Tests of Standard Cosmology in Horava Gravity and Bayesian Evidence for
  a Closed Universe without the Hubble Tension
  We consider some background tests of standard cosmology in the context of
Horava 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 evidence for our two cosmology models A and B, respectively, depending
on the choice of parametrization based on Horava gravity, against the standard,
spatially-flat, LCDM cosmology model based on general relativity. An MCMC
analysis with observational data, including BAO, shows (a) preference of a
"closed" universe with the curvature density parameter Omega_k=-0.005+- 0.0007,
-0.004+0.003-0.001 and (b) reduction of the Hubble tension with the Hubble
constant H_0=71.4+1.2-0.9, 69.5+1.6-0.9 km s^{-1} Mpc^{-1} for the models A, B.
We comment on some possible further improvements for the "cosmic-tension
problem" by considering more complete early universe physics, based on the
Lorentz-violating standard model with anisotropic space-time scaling,
consistently with Horava gravity, as well as the observational data which are
properly adopted for the closed universe.
