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.
Forthcoming experiments will enable us to determine tomographic shear spectra at a high precision level. Most predictions about them have until now been biased on algorithms yielding the expected linear and non-linear spectrum of density fluctuations
. Even when simulations have been used, so-called Halofit (Smith et al 2003) predictions on fairly large scales have been needed. We wish to go beyond this limitation. We perform N-body and hydrodynamical simulations within a sufficiently large cosmological volume to allow a direct connection between simulations and linear spectra. While covering large length-scales, the simulation resolution is good enough to allow us to explore the high-l harmonics of the cosmic shear (up to l ~ 50000), well into the domain where baryon physics becomes important. We then compare shear spectra in the absence and in presence of various kinds of baryon physics, such as radiative cooling, star formation, and supernova feedback in the form of galactic winds. We distinguish several typical properties of matter fluctuation spectra in the different simulations and test their impact on shear spectra. We compare our outputs with those obtainable using approximate expressions for non--linear spectra, and identify substantial discrepancies even between our results and those of purely N-body results. Our simulations and the treatment of their outputs however enable us, for the first time, to obtain shear results taht are fully independent of any approximate expression, also in the high-l range, where we need to incorporate a non-linear power spectrum of density perturbations, and the effects of baryon physics. This will allow us to fully exploit the cosmological information contained in future high--sensitivity cosmic shear surveys, exploring the physics of cosmic shears via weak lensing measurements.
