On higher derivative gravity, c-theorems and cosmology

TL;DR

The paper develops higher derivative gravity theories in D=3 and D=4 with up to six curvature invariants, tuned so fluctuations around (A)dS are governed by second-order EOM and admit simple $c$-theorems in both AdS/CFT and cosmology. In D=3, a New Massive Gravity extension yields a monotone $c(r)$ under NEC and exact black holes with corrected AdS radius, while in D=4, a five-parameter family achieves two-derivative fluctuations around AdS and a subset with exact black holes, plus a de Sitter entropy bound arising from a four-derivative curvature term. Cosmological c-theorems are established via Wald entropy on the apparent horizon, yielding monotonic entropy $s(t)$ under NEC and explicit GB-limit expressions for $s(t)$ and a lower bound on de Sitter entropy $s_0$, linking horizon thermodynamics to holographic notions. The work provides a controlled, nonperturbative framework to probe higher-derivative corrections, holographic transport, entanglement interpretations, and horizon thermodynamics with potential extensions to other dimensions and dynamical backgrounds.

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.