Jordan frame in supergravity and cosmology

A bstract The superconformal action can be gauge-fixed in a gauge where it leads to the Einstein frame supergravity defined by a Kähler potential $$ \mathcal{K}\left(z,\overline{z}\right) $$ K z z ¯ , or in a gauge where it leads to a Jordan frame supergravity defined by the frame function $$ \Omega \left(z,\overline{z}\right) $$ Ω z z ¯ , in addition to $$ \mathcal{K}\left(z,\overline{z}\right) $$ K z z ¯ . We present new supergravity ξ-attractor models with non-minimal gravity coupling . They describe potentials with an exponential and a polynomial approach to the plateau. The previously known ξ -attractors in the large ξ limit predicted the spectral index n s = 1 − 2 /N and the tensor-to-scalar ratio $$ r\to \frac{12}{N^2} $$ r → 12 N 2 . The new ξ -attractors in the large ξ limit predict n s ≥ 1 − 2 /N and r → 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 ξ -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.