

Abstract We consider some background tests of standard cosmology in the context of Hořava gravity with different scaling dimensions for space and time, which has been proposed as a renormalizable, higher-derivative, Lorentz-violating quantum gravity model without ghost problems. We obtain the “very strong” and “strong” Bayesian evidences for our two cosmology models A and B, respectively, depending on the choice of parametrization based on Hořava gravity, against the standard, spatially-flat, LCDM cosmology model based on general relativity. An MCMC analysis with the observational data, including BAO, shows (a) preference of a closed universe with the curvature density parameter $$\Omega _k=-0.005\pm 0.001$$ Ω k = - 0.005 ± 0.001 , $$-0.004^{+0.003}_{-0.001}$$ - 0 . 004 - 0.001 + 0.003 , (b) reduction of the Hubble tension with the Hubble constant $$H_0=71.4^{+1.2}_{-0.9}$$ H 0 = 71 . 4 - 0.9 + 1.2 , $$69.5^{+1.6}_{-0.9}~ \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$$ 69 . 5 - 0.9 + 1.6 km s - 1 Mpc - 1 for the models A, B, respectively, and also (c) a positive result on the discordance problem. We comment on some possible further improvements for the “cosmic-tension problem” by considering the more complete early-universe physics, based on the Lorentz-violating standard model with anisotropic space-time scaling, consistently with Hořava gravity, as well as the observational data which are properly adopted for the closed universe.