On the role of the Parity Violating Hojman--Holst term in Gravity Theories

TL;DR

This paper investigates parity-violating gravity theories involving the Holst term, showing that non-degenerate cases are equivalent to scalar-tensor theories with specific kinetic and potential functions.

Contribution

It generalizes previous results by explicitly deriving the form of the scalar-tensor equivalent for non-degenerate Holst term theories.

Findings

Non-degenerate Hessian implies equivalence to scalar-tensor theories

Explicit form of kinetic coupling and scalar potential derived

On-shell equivalence established for a broad class of theories

Abstract

We study Parity Violating Gravity Theories whose gravitational Lagrangian is a generic function of the scalar curvature and the parity odd curvature pseudoscalar, commonly known as the Holst (or Hojmann) term. Generalizing some previous results in the literature, we explicitly show that if the Hessian of this function is non-degenerate, the initial non-Riemannian Theory is on-shell equivalent to a metric Scalar-Tensor Theory. The generic form of the kinetic coupling function and the scalar potential of the resulting Theory are explicitly found and reported.