Cosmological reconstruction of realistic modified F(R) gravities

TL;DR

This paper develops a method to reconstruct modified F(R) gravity models that can produce any desired cosmological evolution, including well-known scenarios like Lambda-CDM, and explores their unification of inflation and dark energy.

Contribution

The authors introduce a reconstruction scheme for F(R) gravity based on e-folding, enabling the derivation of models for arbitrary cosmologies, including scalar field extensions.

Findings

Reconstructed F(R) models for Lambda-CDM and other cosmologies.

Proposed unification of inflation and dark energy within F(R) gravity.

Showed how to incorporate scalar fields into the reconstruction scheme.

Abstract

The cosmological reconstruction scheme for modified $F(R)$ gravity is developed in terms of e-folding (or, redshift). It is demonstrated how any FRW cosmology may emerge from specific $F(R)$ theory. The specific examples of well-known cosmological evolution are reconstructed, including $\Lambda$CDM cosmology, deceleration with transition to phantom superacceleration era which may develop singularity or be transient. The application of this scheme to viable $F(R)$ gravities unifying inflation with dark energy era is proposed. The additional reconstruction of such models leads to non-leading gravitational correction mainly relevant at the early/late universe and helping to pass the cosmological bounds (if necessary). It is also shown how cosmological reconstruction scheme may be generalized in the presence of scalar field.