Consistency of Higher Derivative Gravity in the Brane Background

TL;DR

This paper explores higher derivative gravity theories in brane-world scenarios, deriving metric solutions and analyzing their consistency with string-inspired actions, including time-dependent dilaton solutions.

Contribution

It provides new solutions for higher derivative gravity in brane backgrounds and demonstrates their consistency with string-inspired effective actions.

Findings

Derived metric solutions for p-brane in higher dimensions.

Showed consistency with string-inspired dilaton Gauss-Bonnet actions.

Presented a time-dependent dilaton solution in fourth-derivative gravity.

Abstract

We consider the theory of higher derivative gravity with non-factorizable Randall-Sundrum type space-time and obtain the metric solutions which characterize the $p$-brane world-volume as a curved or planar defect embedded in the higher dimensions. We consider the string inspired effective actions of the dilatonic Gauss-Bonnet type in the brane background and show its consistency with the RS brane-world scenario and the conformal weight of the dilaton couplings in the string theory with apppropriate choice of Regge slope ($\alpha'$) or Gauss-Bonnet coupling ($\alpha$) or both. We also discuss a time dependent dilaton solution for a string-inspired fourth-derivative gravity.