The MESS of cosmological perturbations

There has been some evidence of features in the primordial curvature spectrum from cosmic microwave background (CMB) radiation data analysis, and curvature enhancements could also produce primordial black holes (PBH) which may affect gravitational wave observations. For the purpose of studying the evolution of comoving curvature perturbations ζ we introduce two new effective quantities: 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 multi-fields systems 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 MESS is the natural quantity to parametrize in a model independent way the effects produced on curvature perturbations by multi-fields systems and modified gravity theories and could be conveniently used in the analysis of LSS observations, such as the ones from the upcoming EUCLID mission, CMB radiation measurements, or to constrain phenomenologically the curvature perturbations enhancements which could produce PBH.