Model-independent approach to effective sound speed in multi-field inflation

TL;DR

This paper derives a general, model-independent formula for the effective sound speed of curvature perturbations in multi-field inflation, applicable to various models and capturing entropy effects without approximations.

Contribution

It provides a novel, comprehensive formula for the momentum-dependent effective sound speed in multi-field inflation, valid for any field-space metric and without integrating out entropy perturbations.

Findings

The formula accurately describes the power spectrum in two-field models with kinetic coupling.

Momentum-dependent effective sound speed accounts for entropy perturbations effects.

The approach simplifies the analysis of single-field effective theories in multi-field inflation.

Abstract

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 perturbations present in multi-fields systems.