Generalized second law of thermodynamics in scalar-tensor gravity

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.Comment: 27 pages, 5 figure

Resurrecting the Power-law, Intermediate, and Logamediate Inflations in the DBI Scenario with Constant Sound Speed

We investigate the power-law, intermediate, and logamediate inflationary models in the framework of DBI non-canonical scalar field with constant sound speed. In the DBI setting, we first represent the power spectrum of both scalar density and tensor gravitational perturbations. Then, we derive different inflationary observables including the scalar spectral index $n_s$, the running of the scalar spectral index $dn_s/d\ln k$, and the tensor-to-scalar ratio $r$. We show that the 95\% CL constraint of the Planck 2015 T+E data on the non-Gaussianity parameter $f_{{\rm NL}}^{{\rm DBI}}$ leads to the sound speed bound $c_{s}\geq0.087$ in the DBI inflation. Moreover, our results imply that, although the predictions of the power-law, intermediate, and logamediate inflations in the standard canonical framework ($c_s=1$) are not consistent with the Planck 2015 data, in the DBI scenario with constant sound speed $c_s<1$, the result of the $r-n_s$ diagram for these models can lie inside the 68\% CL region favored by the Planck 2015 TT,TE,EE+lowP data. We also specify the parameter space of the power-law, intermediate, and logamediate inflations for which our models are compatible with the 68\% or 95\% CL regions of the Planck 2015 TT,TE,EE+lowP data. Using the allowed ranges of the parameter space of the intermediate and logamediate inflationary models, we estimate the running of the scalar spectral index and find that it is compatible with the 95\% CL constraint from the Planck 2015 TT,TE,EE+lowP data.Comment: 18 pages, 6 figure