Cosmological and black hole brane-world Universes in higher derivative gravity

TL;DR

The paper analyzes a multidimensional higher-derivative gravity model with $R^2$ terms, including the nonzero $c$-term $R_{  }$, to construct and study brane-world cosmologies, black-hole thermodynamics, and de Sitter configurations. It derives generalized FRW dynamics on the brane, formulates boundary terms to render the action finite, and computes BH thermodynamics perturbatively in $c$, revealing that $c eq0$ breaks conformal invariance of the dual QFT and decouples the holographic (Hubble) entropy from the BH entropy. The work also explores asymmetrically warped spacetimes, Lorentz-violating effects on the brane, and branes in de Sitter space, along with the dS/CFT conformal anomaly, highlighting substantial deviations from standard AdS/CFT expectations due to higher-derivative corrections. Overall, the results show that the Riemann-squared term crucially modifies brane cosmology, holographic relations, and potential non-CFT holographic duals in higher-derivative gravity scenarios.

Abstract

General model of multidimensional $R^2$-gravity including Riemann tensor square term (non-zero $c$ case) is considered. The number of brane-worlds in such model is constructed (mainly in five dimensions) and their properties are discussed. Thermodynamics of S-AdS BH (with boundary) is presented when perturbation on $c$ is used. The entropy, free energy and energy are calculated. For non-zero $c$ the entropy (energy) is not proportional to the area (mass). The equation of motion of brane in BH background is presented as FRW equation. Using dual CFT description it is shown that dual field theory is not conformal one when $c$ is not zero. In this case the holographic entropy does not coincide with BH entropy (they coincide for Einstein gravity or $c=0$ HD gravity where AdS/CFT description is well applied). Asymmetrically warped background (analog of charged AdS BH) where Lorentz invariance violation occurs is found. The cosmological 4d dS brane connecting two dS bulk spaces is formulated in terms of parameters of $R^2$-gravity. Within proposed dS/CFT correspondence the holographic conformal anomaly from five-dimensional higher derivative gravity in de Sitter background is evaluated.