A reconstruction method for anisotropic universes in unimodular $F(R)$-gravity

TL;DR

This paper develops a reconstruction method within unimodular $F(R)$ gravity to model anisotropic universe evolutions, providing explicit examples including de Sitter spacetime for early and late universe epochs.

Contribution

It introduces a novel reconstruction approach for anisotropic universes in unimodular $F(R)$ gravity, addressing metric compatibility and demonstrating explicit solutions.

Findings

Reconstruction method for anisotropic universe evolution in unimodular $F(R)$ gravity.

Explicit examples including de Sitter spacetime for different universe epochs.

Framework accommodates early- and late-time cosmological scenarios.

Abstract

An extension of unimodular Einsteinian gravity in the context of $F(R)$ gravities is used to construct a class of anisotropic evolution scenarios. In unimodular GR the determinant of the metric is constrained to be a fixed number or a function. However, the metric of a generic anisotropic universe is not compatible with the unimodular constraint, so that a redefinition of the metric, to properly take into account the constraint, need be performed. The unimodular constraint is imposed on $F(R)$ gravity in the Jordan frame by means of a Lagrangian multiplier, to get the equations of motion. The resulting equations can be viewed as a reconstruction method, which allows to determine what function of the Ricci scalar can realize the desired evolution. For the sake of clarity, some characteristic examples are invoked to show how this reconstruction method works explicitly. The de Sitter spacetime here considered, in the context of unimodular $F(R)$ gravity, is suitable to describe both the early- and late-time epochs of the universe history.