Cosmological consequences and thermodynamics of modified gravity with extended nonminimal derivative couplings

Abstract

We consider the newly proposed gravitational modifications that go beyond Horndeski’s theory, named as theories with extended nonminimal derivative couplings. By these modifications, the coefficient functions depend on the scalar field and its kinetic energy. These theories become ghost-free in cosmological background. We consider the flat FRW universe and explore the equation-of-state parameter, [Formula: see text]–[Formula: see text] plane and the squared speed of sound. The equation-of-state parameter exhibits phantom behavior of the universe, [Formula: see text]–[Formula: see text] plane represents the freezing region of the universe while the squared speed of sound denotes the stability of the model for the specific choice of constant parameters. Also, we investigate the validity of generalized second law of thermodynamics on the Hubble horizon taking into account the Bekenstein, power-law, Renyi and logarithmic corrections to the horizon entropy.