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2016

Sound Speed of Primordial Fluctuations in Supergravity Inflation

Hetz, Alexander, Palma, Gonzalo A.

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We study the realization of slow-roll inflation in $\mathcal N = 1$ supergravities where inflation is the result of the evolution of a single chiral field.

When there is only one flat direction in field space, it is possible to derive a single-field effective field theory parametrized by the sound speed $c_s$ at which curvature perturbations propagate during inflation.
The value of $c_s$ is determined by the rate of bend of the inflationary path resulting from the shape of the $F$-term potential.
We show that $c_s$ must respect an inequality that involves the curvature tensor of the Kahler manifold underlying supergravity, and the ratio $M/H$ between the mass $M$ of fluctuations ortogonal to the inflationary path, and the Hubble expansion rate $H$.

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For example, in DBI models Alishahiha:2004eh one has that c ~ 3 = 3 ( 1 − c s 2 ) / 2 \tilde{c}_{3}=3(1-c_{s}^{2})/2 Senatore:2009gt whereas in single field EFT’s obtained by integrating out a heavy field in canonical multi-field models one finds c ~ 3 = 3 ( 1 − c s 2 ) / 4 \tilde{c}_{3}=3(1-c_{s}^{2})/4 Achucarro:2012sm

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