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.
Comment: 25 pages, 7 figures, accepted for publication on JCAP; updated to match the published version