Constraining a dark matter and dark energy interaction scenario with a dynamical equation of state

TL;DR

This work investigates a flat FLRW cosmology in which dark energy and dark matter interact while the dark energy equation of state evolves with redshift, described by $w_{DE}(z)=w_0 - w_{\beta}\left[\frac{(1+z)^{-\beta}-1}{\beta}\right]$ and a slowly varying coupling $\delta$ governing energy transfer, with $\rho_{dm} \propto a^{-3+\delta}$. A joint analysis using cosmic chronometers, local $H_0$, JLA SN Ia, BAO, and Planck TT+lowP CMB data constrains a 10-parameter space including $\delta$, $w_0$, $w_{\beta}$, and $\beta$, revealing that $\delta$ is compatible with zero at $1\sigma$ and that the data can be accommodated by a noninteracting model with a small CDM pressure via $\delta=-3\eta$. The study further examines the impact on CMB and matter power spectra, showing that larger $\delta$ modifies the CMB peak structure and the matter power spectrum, and notes that the IDE framework can modestly alleviate the tension between Planck and local $H_0$ measurements by about $2\sigma$. An important takeaway is the equivalence between a constant IDE coupling and a small CDM pressure, offering an alternate physical picture while yielding similar observational constraints. Overall, the results provide a general, data-driven assessment of dark sector coupling under a dynamical DE EoS and highlight the subtle interplay between late-time physics and early-universe observables.

Abstract

In this work we have used the recent cosmic chronometers data along with the latest estimation of the local Hubble parameter value, $H_0$ at 2.4\% precision as well as the standard dark energy probes, such as the Supernovae Type Ia, baryon acoustic oscillation distance measurements, and cosmic microwave background measurements (PlanckTT $+$ lowP) to constrain a dark energy model where the dark energy is allowed to interact with the dark matter. A general equation of state of dark energy parametrized by a dimensionless parameter `$β$' is utilized. From our analysis, we find that the interaction is compatible with zero within the 1$σ$ confidence limit. We also show that the same evolution history can be reproduced by a small pressure of the dark matter.

Figures (6)

• Figure 1: Qualitative evolution of the dark energy equation of state $w_{DE} (z)$ in Eq. (\ref{['model1']}) has been shown for $w_{\beta} = 1$, with different values of the $\beta$ parameter such as $\beta =$$-2, -1.5, -1, -0.5,~ 0.001,~ 0.5,~ 1,~ 1.5,~ 2$. The lowest plot is for $\beta = 2$, and as $\beta$ decreases, the plots go up in the anticlockwise direction.
• Figure 2: 68.3%, 95.5%, and 99.7% confidence-level contour plots for the various pairs of the free parameters of the interacting scenario have been shown using the observational data CC $+$$H_0$$+$ JLA $+$ BAO $+$ CMB (Planck TT $+$ lowP). Additionally, we have also shown the 1-dimensional marginalized posterior distributions of individual free parameters. We note that $\Omega_{m0}= \Omega_{dm,0}+ \Omega_{b0}$.
• Figure 3: The effects on the CMB temperature power spectra for different values of the interaction parameter $\delta$. The black solid, red thick dashed, green dash-dot, and blue dotted lines are for $\delta=0, 0.00214, 0.05$, and $0.1$, respectively; the other relevant parameters are fixed with the mean values as shown in the third column of Table \ref{['tab:results']}. We note that the curves for $\delta=0$ (black solid) and $\delta = 0.00214$ (red thick dashed) are almost indistinguishable.
• Figure 4: The evolution for the ratio of matter and radiation $\Omega_m/\Omega_r$ (Here, $\Omega_m= \Omega_{dm}+ \Omega_b$) when the interaction parameter $\delta$ is varied. The different lines correspond to the cases of the Fig. \ref{['fig:CMBTTpower']}; the horizontal gray thick line responds to the case of $\Omega_m=\Omega_r$, and the other relevant parameters are fixed with the mean values as shown in the third column of Table \ref{['tab:results']}. We see that the curves for $\delta=0$ (black solid) and $\delta = 0.00214$ (red thick dashed) are almost indistinguishable
• Figure 5: The effects on the matter power spectra for different values of the interaction parameter $\delta$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\delta=0, 0.00214, 0.05$, and $0.1$, respectively; the other relevant parameters are fixed with the mean values as shown in the third column of Table \ref{['tab:results']}. Similar to the Figures \ref{['fig:CMBTTpower']} and \ref{['fig:OmOr']} we find that the curves for $\delta=0$ (black solid) and $\delta = 0.00214$ (red thick dashed) cannot be distinguished from each other.