Jordan Frame in Supergravity and Cosmology

Abstract

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 $\hat{I}\text{c◯}(z,\bar{z})$, in addition to $K(z,\bar{z})$. We present new supergravity $\hat{I}¾$-attractor models with non-minimal gravity coupling. They describe potentials with an exponential and a polynomial approach to the plateau. The previously known $\hat{I}¾$-attractors in the large $\hat{I}¾$ limit predicted the spectral index $n_s=1-2/N$ and the tensor-to-scalar ratio $r\to \frac{12}{N^2}$. The new $\hat{I}¾$-attractors in the large $\hat{I}¾$ limit predict $n_s\ge 1-2/N$ and $r\to 0$, which provides a better match to the recent observational data and makes these models a target for the future B-mode experiments with small $r$. New $\hat{I}¾$-attractors have some features similar to those of Palatini attractors. However, we show that the Palatini gravity with nonminimal scalar coupling and an independent affine connection has no supergravity embedding.

25p