Regular Article - Theoretical Physics
Model-independent approach to effective sound speed in multi-field inflation
Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
2 ICRANet, Piazza della Repubblica 10, 65122, Pescara, Italy
3 Instituto de Fisica, Universidad de Antioquia, A.A.1226, Medellin, Colombia
4 Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland
Accepted: 3 August 2022
Published online: 30 August 2022
For any physical system satisfying the Einstein’s equations, the comoving curvature perturbations satisfy an equation involving the momentum-dependent effective sound speed, valid for any system with a well defined energy-stress tensor, including multi-fields models of inflation. We derive a general model-independent formula for the effective sound speed of comoving adiabatic perturbations, valid for a generic field-space metric, without assuming any approximation to integrate out entropy perturbations, but expressing the momentum-dependent effective sound speed in terms of the components of the total energy-stress tensor. As an application, we study a number of two-field models with a kinetic coupling between the fields, identifying the single curvature mode of the effective theory and showing that momentum-dependent effective sound speed fully accounts for the predictions for the power spectrum of curvature perturbations. Our results show that the momentum-dependent effective sound speed is a convenient scheme for describing all inflationary models that admit a single-field effective theory, including the effects of entropy pertubations present in multi-fields systems.
© The Author(s) 2022
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