On higher derivative gravity, c-theorems and cosmology

TL;DR

This paper explores higher derivative gravity theories in 3 and 4 dimensions that support c-theorems, analyzing their implications in AdS/CFT and cosmology, and presenting exact black hole solutions with entropy bounds.

Contribution

It introduces specific higher derivative gravity lagrangians with second order linearized equations around (A)dS spaces, extending c-theorems to cosmological contexts.

Findings

Existence of simple c-theorems in higher derivative gravity models.

Exact asymptotically (A)dS black hole solutions found.

Lower entropy bounds in de Sitter space established.

Abstract

We consider higher derivative gravity lagrangians in 3 and 4 dimensions, which admit simple c-theorems, including upto six derivative curvature invariants. Following a suggestion by Myers, these lagrangians are restricted such that the fluctuations around (anti) de Sitter spaces have second order linearized equations of motion. We study c-theorems both in the context of AdS/CFT and cosmology. In the context of cosmology, the monotonic function is the entropy defined on the apparent horizon through Wald's formula. Exact black hole solutions which are asymptotically (anti) de Sitter are presented. An interesting lower bound for entropy is found in de Sitter space. Some aspects of cosmology in both D=3 and D=4 are discussed.