On cosmological Inflation In Palatini $F(R,\phi)$ Gravity

Understand

Single field inflationary models are investigated within Palatini quadratic gravity represented by $R+\alpha R^2$ along with a non-minimal coupling of the form $f(\phi) R$ between the inflaton field $\phi$ and the gravity.

• The treatment is performed in the Einstein frame, where the minimal coupling to gravity is recovered through conformal transformation.
• We consider various limits of the model with different inflationary scenarios characterized as canonical slow-roll inflation in the limit $\alpha \dot{\phi}^2\ll (1+f(\phi)) $, constant-roll k-inflation for $\alpha \ll 1$, and slow-roll K-inflation for$ \alpha \gg 1$ .
• A cosine and exponential potential are examined with the limits mentioned above and different well-motivated non-minimal couplings to gravity.