A Class of Minimally Modified Gravity Theories

TL;DR

This paper analyzes a class of modified gravity theories with actions linear in the lapse function, establishing conditions for reduced degrees of freedom and providing concrete examples with two local physical degrees of freedom.

Contribution

It derives the necessary and sufficient conditions for these theories to have two or fewer local physical degrees of freedom and presents explicit examples.

Findings

Identified conditions for minimal degrees of freedom in modified gravity

Constructed concrete examples with exactly two local degrees of freedom

Enhanced understanding of Hamiltonian structure in such theories

Abstract

We investigate the Hamiltonian structure of a class of gravitational theories whose actions are linear in the lapse function. We derive the necessary and sufficient condition for a theory in this class to have two or less local physical degrees of freedom. As an application we then find several concrete examples of modified gravity theories in which the total number of local physical degrees of freedom in the gravity sector is two.