Dark matter-dark energy interaction for a time-dependent equation of state

TL;DR

This study analyzes a dark matter–dark energy interaction where DM dilutes as $\rho_{\rm DM}\propto(1+z)^{3-\epsilon}$ (Wang–Meng law) and dark energy is described by a time-dependent EoS $w(z)=w_0+w'_0\frac{z(1+z)}{1+z^2}$ (Barboza–Alcaniz parametrization). The authors derive the coupling constraint $\epsilon\ge0$ from theoretical considerations ensuring positive DE density and implement a joint observational constraint using SN Ia, BAO, CMB, and $H(z)$ data, finding the best-fit values $w_0=-1.04^{+0.09}_{-0.10}$, $w'_0=-0.11^{+0.38}_{-0.38}$, and $\epsilon=-0.016^{+0.021}_{-0.017}$; crucially, the data show limited sensitivity to the sign of $\epsilon$, and the physical region $\epsilon\ge0$ is restricted to $0\le\epsilon\le0.034$ at $2\sigma$. The work also provides a scalar-field reconstruction for both quintessence and phantom regimes, revealing that coupling effects are most pronounced in the phantom case, where $V(\phi)$ behavior with redshift differs between coupled and uncoupled scenarios. Overall, the paper demonstrates that while a dark sector coupling is not ruled out, current observations favor the uncoupled model and constrain the physically viable coupling to a very small interval.

Abstract

In this work we investigate the interaction between dark matter and dark energy for a coupling that obeys the Wang-Meng decaying law, $ρ_{\rm DM}\propto (1+z)^{3-ε}$, and the Barboza-Alcaniz dark energy parametric model, $w=w_0+w'_0z(1+z)/(1+z^2)$. Theoretically, we show that the coupling constant, $ε$, should satisfy the physical constraint $ε\ge0$. We use the most recent data of type Ia supernovae, baryon acoustic oscillations, cosmic microwave background and the Hubble expansion rate function to constrain the free parameters of the model. From a purely observational point of view, we show that is not possible to discard values of the coupling constant in the unphysical region $ε<0$. We show that the uncoupled case, $ε=0$, is in better agreement with the data than any of coupled models in the physical region. We also find that all physically acceptable interaction in dark sector lies in the narrow range $0<ε\le0.034$ ($95\%$ CL).

Figures (2)

• Figure 1: The $w_0-\epsilon$ (left) and $w_0-w'_0$ (right) parametric spaces. The blank regions in the $w_0-w'_0$ plane indicate models that at some point of the cosmic evolution have switched or will switch from quintessence to phantom behaviors or vice-versa. The Early DE region corresponds to the region where DE dominates over matter in early times. The dashed contours in the $w_0-w'_0$ plane are the ones obtained when we allow that $\epsilon<0$. The contours are drawn for $\Delta \chi^2 = 2.30$ and 6.17.
• Figure 2: Scalar field description of the coupled case for five selected points in the quintessence (left) and phantom (right) regions. The uncoupled case also is shown (full lines). The values of $(w_0,w'_0)$ are $(-0.8, 0.2)$ for quintessence and $(-1.2, 0.1)$ for phantom fields.