Eckart heat-flux applicability in $F(\Phi ,X)R$ theories and the existence of temperature gradients

Abstract

We show that in single--scalar theories of the form $\mathcal{L}=F(\Phi ,X)R+G(\Phi ,X)$, a generic nonminimal coupling $F(\Phi ,X)$ induces, in the scalar--comoving frame, an additional transverse contribution to the effective heat flux, proportional to $(F_X/8\pi F)V_{\perp a}$, where $V_a\equiv h_a{}^c{\nabla }_c{\nabla }_{d}X{u}^d$ and $V_{\perp a}$ denotes the component orthogonal to the 4--acceleration $a_a$. This term cannot in general be written as a spatial temperature gradient, and therefore obstructs a standard Eckart interpretation of the scalar sector for arbitrary timelike scalar configurations. As a result, requiring an Eckart heat flux $q_a=-K(D_a{T}_g+T_g{a}_a)$ for all such configurations is possible if and only if $F_X(\Phi ,X)\equiv 0$, i.e.\ $F(\Phi ,X)=F(\Phi )$, resulting in a theory that is a subclass of Horndeski. Thus, only Jordan--like theories of the type $F(\Phi )R+G(\Phi ,X)$ admit a global Eckart fluid picture of the scalar sector, while models with $F_X\ne 0$ can recover an Eckart--like form only on highly symmetric backgrounds where the transverse contribution vanishes or collapses to a single gradient direction. We also make a brief comment on the existence of temperature gradients $D_a{T}_g$.

10 pages. Matches published version

References in corpus (24)

• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Horndeski theory and beyond: a review
• Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling
• Relativistic cosmology and large-scale structure
• Generalized energy conditions in Extended Theories of Gravity
• Assessing cosmological evidence for non-minimal coupling
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Unveiling the Dynamics of the Universe
• First-order thermodynamics of Horndeski gravity
• Thermodynamics of scalar-tensor gravity
• Considerations on the thermal equilibrium between matter and the cosmic horizon
• First-order thermodynamics of scalar-tensor cosmology
• Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar-tensor gravity
• Extended Theories of Gravity with Generalized Energy Conditions
• Covariant formulation of non-equilibrium thermodynamics in General Relativity
• More on the first-order thermodynamics of scalar-tensor and Horndeski gravity
• Fluid nature constrains Horndeski gravity
• Primordial non-Gaussianity in noncanonical warm inflation
• Past-directed scalar field gradients and scalar-tensor thermodynamics
• Thermal origin of the attractor-to-general-relativity in scalar-tensor gravity
• Constructing black hole entropy from gravitational collapse
• First-order thermodynamics of Horndeski cosmology
• Thermodynamics of the Primordial Universe

Cited by in corpus (1)

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