Coupled DM heating in SCDEW cosmologies

Strongly Coupled Dark Energy plus Warm dark matter (SCDEW) cosmologies admit the stationary presence of $\sim 1\, \%$ of coupled-DM and DE, since inflationary reheating. Coupled-DM fluctuations therefore grow up to non-linearity even in the early radiative expansion. Such early non-linear stages are modelized here through the evolution of a top-hat density enhancement, reaching an early virial balance when the coupled-DM density contrast is just 25-26 and DM density enhancement is $ \sim 10\, \%$ of total density. During the time needed to settle in virial equilibium, the virial balance conditions however continue to modify, so that "virialized" lumps undergo a complete evaporation. Here we outline that DM particles processed by overdentities preserve a fraction of their virial momentum. Although fully non-relativistic, the resulting velocities (moderately) affect the fluctuation dynamics over greater scales, entering the horizon later on.