Reconstructing the dark matter and dark energy interaction scenarios from observations

TL;DR

The paper investigates a class of interacting dark energy models by letting the cold dark matter density evolve as ρ_c ∝ a^{-3+δ(a)} in both flat and nonflat FLRW universes, where δ(a) is expanded around the present epoch. Using a Taylor series δ(a) = δ_0 + δ_1(1−a) + δ_2(1−a)^2 + … and combining Planck 2015 CMB data with JLA SN Ia, BAO, and cosmic chronometers, the authors reconstruct the interaction for three dark energy scenarios (vacuum, constant EOS, and dynamical EOS CPL). Across all cases and geometries, higher-order terms δ_2, δ_3 are statistically consistent with zero, with δ_0 and δ_1 strongly anti-correlated, indicating that the linear form δ(a) ≈ δ_0 + δ_1(1−a) suffices to describe any present-day interaction. The non-interacting ΛCDM model remains compatible with the data, and there is no compelling evidences for a substantial dark sector coupling within current observational precision. The framework provides a principled, model-independent route to test DM–DE interactions as data improve.

Abstract

We consider a class of interacting dark energy models in a flat and nonflat FLRW universe where the interaction is characterized by the modified evolution of the pressureless dark matter as $a^{-3+δ(a)}$, $a$ being the FLRW scale factor and $δ(a)$ quantifies the interaction rate. By assuming the most natural and nonsingular parametrization for $δ(a)$ as $δ\left( a\right) =\sum_{i} δ_i (1-a)^i $, where $δ_{i}$'s ($i=0,1,2,3,..$) are constants, we reconstruct the expansion history of the universe for three particular choices of the DE sector using different cosmological datasets. Our analyses show that the non-interacting scenario is consistent with the observations while the interaction is not strictly ruled out. We reconstruct in the following way. We start with the first two terms of $δ(a)$ above and constrain $δ_0$, $δ_1$. Then we consider up to the second order terms in $δ(a)$ but fix $δ_0$, $δ_1$ to their constrained values and constrain $δ_2$; similarly we constrain $δ_3$, and finally we constrain $(δ_0, δ_1, δ_1, δ_3)$ by keeping all of them to be free as a generalized case. Our reconstruction technique shows that the constraints on $δ_2$ (fixing $δ_0$ and $δ_1$) and $δ_3$ (fixing $δ_0$, $δ_1$ and $δ_2$) are almost zero for any interaction model and thus the effective scenario is well described by the linear parametrization $δ(a)\simeq δ_{0}+δ_{1}(1-a)$. Additionally, a strong negative correlation between $δ_0$, $δ_1$ is observed independently of the dark energy fluid and the curvature of our universe.

Figures (24)

• Figure 1: 68% and 95% CL contour plots for different combinations of the model parameters as well as the one dimensional posterior distributions of some selected model parameters of the interacting vacuum scenario (in a spatially flat universe) where the interaction is parametrized by $\delta (a) = \delta_0 + \delta_1 (1-a)$. The combined data for this analysis has been set to be CMB $+$ JLA $+$ BAO $+$ CC. The results are summarized in the second and third columns of Table \ref{['tab:Int-vacuum-flat']}.
• Figure 2: 68% and 95% CL contour plots for different combinations of the model parameters as well as the one dimensional posterior distributions of some selected model parameters of the interacting vacuum scenario (in a spatially flat universe) where the interaction is parametrized by $\delta (a) = \delta_0 + \delta_1 (1-a) + \delta_2 (1-a)^2$ in which we fix the mean values of ($\delta_0$, $\delta_1$) from Table \ref{['tab:Int-vacuum-flat']}. The combined data for this analysis has been set to be CMB $+$ JLA $+$ BAO $+$ CC and the corresponding results are summarized in the fourth and fifth columns of Table \ref{['tab:Int-vacuum-flat']}.
• Figure 3: 68% and 95% CL contour plots for different combinations of the free parameters as well as the one dimensional posterior distributions of some selected model parameters of the interacting vacuum scenario (in a spatially flat universe) where the interaction is parametrized by $\delta (a) = \delta_0 + \delta_1 (1-a) + \delta_2 (1-a)^2+ \delta_3 (1-a)^3$ in which the mean values of ($\delta_0$, $\delta_1$, $\delta_2$) have been fixed from the previous analysis summarized in Table \ref{['tab:Int-vacuum-flat']}. The combined data for this analysis has been set to be CMB $+$ JLA $+$ BAO $+$ CC and the corresponding results are summarized in the sixth and seventh columns of Table \ref{['tab:Int-vacuum-flat']}.
• Figure 4: 68% and 95% CL contour plots for different combinations of the free parameters as well as the one dimensional posterior distributions of some selected model parameters of the interacting vacuum scenario (in a spatially flat FLRW universe) where the interaction is parametrized by the most general parametrization $\delta (a) = \delta_0 + \delta_1 (1-a) + \delta_2 (1-a)^2+ \delta_3 (1-a)^3$. The interaction parameters $\delta_i$'s are kept free and we use the combined analysis CMB $+$ JLA $+$ BAO $+$ CC. The results are summarized in Table \ref{['tab:Int-vacuum-flat-general']}. One can clearly notice that the parameters $\delta_2$ and $\delta_3$ are degenerate while other parameters are not.
• Figure 5: 68% and 95% CL contour plots for different combinations of the model parameters as well as the one dimensional posterior distributions of some selected model parameters of the interacting DE scenario (for spatially flat case) with constant DE state parameter $w_x$, where the interaction is parametrized by $\delta (a) = \delta_0 + \delta_1 (1-a)$ and the combined observational analysis is CMB $+$ JLA $+$ BAO $+$ CC. The results are summarized in the second and third columns of Table \ref{['tab:Int-wCDM-flat']}.