Cosmological Perturbations in Palatini Formalism

Understand

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 of a scalar field and its kinetic term and there is also a k-essence term consisting of the scalar and its kinetic term.
• This action has three frames that are equivalent to one another: the original Jordan frame, the Einstein frame where the metric is redefined, and the Riemann frame where the connection is redefined.
• For the first time in the literature, we calculate the quadratic action and the sound speed of scalar and tensor perturbations in three different frames and show explicitly that they coincide.