Variational Principles and Cosmological Models in Higher-Order Gravity

TL;DR

This paper explores higher-order gravity theories in four dimensions, focusing on their variational, conformal, and Hamiltonian structures, and applies these methods to analyze complex cosmological models.

Contribution

It provides a detailed analysis of the variational, conformal, and Hamiltonian formulations of higher-order gravity theories and demonstrates their application to cosmological models.

Findings

Established the variational and conformal structure of higher-order gravity theories.

Analyzed the Hamiltonian formulation and its relation to ADM formalism.

Applied Hamiltonian methods to simplify higher-order cosmological models.

Abstract

This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of those theories. Next, we analyse their Hamiltonian formulation and in particular its relationship with the famous ADM canonical version of general relativity. Finally, we study higher-order spatially homogeneous cosmologies and exemplify how Hamiltonian methods can be utilised to simplify the analysis of the associated field equations.