Validating variational principle for higher order theory of gravity

TL;DR

This paper justifies fixing the Ricci scalar boundary condition in higher order gravity theories using Noether symmetry, impacting the understanding of classical solutions like de-Sitter and anti de-Sitter spaces.

Contribution

It provides a theoretical justification for boundary conditions in higher order gravity theories based on Noether symmetry principles.

Findings

Fixing Ricci scalar at the boundary constrains classical solutions.

Noether symmetry supports the boundary condition choice.

Implications for de-Sitter and anti de-Sitter solutions.

Abstract

Metric variation of higher order theory of gravity requires to fix the Ricci scalar in addition to the metric tensor at the boundary. Fixing Ricci scalar at the boundary implies that the classical solutions are fixed once and forever to the de-Sitter or anti de-Sitter solutions. Here, we justify such requirement from the standpoint of Noether Symmetry.