Thermodynamic properties of modified gravity theories

We review thermodynamic properties of modified gravity theories such as $F(R)$ gravity and $f(T)$ gravity, where $R$ is the scalar curvature and $T$ is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in $f(T)$ gravity. We show both equilibrium and non-equilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it.Comment: 27 pages, no figure, version accepted for publication in International Journal of Geometric Methods in Modern Physic

Inflationary cosmology in modified gravity theories

We review inflationary cosmology in modified gravity such as $R^2$ gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the $R^2$ term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of scalar modes of the density perturbations and the tensor-to-scalar ratio can be consistent with the Planck results. Bounce cosmology in $F(R)$ gravity is also explained.Comment: 24 pages, no figure, invited review to appear in Symmetr

Kaluza-Klein reduction and Bergmann-Wagoner bi-scalar general action of scalar-tensor gravity

We examine the Kaluza-Klein (KK) dimensional reduction from higher-dimensional space-time and the properties of the resultant Bergmann-Wagoner general action of scalar-tensor theories. With the analysis of the perturbations, we also investigate the stability of the anti-de Sitter (AdS) space-time in the $D\in\mathcal{N}$-dimensional Einstein gravity with the negative cosmological constant. Furthermore, we derive the conditions for the dimensional reduction to successfully be executed and present the KK compactification mechanism.Comment: 18 pages, no figure, version accepted for publication in International Journal of Geometric Methods in Modern Physic