Interacting dark energy with time varying equation of state and the $H_0$ tension

TL;DR

The study examines an interacting dark energy model with a time-varying equation of state, employing a coupling $Q = 3 H \xi (1+w_x) \rho_x$ to avoid instabilities at the phantom divide and a one-parameter dynamical $w_x(z)$ to fit data. Using Planck, JLA, BAO, CC, HST, RSD, and WL datasets with an eight-parameter IDE framework, the analysis finds a tiny $\xi$ and a phantom current $w_0$, with the interaction marginally alleviating the $H_0$ tension in some combinations. However, Bayesian evidence consistently favors ΛCDM over IDE, indicating that the standard model remains preferred despite the model’s ability to accommodate phantom behavior and slight tension relief. Overall, IDE with a dynamical $w_x$ is data-compatible but statistically disfavored relative to ΛCDM when model complexity is accounted for.

Abstract

Almost in all interacting dark energy models present in the literature, the stability of the model becomes potentially sensitive to the dark energy equation of state parameter $w_x$, and a singularity arises at `$w_x = -1$'. Thus, it becomes mandatory to test the stability of the model into two separate regions, namely, for quintessence and phantom. This essentially brings in a discontinuity into the parameters space for $w_x$. Such discontinuity can be removed with some specific choices of the interaction or coupling function. In the present work we choose one particular coupling between dark matter and dark energy which can successfully remove such instability and we allow a dynamical dark energy equation of state parameter instead of the constant one. In particular, considering a dynamical dark energy equation of state with only one free parameter $w_0$, representing the current value of the dark energy equation of state, we confront the interacting scenario with several observational datasets. The results show that the present cosmological data allow an interaction in the dark sector, in agreement with some latest claims by several authors, and additionally, a phantom behaviour in the dark energy equation of state is suggested at present. Moreover, for this case the tension on $H_0$ is clearly released. As a final remark, we mention that according to the Bayesian analysis, $Λ$-cold dark matter ($Λ$CDM) is always favored over this interacting dark energy model.

Figures (9)

• Figure 1: Qualitative evolution of the interaction model $Q = 3 H \xi (1+w_x) \rho_{x}$ where $w_x$ is given in eqn. (\ref{['eq:ZG-II']}) has been shown for some specific choices of the coupling parameter, $\xi$. In the left panel we exhibit the behaviour of the interaction function for quintessence kind of dark energy, i.e., $w_0 > -1$ (in particular, we set $w_0 = -0.95$) while the right panel depicts the evolution of the interaction function but for phantom dark energy state parameter, that means for $w_0 < -1$ (in particular, $w_0 = -1.1$). Let us note that $Q_0 = H_0 \rho_{tot,0} = 3 H_0^3 /(8 \pi G)$ where $\rho_{tot} = \left( \rho _{r}+\rho_{b}+\rho _{c}+\rho _{x}\right)$, is the total energy density of the universe and $\rho_{tot,0} = \rho_{tot} (z=0)$.
• Figure 2: The figure depicts the evolution of the interaction function for different values of $w_0$ with some fixed coupling strengths. The left panel portrays the evolution of $Q$ for different values of $w_0$ with a fixed and low coupling strength $\xi = 0.001$ while on the other hand, the right panel shows the same evolution but for a large coupling strength $\xi = 0.5$. We note that $Q_0$ has similar meaning as described for Fig. \ref{['fig:Q-xi']}.
• Figure 3: The 2D confidence contours of various model parameters as well as their 1D marginalized likelihood functions for the reconstructed interacting scenarios with the one parameter $w_x(z)$ parametrization given in equation (\ref{['eq:ZG-II']}). 68.3% ($1\sigma$) and 95.4% ($2\sigma$) confidence-level contours and the marginalized likelihood functions are obtained for different combinations of the data sets. Confidence contours clearly show that the coupling parameter $\xi$ is almost uncorrelated with $w_0$ and other parameters. The present value of dark energy equation of state parameter $w_0$ strictly remains in the phantom regime.
• Figure 4: The 2D confidence contours of various model parameters as well as their 1D marginalized likelihood functions for the interacting and non-interacting scenarios with the one parameter $w_x(z)$ parametrization given in equation (\ref{['eq:ZG-II']}). The results of this figure are shown for the combined analysis CMB $+$ BAO $+$ RSD $+$ HST $+$ WL $+$ JLA $+$ CC. One can note that the common parameters of these two cosmological scenarios assume similar values.
• Figure 5: The 2D confidence contours of various model parameters as well as their 1D marginalized likelihood functions for the interacting and non-interacting scenarios with the one parameter $w_x(z)$ parametrization given in equation (\ref{['eq:ZG-II']}). The results of this figure are shown for the CMB data only. One can note that the 2D contours and the 1D marginalized posterior distributions of the parameters for the interacting scenario are shrinked compared to that in the absence of interaction.