Fluctuations in strongly coupled cosmologies
  In the early Universe, a dual component made of coupled CDM and a scalar
field $\Phi$, if their coupling $\beta > \sqrt{3}/2$, owns an attractor
solution, making them a stationary fraction of cosmic energy during the
radiation dominated era. Along the attractor, both such components expand
$\propto a^{-4}$ and have early density parameters $\Omega_{d} = 1/ (4\beta^2)$
and $\Omega_c= 2, \Omega_d$ (field and CDM, respectively). In a previous paper
it was shown that, if a further component, expanding $\propto a^{-3}$, breaks
such stationary expansion at $z \sim 3$--$5 \times 10^3$, cosmic components
gradually acquire densities consistent with observations. This paper, first of
all, considers the case that this component is warm. However, its main topic is
the analysis of fluctuation evolution: out of horizon modes are then
determined; their entry into horizon is numerically evaluated as well as the
dependence of Meszaros effect on the coupling $\beta$; finally, we compute: (i)
transfer function and linear spectral function; (ii) CMB $C_l$ spectra. Both
are close to standard $\Lambda$CDM models; in particular, the former one can be
so down to a scale smaller than Milky Way, in spite of its main DM component
being made of particles of mass $<1$ keV. The previously coupled CDM component,
whose present density parameter is $\cal O$$(10^{-3})$, exhibits wider
fluctuations $\delta \rho/\rho$, but approximately $\beta$-independent $\delta
\rho$ values. We discuss how lower scale features of these cosmologies might
ease quite a few problems that $\Lambda$CDM does not easily solve.
