Abstract:
This thesis explores the existence of higher-derivative theories beyond the Lanczos-Lovelock models of gravity which are ghost-free in arbitrary backgrounds by having a second-order equation of motion (which we shall refer to as ‘Lovelockian’). First, we review the instabilities associated with generic higher-derivative theories of gravity and show that the Lanczos- Lovelock models constitute the unique class of theories with polynomial contractions of the curvature tensor with a second-order equation of motion. Next, we investigate the case of Abelian gauge fields non-minimally coupled to gravity and demonstrate that there exists theories at arbitrary order in derivatives (and arbitrary form degree of the Abelian gauge field) which are Lovelockian. Furthermore, we analyze the flat-space expansion of theories involving covariant derivatives of the curvature tensor, thereby providing justification for a key assumption underlying an important result in the field. We conclude with a brief overview of the recently proposed Generalized Quasi-Topological theories of gravity – which propagate just the graviton mode in maximally symmetric backgrounds and discuss some of the remarkable properties of these theories.
