Abstract
We study metric transformations which depend on a scalar field 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 unitary gauge. 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 for the recently called “hidden” constraints and for the case of a singular transformation, also known as mimetic gravity.
Guillem Domènech
Researcher in gravity and cosmology
I am an Emmy Noether Research Group Leader at the Insitute for Theoretical Physics at the Leibniz University Hannover. My research focuses in various aspects of cosmology, gravity and particle physics.