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 $$ \mathcal{K}\left(z,\overline{z}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> <mml:mfenced> <mml:mi>z</mml:mi> <mml:mover> <mml:mi>z</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mfenced> </mml:math> , or in a gauge where it leads to a Jordan frame supergravity defined by the frame function $$ \Omega \left(z,\overline{z}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> <mml:mfenced> <mml:mi>z</mml:mi> <mml:mover> <mml:mi>z</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mfenced> </mml:math> , in addition to $$ \mathcal{K}\left(z,\overline{z}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> <mml:mfenced> <mml:mi>z</mml:mi> <mml:mover> <mml:mi>z</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mfenced> </mml:math> . 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 $$ r\to \frac{12}{N^2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>r</mml:mi> <mml:mo>→</mml:mo> <mml:mfrac> <mml:mn>12</mml:mn> <mml:msup> <mml:mi>N</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfrac> </mml:math> . 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.