Manifestly Gauge Invariant Perturbations of Scalar-Tensor Theories of Gravity

TL;DR

This paper develops a gauge invariant Hamiltonian approach to study linear perturbations in scalar-tensor theories of gravity, analyzing their evolution in different frames and comparing with standard cosmological perturbation theory.

Contribution

It introduces a manifestly gauge invariant Hamiltonian formalism for scalar-tensor gravity perturbations and explores frame equivalence and consistency with standard methods.

Findings

Perturbation equations in different frames are equivalent under certain conditions.

The formalism reproduces standard cosmological perturbation results.

Provides a new gauge invariant approach for scalar-tensor theories.

Abstract

The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge invariant formalism is used to compute the evolution equations of linear perturbations around a general relativistic spacetime background in the Jordan frame. These equations are then specialized to the case of a flat FRW cosmological background. Furthermore, the equivalence between the Jordan frame and the Einstein frame of STT in the manifestly gauge invariant Hamiltonian formalism is analyzed, and it is shown that also in this framework they can be related by a conformal transformation. Finally, the obtained evolution equations for the linear perturbations in our formalism are compared with those in the standard cosmological perturbation theory. It turns out that the perturbation equations in the two different formalisms coincide with each other in a suitable limit.