In this first paper we discuss the linear theory and the background evolution of a new class of models we dub SCDEW: Strongly Coupled DE, plus WDM. In these models, WDM dominates todays matter density; like baryons, WDM is uncoupled. Dark Energy is a
scalar field $Phi$; its coupling to ancillary CDM, whose todays density is $ll 1, %$, is an essential model feature. Such coupling, in fact, allows the formation of cosmic structures, in spite of very low WDM particle masses ($sim 100$ eV). SCDEW models yields Cosmic Microwave Background and linear Large Scale features substantially undistinguishable from $Lambda$CDM, but thanks to the very low WDM masses they strongly alleviate $Lambda$CDM issues on small scales, as confirmed via numerical simulations in the II associated paper. Moreover SCDEW cosmologies significantly ease the coincidence and fine tuning problems of $Lambda$CDM and, by using a field theory approach, we also outline possible links with inflationary models. We also discuss a possible fading of the coupling at low redshifts which prevents non linearities on the CDM component to cause computational problems. The (possible) low-$z$ coupling suppression, its mechanism, and its consequences are however still open questions -not necessarily problems- for SCDEW models. The coupling intensity and the WDM particle mass, although being extra parameters in respect to $Lambda$CDM, are found to be substantially constrained a priori so that, if SCDEW is the underlying cosmology, we expect most data to fit also $Lambda$CDM predictions.
The properties of dynamical Dark Energy (DE) and, in particular, the possibility that it can form or contribute to stable inhomogeneities, have been widely debated in recent literature, also in association to a possible coupling between DE and Dark M
atter (DM). In order to clarify this issue, in this paper we present a general framework for the study of the nonlinear phases of structure formation, showing the equivalence between two possible descriptions of DE: a scalar field phi self-interacting through a potential V(phi) and a perfect fluid with an assigned negative equation of state w(a). This enables us to show that, in the presence of coupling, the mass of DE quanta may increase where large DM condensations are present, so that also DE may partake to the clustering process.
