Thermal channels of scalar and tensor waves in Jordan-frame scalar--tensor gravity

TL;DR

This paper analyzes scalar and tensor perturbations in Jordan-frame scalar-tensor gravity, revealing how effective fluid quantities govern linearized field equations and identifying modifications to gravitational-wave damping.

Contribution

It provides an exact effective-fluid decomposition of perturbations and links gravitational-wave damping to the transverse-traceless anisotropic stress in scalar-tensor gravity.

Findings

Effective density, pressure, heat flux, and anisotropic stress are explicitly identified in the linearized equations.

Jordan-frame modifications to gravitational-wave damping are characterized by the transverse-traceless anisotropic stress.

Flux matching constrains only the background value of $ar{ ext{kappa} T}$, not its perturbation.

Abstract

We study first-order scalar and tensor perturbations of Jordan-frame scalar--tensor gravity about a spatially flat FLRW background using the Einstein-like effective-fluid decomposition of the scalar sector. In the scalar-gradient frame, we derive the perturbed effective density, pressure, heat flux, and anisotropic stress, and show that they admit an exact Eckart-type constitutive identification at linear order. We then show that these same quantities appear explicitly and exhaustively in the linearized field equations: the scalar Hamiltonian, momentum, trace, and traceless Einstein-like equations are governed, respectively, by the effective density, heat-flux, pressure, and anisotropic-stress channels, while the tensor propagation equation is governed by the transverse-traceless anisotropic-stress channel. In particular, the Jordan-frame modification of gravitational-wave damping is identified with the effective transverse-traceless anisotropic stress of the scalar sector. We also derive the perturbed evolution equation for the invariant product $\kappa T$, clarify its gauge behavior, and show that flux matching on FLRW fixes only the background value $\overline{\kappa T}$, not its perturbation. These results leave open the possibility that gravitational waves in scalar--tensor gravity admit a deeper thermodynamic characterization, perhaps even an intrinsic one, although the present analysis establishes this only at the level of an effective constitutive description.