<p>The superconformal action can be gauge-fixed in a gauge where it leads to the Einstein frame supergravity defined by a Kähler potential <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">K</mi> <mfenced close=")" open="(" separators=","> <mi>z</mi> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{K}\left(z,\overline{z}\right) \)</EquationSource> </InlineEquation>, or in a gauge where it leads to a Jordan frame supergravity defined by the frame function <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="normal">Ω</mi> <mfenced close=")" open="(" separators=","> <mi>z</mi> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \Omega \left(z,\overline{z}\right) \)</EquationSource> </InlineEquation>, in addition to <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">K</mi> <mfenced close=")" open="(" separators=","> <mi>z</mi> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{K}\left(z,\overline{z}\right) \)</EquationSource> </InlineEquation>. We present <i>new supergravity ξ-attractor models with non-minimal gravity coupling</i>. They describe potentials with an exponential and a polynomial approach to the plateau. The previously known <i>ξ</i>-attractors in the large <i>ξ</i> limit predicted the spectral index <i>n</i><sub><i>s</i></sub> = 1 − 2<i>/N</i> and the tensor-to-scalar ratio <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi>r</mi> <mo>→</mo> <mfrac> <mn>12</mn> <msup> <mi>N</mi> <mn>2</mn> </msup> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( r\to \frac{12}{N^2} \)</EquationSource> </InlineEquation>. The new <i>ξ</i>-attractors in the large <i>ξ</i> limit predict <i>n</i><sub><i>s</i></sub> ≥ 1 − 2<i>/N</i> and <i>r</i> → 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 <i>r</i>.</p><p>New <i>ξ</i>-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.</p>

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Jordan frame in supergravity and cosmology

  • Renata Kallosh

摘要

The superconformal action can be gauge-fixed in a gauge where it leads to the Einstein frame supergravity defined by a Kähler potential K z z ¯ \( \mathcal{K}\left(z,\overline{z}\right) \) , or in a gauge where it leads to a Jordan frame supergravity defined by the frame function Ω z z ¯ \( \Omega \left(z,\overline{z}\right) \) , in addition to K z z ¯ \( \mathcal{K}\left(z,\overline{z}\right) \) . 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 ns = 1 − 2/N and the tensor-to-scalar ratio r 12 N 2 \( r\to \frac{12}{N^2} \) . The new ξ-attractors in the large ξ limit predict ns ≥ 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.