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

Understand

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, $h_{\mu\nu} = f g_{\mu\nu}$ 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/ \dot{\phi}^{2} < \kappa \leq \infty $ preserving Lorentz signature of the effective metric.