Derivative-dependent metric transformation and physical degrees of freedom

TL;DR

This paper demonstrates that metric transformations depending on a scalar field and its derivatives do not alter the physical degrees of freedom, provided the transformations are regular and invertible, with implications for various gravitational theories.

Contribution

It provides a Hamiltonian analysis confirming the invariance of degrees of freedom under derivative-dependent metric transformations and extends this to general gravitational theories.

Findings

Degrees of freedom remain unchanged under regular, invertible metric transformations.

Transformation and gauge fixing commute in the analyzed models.

Implications for hidden constraints and mimetic gravity are discussed.

Abstract

We study metric transformations which depend on a scalar field $\phi$ and its first derivatives and confirm that the number of physical degrees of freedom does not change under such transformations, as long as they are not singular. We perform a Hamiltonian analysis of a simple model in the gauge $\phi = t$. In addition, we explicitly show that the transformation and the gauge fixing do commute in transforming the action. We then extend the analysis to more general gravitational theories and transformations in general gauges. We verify that the set of all constraints and the constraint algebra are left unchanged by such transformations and conclude that the number of degrees of freedom is not modified by a regular and invertible generic transformation among two metrics. We also discuss the implications on the recently called "hidden" constraints and on the case of a singular transformation, a.k.a. mimetic gravity.