It has been argued that supergravity models of inflation with vanishing sound speeds, cs, lead to an unbounded growth in the production rate of gravitinos. We consider several models of inflation to delineate the conditions for which cs=0. In models with unconstrained superfields, we argue that the mixing of the Goldstino and inflatino in a time-varying background prevents the uncontrolled production of the longitudinal modes. This conclusion is unchanged if there is a nilpotent field associated with supersymmetry breaking with constraint S2=0, i.e., (s)Goldstino-less models. Models with a second orthogonal constraint, S(φ-φ¯)=0, where φ is the inflaton superfield, which eliminates the inflatino, may suffer from the overproduction of gravitinos. However, we point out that these models may be problematic if this constraint originates from a UV Lagrangian, as this may require using higher derivative operators. These models may also exhibit other pathologies, such as cs>1, which are absent in theories with the single constraint or unconstrained fields.
Bibliographical noteFunding Information:
The authors want to thank T. Gherghetta, H. P. Nilles, and L. Sorbo for helpful discussions. This project has received support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 860881-HIDDeN, by the ANR grant Black-dS-String Grant No. ANR-16-CE31-0004-01, the CNRS PICS MicroDark, and the IN2P3 Master Project UCMN. The work of K. A. O. was supported in part by DOE Grant No. DE-SC0011842 at the University of Minnesota. The work of M. G. was supported by the Spanish Agencia Estatal de Investigación through Grants No. FPA2015-65929-P (MINECO/FEDER, UE) and No. PGC2018095161-B-I00, IFT Centro de Excelencia Severo Ochoa Grant No. SEV-2016-0597, and Red Consolider MultiDark Grant No. FPA2017-90566-REDC.
© 2021 authors.