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

TL;DR

The paper surveys a broad spectrum of modified gravity theories that could unify early-universe inflation with late-time cosmic acceleration. It develops a cosmological reconstruction framework to realize any prescribed FRW evolution by choosing appropriate functionals of curvature invariants (e.g., F(R), f(G), or non-local terms), and demonstrates explicit pathways to reproduce ΛCDM-like expansion and phantom-divide crossing. It discusses theoretical challenges such as matter instabilities, Newtonian limits, and future singularities, offering strategies like R^2 terms or higher-derivative invariants to cure these issues. The findings highlight the versatility of modified gravity in capturing the full cosmic history, while emphasizing the need for consistency with local tests and the development of perturbation theory to solidify viability and predictive power.

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 Hořava-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 $Λ$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.

Figures (2)

• Figure 1: The qualitative behavior of $\frac{F(R)}{R^2}$ versus $R$ in a viable model.
• Figure 2: Behavior of $t_s^2F(\tilde{R})$ as a function of $\tilde{R}$ for $\gamma =1/2$, $\tilde{p}_+ =-1/t_s^{\beta_+}$, $\tilde{p}_- =0$, $\beta_+ = \left(1+2\sqrt{19}\right)/2$ and $t_s =2t_0$.