Canonical formulation of scalar curvature squared action in higher dimensions

TL;DR

This paper develops a canonical formulation for scalar curvature squared actions in higher dimensions, showing quantum dynamics similar to four-dimensional cases and confirming classical solutions align with Starobinsky's model.

Contribution

It extends the canonical formulation of $R^2$ gravity to arbitrary dimensions and analyzes quantum and classical solutions in maximally symmetric space-times.

Findings

Quantum dynamics in higher dimensions resembles four-dimensional case.

Classical solutions match Starobinsky's model.

WKB approximation peaks around classical solutions.

Abstract

Canonical formulation for an action containing scalar curvature squared term $(R^2)$ in arbitrary dimension has been performed in maximally symmetric space-time. The quantum dynamics does not alter significantly from the same in $4$-dimension. Classical solution is also at par with the one presented by Starobinsky. WKB approximation peaks around the classical solution.