Finsleroid Corrects Pressure and Energy of Universe. Respective Cosmological Equations

TL;DR

This paper introduces a Finslerian extension to cosmological models, deriving new equations that relate pressure and energy density to a deviation parameter, potentially explaining cosmic acceleration without negative pressure.

Contribution

It provides a covariantly conserved pseudo-Finsleroid gravitational tensor and extends Friedmann metrics within Finsler geometry, linking the Hubble constant to Finslerian parameters.

Findings

Cosmological pressure and energy density are linear in g^2.

Negative pressure may not be necessary for cosmic acceleration.

Finslerian deviation parameter g influences universe's curvature and dynamics.

Abstract

The Hubble constant proves to be the pseudo-Finsleroid--Landsberg factor. The covariantly conserved pseudo-Finsleroid--gravitational tensor is explicitly found after evaluating the respective Finsleroid--case curvature tensor and required contractions in attentive way. The equations arisen involve one parameter g of extension which measures the Finslerian deviation of the curvature of the indicatrix of unit vectors. The vector field b^i(x) of the axes of the pseudo--Finsleroids is naturally identified to the field of average velocity vectors of matter of the universe. The consistent (and unique) continuation of the Robertson--Walker metric, and hence the Friedmann metrics, in the Finslerian domain with respect to the parameter g is arisen. The cosmological pressure and energy density prove to be linear functions of g^2, so that the presence of the negative pressure seems to be not necessary to get the agreement with the observed negative nature of deceleration parameter. We clarify the explicit structure of all the involved tensorial objects.