Cosmological constraints on an exponential interaction in the dark sector

TL;DR

The paper investigates cosmological constraints on a phenomenological exponential interaction between dark matter and dark energy in a spatially flat FLRW universe with a constant dark energy equation of state w_x. It derives the background and perturbation evolution under the interaction Q=3H ξ ρ_x exp(ρ_x/ρ_c - 1) and analyzes the model using state-of-the-art data with a CosmoMC MCMC framework. The main findings are that the coupling ξ is constrained to be very small and consistent with zero, while w_x remains close to -1; the background evolution remains near ΛCDM, but perturbations show mild deviations, especially in σ_8 and the matter power spectrum. Overall, current observations favor a weakly interacting dark sector with an exponential coupling, keeping the model in a close neighbourhood of ΛCDM and w_xCDM at the background level.

Abstract

Cosmological models where dark matter (DM) and dark energy (DE) interact with each other are the general scenarios in compared to the non-interacting models. The interaction is usually motivated from the phenomenological ground and thus there is no such rule to prefer a particular interaction between DM and DE. Being motivated, in this work, allowing an exponential interaction between DM and DE in a spatially flat homogeneous and isotropic universe, we explore the dynamics of the universe through the constraints of the free parameters where the strength of the interaction is characterized by the dimensionless coupling parameter $ξ$ and the equation of state (EoS) for DE, $w_x$, is supposed to be a constant. The interaction scenario is fitted using the latest available observational data. Our analyses report that the observational data permit a non-zero value of $ξ$ but it is very small and consistent with $ξ=0$. From the constraints on $w_x$, we find that both phantom ($w_x< -1$) and quintessence ($w_x> -1$) regimes are equally allowed but $w_x$ is very close to `$-1$'. The overall results indicate that at the background level, the interaction model cannot be distinguished from the base $Λ$-cold dark matter model while from the perturbative analyses, the interaction model mildly deviates from the base model. We highlight that, even if we allow DM and DE to interact in an exponential manner, but according to the observational data, the evidence for a non-zero coupling is very small.

Figures (7)

• Figure 1: We compare the exponential interaction model (\ref{['exp-int']}) with some known interaction models, namely, $Q_1 = 3 H \xi \rho_x$, $Q_2 = 3 H \xi \rho_c$ and $Q_3 = 3 H \xi \rho_c \rho_x/(\rho_c +\rho_x)$ for some specific values of the coupling parameter $\xi$ as $\xi = 0.001$ (upper panel), $\xi = 0.05$ (middle panel) and $\xi = 0.01$ (lower panel). We note that $Q_0 = H_0 \rho_{tot,0} = 3 H_0^3 /(8 \pi G)$ where $\rho_{tot,0}$ is the present value of the total energy density $\rho_{tot}$ of the universe, i.e. $\rho_{tot} = \left( \rho _{r}+\rho_{b}+\rho _{c}+\rho _{x}\right)$. The introduction of $Q_0$ makes the quantities $Q_i/Q_0$ ($i \in \{e, 1, 2, 3,\}$) dimensionless.
• Figure 2: One dimensional posterior distributions of some selected parameters of the interacting model have been shown for different combined analysis employed in this work.
• Figure 3: We display the 68% and 95% confidence-level contour plots for various combinations of the model parameters for the exponential interaction model using the different combined analysis. The parameter $\Omega_{m0}$ is the present value of the total matter density parameter $\Omega_m = \Omega_b +\Omega_c$ and $H_0$ is the current value of the Hubble parameter in the units km/Mpc/s. From the upper panel one can see that the coupling strength $\xi$ is uncorrelated with the parameters $w_x$, $H_0$ and $\Omega_{m0}$, while from the lower panel one can clearly observe the existing correlations amongst the parameters $w_x$, $H_0$ and $\Omega_{m0}$.
• Figure 4: 68% and 95% confidence level dependence of the matter fluctuation amplitude $\sigma _{8}$ with various model parameters in presence of the exponential interaction in the dark sector. Here too we have shown the figures for different combined analysis as in other plots. From the above figures we find that $\sigma_8$ is uncorrelated with $w_x$, but the remaining combinations do exhibit the correlations.
• Figure 5: The evolution of the Hubble rate (left panel) and the density parameters for CDM and DE (right panel) for different coupling strengths of the exponential interaction model have been shown for the parameters fixed from the mean values of the combined analysis CMB $+$ BAO $+$ RSD $+$ HST $+$ WL $+$ JLA $+$ CC.