We study first-order scalar and tensor perturbations of Jordan-frame scalar-tensor gravity about a spatially flat Friedmann-Lemaître-Robertson-Walker (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.

Close

PrevNext

View figure in article

• Alternative gravity theories
• Fluids & classical fields in curved spacetime
• Gravitation
• Nonequilibrium & irreversible thermodynamics