Generalised Boundary Terms for Higher Derivative Theories of Gravity

TL;DR

This paper derives generalized boundary terms for the most comprehensive quadratic curvature gravity theories using Coframe slicing and ADM decomposition, and explores boundary terms for covariant infinite derivative gravity to ensure ghost-free conditions.

Contribution

It introduces a method to find boundary terms for general quadratic curvature gravity and extends this to covariant infinite derivative theories, ensuring ghost-free conditions.

Findings

Derived boundary terms for quadratic curvature gravity.

Extended boundary term formulation to infinite derivative gravity.

Ensured ghost and tachyon freedom at perturbative level.

Abstract

In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.