Requiring stealth Schwarzschild and de Sitter solutions in quadratic/cubic scalar-tensor theories eliminates odd-parity deviations from GR when all solutions are required, while allowing some deviations and non-trivial GW speeds in less restrictive cases.
Derivative-dependent metric transformation and physical degrees of freedom
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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.
fields
gr-qc 2years
2025 2representative citing papers
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