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With the usual definitions for the entropy and the temperature associated with the apparent horizon, we show that the unified first law on the apparent horizon is equivalent to the Friedmann equation for the scalar--tensor theory with non-minimally derivative coupling. The second law of thermodynamics on the apparent horizon is also satisfied. The results support a deep and fundamental connection between gravitation, thermodynamics, and quantum theory.
We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein
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 diss
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 covaria
We derive the odd parity perturbation equation in scalar-tensor theories with a non minimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of t
For a theory in which a scalar field $phi$ has a nonminimal derivative coupling to the Einstein tensor $G_{mu u}$ of the form $phi,G_{mu u} abla^{mu} abla^{ u} phi$, it is known that there exists a branch of static and spherically-symmetric relativ