Abstract
We introduce two new effective quantities for the study of comoving curvature perturbations ζ: 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 ζ 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 ζ 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.
Highlights
The evolution of comoving curvature perturbations ζ has a fundamental importance in cosmology since it is the basis for the study of different phenomena such as the CMB anisotropy or LSS
When the Universe is dominated by more than a scalar field the standard approach consists in deriving an equation for ζ, with a time dependent sound speed, obtaining a new source term [1] compared to the single field case, related to the field perturbations, which is interpreted as entropy perturbation
After introducing a new definition of the space dependent effective sound speed (SESS) and the momentum dependent effective sound speed (MESS) we have derived a set of new equations (20)–(25) and (55)–(53) for the comoving curvature perturbations valid for any system described by an EST, including multi-fields systems, modified gravity theories, or a combination of the two
Summary
In this paper we show that there exist a completely equivalent form of the equations which involves a space dependent effective sound speed (SESS) and no source term. The advantage of this new approach is that it allows to study the evolution of curvature perturbations using only one equation for ζ without the need to introduce the notion of entropy perturbations or to integrate the system of differential equations for all the fields, as done in the standard approach [1]. We derive the equation for ζ for some single and multi-fields modified gravity scalar theories belonging to the Horndeski’s family
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