Fractional Einstein-Hilbert Action Cosmology

TL;DR

This paper introduces a novel fractional variational principle-based cosmological model that maintains the standard continuity equation and explores solutions where the cosmological term emerges from kinematic effects, aligning closer to observed universe behavior.

Contribution

The paper develops a new fractional cosmological model with a preserved continuity equation and offers exact solutions and interpretations linking the cosmological term to Hubble parameter dynamics.

Findings

Exact solutions for the model are obtained.

The cosmological term can be interpreted as arising from kinematic induction.

The model aligns more closely with the universe's observed behavior.

Abstract

We propose a new type of cosmological model derived from the fractional variational principle when it is applied to the gravitational sector of action functional. In contrast to the fractional cosmological model developed earlier by the author from a fractional total action, in our new model the continuity equation remains valid in its usual form. For this model, a lot of exact solutions are obtained from a specific ansatz which is proposed for the cosmological term in this paper. Several examples arising from the given variations of the Hubble parameter with time are provided. Besides, we suggest an original interpretation of the main equations for our model. It supposes that the effective cosmological term could arise as a result of kinematical induction through the non-zero Hubble parameter. With the help of particular example, we demonstrate how this approach could lead our model quite closer to the real behavior of the universe.