Cosmological consequences of parameterized f(R,∇R) gravity

Abstract

Abstract This paper is based on analysis of cosmological parameters and thermodynamics in a modified theory of gravity whose action contains linear coupling of Ricci scalar R and a second degree term of its covariant derivative. The Friedmann equations obtained in result of considering the spatially flat FRW universe filled with dark energy and pressureless matter, are of fifth-order in the Hubble function. Three different deceleration parameters q are used in an integral relation to obtain the Hubble parametric models H ( z ) . We explore the equation of state parameter ω D E , the behavior of phase plane ω D E − ω D E ′ and the stability of each Hubble parametric model H ( z ) via squared speed of sound. The equation of state parameter indicates phantom era of the universe, the phase plane ω D E − ω D E ′ lies in the range of freezing region of the accelerated universe while v s 2 gives the stability of these models under choice of some specific constant parameters. For these models, we also examine the viability of generalized second law of thermodynamics on the apparent horizon with Bekenstein entropy and find that for two models, this law is verified.