The MESS of cosmological perturbations

TL;DR

This paper introduces the MESS and SESS, two new effective quantities for analyzing cosmological perturbations, simplifying equations and enabling model-independent analysis of curvature perturbations across various theories and observations.

Contribution

The paper develops the MESS and SESS, new effective quantities that simplify the study of curvature perturbations and are applicable to a wide range of cosmological models.

Findings

The new equations are equivalent to standard ones but require solving only one differential equation.

The approach is valid for any flat homogeneous background, including inflationary and bounce models.

The MESS can be used to parametrize effects on curvature perturbations in a model-independent way.

Abstract

We introduce two new effective quantities for the study of comoving curvature perturbations $\zeta$: the space dependent effective sound speed (SESS) and the momentum dependent effective sound speed (MESS) . We use the SESS and the MESS to derive a new set of equations which can be applied to any system described by an effective stress-energy-momentum tensor (EST), including multi-fields systems, supergravity and modified gravity theories. We show that this approach is completely equivalent to the standard one and it has the advantage of requiring to solve only one differential equation for $\zeta$ instead of a system, without the need of explicitly computing the evolution of entropy perturbations. The equations are valid for perturbations respect to any arbitrary flat spatially homogeneous background, including any inflationary and bounce model. As an application we derive the equation for $\zeta$ for multi-fields $KGB$ models and show that observed features of the primordial curvature perturbation spectrum are compatible with the effects of an appropriate local variation of the MESS in momentum space. The MESS is the natural quantity to parametrize in a model independent way the effects produced on curvature perturbations by multi-fields systems, particle production and modified gravity theories and could be conveniently used in the analysis of LSS observations, such as the ones from the upcoming EUCLID mission or CMB radiation measurements.