Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

TL;DR

This paper reviews and unifies various modified gravity theories, demonstrating their potential to describe the entire cosmic history from inflation to dark energy, and explores their cosmological reconstruction and singularity issues.

Contribution

It provides a comprehensive analysis of multiple modified gravity models, their relations, and their capability to unify early and late-time cosmic acceleration.

Findings

Some models are consistent with local tests.

Unified description of inflation and dark energy is possible.

Singularities can be cured with higher-derivative invariants.

Abstract

Classical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosmological properties of number of modified theories, including traditional $F(R)$ and Ho\v{r}ava-Lifshitz $F(R)$ gravity, scalar-tensor theory, string-inspired and Gauss-Bonnet theory, non-local gravity, non-minimally coupled models, and power-counting renormalizable covariant gravity are discussed. Different representations and relations between such theories are investigated. It is shown that some versions of above theories may be consistent with local tests and may provide qualitatively reasonable unified description of inflation with dark energy epoch. The cosmological reconstruction of different modified gravities is made in great detail. It is demonstrated that eventually any given universe evolution may be reconstructed for the theories under consideration: the explicit reconstruction is applied to accelerating spatially-flat FRW universe. Special attention is paid to Lagrange multiplier constrained and conventional $F(R)$ gravities, for last theory the effective $\Lambda$CDM era and phantom-divide crossing acceleration are obtained. The occurrence of Big Rip and other finite-time future singularities in modified gravity is reviewed as well as its curing via the addition of higher-derivative gravitational invariants.