Derivative couplings in gravitational production in the early universe

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Gravitational particle production in the early universe is due to the coupling of matter fields to curvature. This coupling may include derivative terms that modify the kinetic term. The most general first order action contains derivative couplings to the curvature scalar and to the traceless Ricci tensor, which can be dominant in the case of (pseudo-)Nambu-Goldstone bosons or disformal scalars, such as branons. In the presence of these derivative couplings, the density of produced particles for the adiabatic regime in the de Sitter phase (which mimics inflation) is constant in time and decays with the inverse effective mass (which in turn depends on the coupling to the curvature scalar). In the reheating phase following inflation, the presence of derivative couplings to the background curvature modifies in a nontrivial way the gravitational production even in the perturbative regime. We also show that the two couplings - to the curvature scalar and to the traceless Ricci tensor - are drastically different, specially for large masses. In this regime, the production becomes highly sensitive to the former coupling while it becomes independent of the latter.
© 2020 The Authors. We wish to thank Francisco J. L~opez Encinas for valuable discussions in the early stages of this work. This work has been financially supported in part by the MINECO (Spain) projects FIS2016-78859-P (AEI/FEDER) and FIS2017-86497-C2-2-P (with FEDER contribution). JMSV acknowledges financial support from Universidad Complutense de Madrid through the predoctoral grant CT27/16. This work was made possible by Institut Pascal at Universit~e Paris-Saclay with the support of the P2I and SPU research departments and the P2IO Laboratory of Excellence (program Investissements davenir ANR-11-IDEX-0003-01 Paris-Saclay and ANR-10-LABX-0038), as well as the IPhT.
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