Some generalizations of the notion of Lie algebra

We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them, called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are particular substructures.Comment: Second version. 14 pages. Included some comments about previous works related to Leibniz algebras, and updated bibliography. A new example adde

The MESS of cosmological perturbations

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.Comment: We study the MESS of cosmological perturbations, version accepted in Physics Letters