Cosmological perturbations in Palatini formalism

We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function field and its kinetic term there also k-essence consisting term. This has three frames that are equivalent one another: original Jordan frame, Einstein frame metric redefined, Riemann connection redefined. For first time literature, calculate quadratic sound speed tensor different show explicitly they coincide. Furthermore, for such gravitational waves unity. Thus, this model serves as dark energy well inflaton even though presence dependence non-minimal coupling, from case then proceed construct L3 called Galileon terms formalism compute perturbations. found essentially 10 (inequivalent) definitions given see that, general, have ghost due Ostrogradsky instability could potentially deviate unity, sharp contrast with Interestingly, once eliminate ghost, becomes ghost-free can still serve inflaton, like