Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation

We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, h(mu nu) = fg(mu nu) between effective metric, h(mu nu) and the usual metric g(mu nu) where f = 1 - kappa phi(,alpha)phi(,alpha)/2. In FLRW universe, NMDC coupling constant is limited in a range of -2/(phi) over dot(2) < kappa <= infinity preserving Lorentz signature of the effective metric. Slowly-rolling regime provides kappa < 0 forbidding graviton from traveling at superluminal speed. Effective gravitational coupling and entropy of blackhole's apparent horizon are derived. In case of negative coupling, acceleration could happen even with weff > -1/3. Power-law potentials of chaotic inflation are considered. For V proportional to phi(2) and V proportional to phi(4), it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies r < 0.12 as constrained by Planck 2015 (Ade et al., 2016). The V proportional to phi(2) case yields acceptable range of spectrum index and r values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of kappa for V proportional to phi(2) case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Plankian field initial value and stronger gravitational constant. (C) 2018 Elsevier B.V. All rights reserved.