Jordan Frame in Supergravity and Cosmology

The superconformal action can be gauge-fixed in a gauge where is leads to the Einstein frame supergravity defined by a Kahler potential $K(z, \bar z)$, or in a gauge where it leads to a Jordan frame supergravity defined by the frame function Omega $(z, \bar z)$, in addition to $K(z, \bar z)$. We present {\it new supergravity $\xi$-attractor models with non-minimal coupling to gravity}, which offer some advantages over the previously known $\xi$-attractors. New attractors include exponential and polynomial $\xi$-attractors and have some features similar to those of the Palatini attractors. However, we show that the Palatini gravity with nonminimal scalar coupling and an independent affine connection has no supergravity embedding.