Gibbons-Hawking Boundary Terms and Junction Conditions for Higher-Order Brane Gravity Models

TL;DR

This paper derives comprehensive junction conditions for fourth-order brane gravity models involving arbitrary curvature invariants, simplifying them to second order with additional scalar and tensor fields, and applies boundary term methods.

Contribution

It introduces a general method to obtain junction conditions for higher-order brane gravity models using Gibbons-Hawking boundary terms, reducing complexity to second order theories.

Findings

Derived general junction conditions for fourth-order brane gravity.

Reduced higher-order theories to second order with scalaron and tensoron fields.

Provided a framework for studying cosmological implications of these models.

Abstract

We derive the most general junction conditions for the fourth-order brane gravity constructed of arbitrary functions of curvature invariants. We reduce these fourth-order theories to second order theories at the expense of introducing new scalar and tensor fields - the scalaron and the tensoron. In order to obtain junction conditions we apply the method of generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. After assuming the continuity of the scalaron and the tensoron on the brane, we recover junction conditions for such general brane universe models previously obtained by different methods. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.