Strongly Coupled Dark Energy with Warm dark matter vs. LCDM
  Cosmologies including strongly Coupled (SC) Dark Energy (DE) and Warm dark
matter (SCDEW) are based on a conformally invariant (CI) attractor solution
modifying the early radiative expansion. Then, aside of radiation, a kinetic
field $\Phi$ and a DM component account for a stationary fraction, $\sim 1\,
\%$, of the total energy. Most SCDEW predictions are hardly distinguishable
from LCDM, while SCDEW alleviates quite a few LCDM conceptual problems, as well
as its difficulties to meet data below the average galaxy scale. The CI
expansion begins at the inflation end, when $\Phi$ (future DE) possibly plays a
role in reheating, and ends at the Higgs' scale. Afterwards, a number of viable
options is open, allowing for the transition from the CI expansion to the
present Universe. In this paper: (i) We show how the attractor is recovered
when the spin degrees of freedom decreases. (ii) We perform a detailed
comparison of CMB anisotropy and polarization spectra for SCDEW and LCDM,
including tensor components, finding negligible discrepancies. (iii) Linear
spectra exhibit a greater parameter dependence at large $k$'s, but are still
consistent with data for suitable parameter choices. (iv) We also compare
previous simulation results with fresh data on galaxy concentration. Finally,
(v) we outline numerical difficulties at high $k$. This motivates a second
related paper, where such problems are treated in a quantitative way.
