Modified gravity: walk through accelerating cosmology

Abstract

We review the accelerating (mainly, dark energy) cosmologies in modified gravity. Special attention is paid to cosmologies leading to finite-time future singularities in $F(R)$, $F(G)$ and $\mathcal{F}(R,G)$ modified gravities. The removal of the finite-time future singularities via addition of $R^2$-term which simultaneously unifies the early-time inflation with late-time acceleration is also briefly mentioned. Accelerating cosmology including the scenario unifying inflation with dark energy is considered in $F(R)$ gravity with Lagrange multipliers. In addition, we examine domain wall solutions in $F(R)$ gravity. Furthermore, covariant higher derivative gravity with scalar projectors is explored.

16 pages, no figure, to appear in: Proceedings of the 7th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physics (Sept. 9--19, 2012, Belgrade, Serbia). Editors B. Dragovich and Z. Rakic. Published by Institute of Physics, Belgrade 2013, Serbia