Matter density perturbations in interacting quintessence models

TL;DR

This paper investigates a dark matter–dark energy coupling within an interacting quintessence model (IQM) as a mechanism to address the coincidence problem. It introduces the phenomenological coupling $Q = 3 H c^{2} ( ho_c + ho_x)$, analyzes linear perturbations in synchronous gauge, and derives both analytic limits and numerical predictions for the matter power spectrum. The study finds that the coupling damps small-scale power and delays matter–radiation equality, with current 2dFGRS data constraining $c^{2} \,\lesssim\ 3\times 10^{-3}$, while the IQM remains compatible with observations as well as ΛCDM. The work highlights distinctive, testable signatures—especially the small-scale suppression—that could be probed by Ly$\alpha$ forest measurements and future large-scale structure surveys to discriminate IQM from non-interacting models.

Abstract

Models with dark energy decaying into dark matter have been proposed to solve the coincidence problem in cosmology. We study the effect of such coupling in the matter power spectrum. Due to the interaction, the growth of matter density perturbations during the radiation dominated regime is slower compared to non-interacting models with the same ratio of dark matter to dark energy today. This effect introduces a damping on the power spectrum at small scales proportional to the strength of the interaction and similar to the effect generated by ultrarelativistic neutrinos. The interaction also shifts matter--radiation equality to larger scales. We compare the matter power spectrum of interacting quintessence models with the measurments of 2dFGRS. We particularize our study to models that during radiation domination have a constant dark matter to dark energy ratio.

Figures (4)

• Figure 1: Evolution of the gravitational potential (upper panels) and the cold dark matter density perturbations (lower panels) for three modes: $k=0.01$ (left) $k=0.1$ (center) and $k=1h^{-1}$Mpc (right panels). We study the evolution of each mode in three different cosmological models: the concordance model ($c^2=0$, solid line) and two interacting quintessence models with the same cosmological parameters, $c^2=10^{-3}$ (dotted) and $c^2=6\times 10^{-3}$ (dashed line).
• Figure 2: (a) Matter power spectra for the interacting quintessence model with different rates of energy transfer. From top to bottom $c^2=0,10^{-3},6\times 10^{-3},10^{-2}$. We took the present value of cosmological parameters to be: $\Omega_{b}=0.04$, $\Omega_{cdm}=0.23$, $H_0=72$km s$^{-1}/$Mpc, $\Omega_\Lambda =0.73$ the dark energy equation of state $w_{x}=-0.9$ and the slope of the matter power spectrum at large scales $n_s=1$. (b) The same for mixed dark matter models with one single species of massive neutrinos. From top to bottom, the fraction of energy density in the form of neutrinos is: $\Omega_\nu= 0.01, 0.05, 0.1, 0.2$. As before, the total dark matter energy density was $\Omega_{dm}=0.23$, the rest was cold dark matter. (c) Variation of the slope of $P(k)$ with $c^2$, and (d) with massive neutrinos. The slope was computed from a straight line fit to the data in the interval $k=[0.1,1] h^{-1}$ Mpc.
• Figure 3: Marginalized likelihood function for the 2dFGRS data.
• Figure 4: Marginalized likelihood function for the 2dFGRS data.