The MESS and dualities of cosmological perturbations

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,  not involving explicitly entropy or anisotropies, which can be applied to any system described by an effective stress-energy-momentum tensor (EST), including any multi-fields systems, supergravity and modified gravity theories.

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. It can be also useful to study in a model independent way the production of primordial black holes.

Beside the degeneracy due to different theoretical scenarios producing the same MESS, we show that in absence of entropy or effective anisotropic stress there is an additional degeneracy related to the freedom in the choice of the initial energy scale of inflation, or to the sign of the Hubble parameter.  This implies the existence of an infinite family of dual slow-roll parameters histories which can produce the same spectrum of comoving curvature perturbations, implying  that in general there is no one-to-one correspondence between the spectrum and higher order correlation functions. Bounce models are  examples of  the members of this infinite class of dual models.

The combined analysis of data from future CMB and gravitational wave experiments could allow to distinguish between dual models  because the primordial tensor perturbations spectra of dual models are in general different.