Observational constraints on a phenomenological f (R, partial derivative R)-model

This paper analyses the cosmological consequences of amodified theory of gravity whose action integral is built from a linear combination of the Ricci scalar R and a quadratic term in the covariant derivative of R. The resulting Friedmann equations are of the fifth-order in the Hubble function. These equations are solved numerically for a flat space section geometry and pressureless matter. The cosmological parameters of the higher-order model are fit using SN Ia data and X-ray gas mass fraction in galaxy clusters. The best-fit present-day t(0) values for the deceleration parameter, jerk and snap are given. The coupling constant beta of the model is not univocally determined by the data fit, but partially constrained by it. Density parameter Omega(m0) is also determined and shows weak correlation with the other parameters. The model allows for two possible future scenarios: there may be either an eternal expansion or a Rebouncing event depending on the set of values in the space of parameters. The analysis towards the past performed with the best-fit parameters shows that the model is not able to accommodate a matter-dominated stage required to the formation of structure.