Limits on coupling between dark components

TL;DR

The paper investigates phenomenological couplings between dark matter and dark energy and shows that such couplings can damp the Meszaros effect, altering the transfer function without strongly affecting the CMB. The authors derive the dynamical equations for the coupled system, identify regimes where the suppression of Meszaros freezing occurs (notably for $\\epsilon=-1$), and quantify how the transfer function shifts with coupling strength $\\beta$ and redshift dependence. They compare predictions to SDSS data and WMAP3-like CMB constraints, finding that models with inverse-power coupling ($\\epsilon<0$) require unrealistically low primeval spectral indices $n$ to fit both data sets, effectively ruling out a broad class of couplings. They suggest that couplings increasing with redshift ($\\epsilon>0$) remain viable options and highlight how future measurements of $\\rho_c$, $\\rho_b$, and $\\rho_{DE}$ at $z\\sim 1$–5 could tighten these limits.

Abstract

DM--DE coupling can be a phenomenological indication of a common origin of the dark cosmic components. In this work we outline a new constraint to coupled--DE models: the coupling can partially or totally suppress the Meszaros effect, yielding transfered spectra with quite a soft bending above $k_{hor,eq}$. Models affected by this anomaly do not show major variation in the CMB anisotropy spectrum and it is herefore hard to reconcile them with both CMB and deep sample data, through the same value of the primeval spectral index.

Figures (11)

• Figure 1: Scale dependence of the density parameters of the various components in coupled DE models with constant coupling. This plot shows also the displacement of $z_{eq}$ and, henceforth, of $k_{hor,eq}$ as $\beta$ increases: thicker (thinner) curves refer to $\beta = 0.01$ (0.0244).
• Figure 2: Best fits of SDSS data for constant $\beta$ from 0 (solid line) to 0.25 (dotted line). Different lines correspond to a $\beta$ increase by 0.05$\,$. The vertical dotted line yields the scale of $C_{10}.$
• Figure 3: If values of $n$ at 1-- or 2--$\sigma$'s from best fits are taken, spectra are significantly modified. Here we show the effect in the case with $C=1/m_p.$
• Figure 4: $n$ intervals for increasing (constant) coupling strength
• Figure 5: Anisotropy spectrum of the $\Lambda$CDM model yielding the best fit to WMAP3 data compared with the spectra for coupled models with $\beta = 0.1$ and $\epsilon = 0,$ for $n = 1$ and $n = 0.7.$ Already in the former case some difference exists, but no major qualitative changes occur; by adjusting other model parameters one can expect a reasonable fit to data. Taking $n = 0.7,$ any fitting to CMB anisotropy data is apparently excluded.