No Arabic abstract
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({cal R})$ gravity as a non-equilibrium one. We apply Eckarts first order thermodynamics to the effective dissipative fluid describing scalar-tensor gravity. Surprisingly, we obtain simple expressions for the effective heat flux, temperature of gravity, shear and bulk viscosity, and entropy density, plus a generalized Fourier law in a consistent Eckart thermodynamical picture. Well-defined notions of temperature and approach to equilibrium, missing in the current thermodynamics of spacetime scenarios, naturally emerge.
Within the context of scalar-tensor gravity, we explore the generalized second law (GSL) of gravitational thermodynamics. We extend the action of ordinary scalar-tensor gravity theory to the case in which there is a non-minimal coupling between the scalar field and the matter field (as chameleon field). Then, we derive the field equations governing the gravity and the scalar field. For a FRW universe filled only with ordinary matter, we obtain the modified Friedmann equations as well as the evolution equation of the scalar field. Furthermore, we assume the boundary of the universe to be enclosed by the dynamical apparent horizon which is in thermal equilibrium with the Hawking temperature. We obtain a general expression for the GSL of thermodynamics in the scalar-tensor gravity model. For some viable scalar-tensor models, we first obtain the evolutionary behaviors of the matter density, the scale factor, the Hubble parameter, the scalar field, the deceleration parameter as well as the effective equation of state (EoS) parameter. We conclude that in most of the models, the deceleration parameter approaches a de Sitter regime at late times, as expected. Also the effective EoS parameter acts like the LCDM model at late times. Finally, we examine the validity of the GSL for the selected models.
A class of scalar-tensor theories (STT) including a non-metricity that unifies metric, Palatini and hybrid metric-Palatini gravitational actions with non-minimal interaction is proposed and investigated from the point of view of their consistency with generalized conformal transformations. It is shown that every such theory can be represented on-shell by a purely metric STT possessing the same solutions for a metric and a scalar field. A set of generalized invariants is also proposed. This extends the formalism previously introduced in cite{kozak2019}. We then apply the formalism to Starobinsky model, write down the Friedmann equations for three possible cases: metric, Palatini and hybrid metric-Palatini, and compare some inflationary observables.
We investigate the correspondence between generally covariant higher derivative scalar-tensor theory and spatially covariant gravity theory. The building blocks are the scalar field and spacetime curvature tensor together with their generally covariant derivatives for the former, and the spatially covariant geometric quantities together with their spatially covariant derivatives for the later. In the case of a single scalar degree of freedom, they are transformed to each other by gauge fixing and recovering procedures, of which we give the explicit expressions. We make a systematic classification of all the scalar monomials in the spatially covariant gravity according to the total number of derivatives up to $d=4$, and their correspondence to the scalar-tensor monomials. We discusse the possibility of using spatially covariant monomials to generate ghostfree higher derivative scalar-tensor theories. We also derive the covariant 3+1 decomposition without fixing any specific coordinate, which will be useful when performing a covariant Hamiltonian analysis.
In this letter we investigate gauge invariant scalar fluctuations of the metric in a non-perturbative formalism for a Higgs inflationary model recently introduced in the framework of a geometrical scalar-tensor theory of gravity. In this scenario the Higgs inflaton field has its origin in the Weyl scalar field of the background geometry. We found a nearly scale invariance of the power spectrum for linear scalar fluctuations of the metric. For certain parameters of the model we obtain values for the scalar spectral index $n_s$ and the scalar to tensor ratio $r$ that fit well with the Planck 2018 results. Besides we show that in this model the trans-planckian problem can be avoided.
We extend to the Horndeski realm the irreversible thermodynamics description of gravity previously studied in first generation scalar-tensor theories. We identify a subclass of Horndeski theories as an out-of--equilibrium state, while general relativity corresponds to an equilibrium state. In this context, we identify an effective heat current, temperature of gravity, and shear viscosity in the space of theories. The identification is accomplished by recasting the field equations as effective Einstein equations with an effective dissipative fluid, with Einstein gravity as the equilibrium state, following Eckarts first-order thermodynamics.