More on the first-order thermodynamics of scalar-tensor and Horndeski gravity

Abstract

Two issues in the first-order thermodynamics of scalar-tensor (including "viable" Horndeski) gravity are elucidated. The application of this new formalism to FLRW cosmology is shown to be fully legitimate and then extended to all Bianchi universes. It is shown that the formalism holds thanks to the almost miraculous fact that the constitutive relations of Eckart's thermodynamics are satisfied, while writing the field equations as effective Einstein equations with an effective dissipative fluid does not contain new physics.

First-order thermodynamics of scalar-tensor cosmology

“…These results spurred some further developments, such as the considerations in [25] that pave the way for extending the study of first-order thermodynamics of Horndeski gravity to FLRW and Bianchi universes. The imperfect fluid analogy developed for this class of theories has also been exploited with the goal of attempting to classify Horndeski theories based on the nature of the effective fluid, specifically on its requirement to be a Newtonian fluid [20].…”

“…Note that the decomposition in (7) applies to any symmetric second-order tensor, although of course the dissipative quantities would vanish if the effective stress-energy tensor for the theory at hand takes the form of a perfect fluid (see Section 4.1 for more details). The special feature of scalar-tensor gravity in first-order thermodynamics is not that the decomposition above can be performed, but rather that the constitutive relations of Eckart's thermodynamics hold [25].…”

Hydrodynamics of (1+1) dimensional fluid in the presence of gravitational anomaly from first order thermodynamics

“…Using more sophisticated models such as those due to Israel and Stewart [19], in the future may provide a clearer picture and this is one of the possible future directions. Like the other applications of Eckart's formalism in different gravitational theories [22][23][24][25][26][27][28][29][30][31][32][33], here we define the four-velocity of the fluid as covariant derivative of the auxiliary scalar field which describes the local form of the effective action, namely the Polyakov action [4]. Only the anomalous part of the EMT of the fluid has been considered.…”

“…Further, although there exist more sophisticated models like the Israel-Stewart formalism [19] at second order in the perturbations, computing and comparing the dissipative perturbations in such models are more intensive, and require solving additional dynamical equations for the perturbations. In the same spirit, such an approach has been widely applied to the recent study of scalar fluids in various gravitational theories, like scalar-tensor theory of gravity [22][23][24][25][26][27][28][29][30][31], Horndeski gravity [30,32,33]. In these analyses, the fluid four-velocity have been described through the covariant derivative of the scalar field of the theory.…”