How Dark Sector Equations of State Govern Interaction Signatures

TL;DR

This study investigates how relaxing dark-sector equation-of-state assumptions affects the inferred interaction between dark energy and dark matter in IDE models. Using three coupling forms $Q=\beta H\rho_{\rm de}$, $Q=\beta H\rho_{\rm dm}$, and $Q=\beta H(\rho_{\rm dm}+\rho_{\rm de})$ along with three EoS scenarios ($w_{\rm de}=-1$, $w_{\rm dm}=0$; free $w_{\rm de}$, $w_{\rm dm}=0$; free $w_{\rm dm}$, $w_{\rm de}=-1$), the authors perform a late-time cosmological analysis using DESI DR2 BAO, DESY5 SNe, cosmic chronometers, strong-lensing time delays, and gamma-ray bursts, with $r_{\rm d}$ as a free parameter and marginalization over $M_{\rm B}$. They find that fixing $w_{\rm de}$ and $w_{\rm dm}$ yields a preference for energy transfer from dark energy to dark matter ($\beta<0$), but allowing $w_{\rm de}$ to vary largely removes this evidence by pushing $w_{\rm de}$ toward quintessence ($w_{\rm de}>-1$). When $w_{\rm dm}$ is freed, the interaction signal persists and exhibits a clear degeneracy: positive $w_{\rm dm}$ favors $\beta<0$ (DE→DM) while negative $w_{\rm dm}$ favors $\beta>0$ (DM→DE). Across coupling forms, AIC/DIC model comparison shows all IDE scenarios receive substantial support over $\Lambda$CDM, though the strength of evidence varies with the assumed EoS; the analysis underscores the need to consider nonstandard dark-sector physics when testing for dark sector interactions. The work highlights limitations of late-time data to break degeneracies and suggests future integration with CMB and other probes to robustly discern IDE signatures.

Abstract

Using late-Universe observations, we demonstrate that freeing dark energy and dark matter equations of state (EoS) dramatically alters the inferred strength and direction of their interactions. When dark sector EoS are fixed to $w_{\mathrm{de}}=-1$ and $w_{\mathrm{dm}}=0$, the data consistently favor an energy transfer from dark energy to dark matter across various interaction forms. This apparent evidence, however, proves highly sensitive to the EoS assumptions: treating $w_{\mathrm{de}}$ as a free parameter substantially weakens the evidence for interaction, with its value converging to the quintessence regime ($w_{\mathrm{de}}>-1$). In contrast, freeing $w_{\mathrm{dm}}$ maintains a preference for interaction, revealing a correlation where positive $w_{\mathrm{dm}}$ is associated with energy transfer from dark energy to dark matter, and negative $w_{\mathrm{dm}}$ with energy transfer from dark matter to dark energy. These findings caution against the simplistic assumption of $Λ$CDM EoS values when attempting to detect a possible interaction. Despite these fundamental degeneracies, model comparison using the Akaike and Deviance information criteria shows that all of the tested interacting dark energy scenarios receive substantial support over the $Λ$CDM model.

Figures (1)

• Figure 1: Analysis of interacting dark energy scenarios: observational constraints and statistical evidence. Left: Marginalized joint constraints (68% confidence level) on the dark energy EoS parameter $w_{\mathrm{de}}$, dark matter EoS parameter $w_{\mathrm{dm}}$, and the interaction coupling parameter $\beta$. Results are shown for three interaction models: $Q = \beta H\rho_{\mathrm{de}}$ (circles), $Q = \beta H\rho_{\mathrm{dm}}$ (squares), and $Q = \beta H(\rho_{\mathrm{dm}} + \rho_{\mathrm{de}})$ (triangles). For each model, we present the constraints under three different parameter assumptions: freeing $w_{\mathrm{de}}$ (blue), freeing $w_{\mathrm{dm}}$ (red), and fixing both EoS to their standard $\Lambda$CDM values (black). The error bars on the data points represent the $1\sigma$ uncertainties. Right: Graphical representation of model comparison results. In this work, we choose flat $\Lambda$CDM model as a reference to calculate the $\Delta$AIC and $\Delta$DIC values. Generally, a negative $\Delta$AIC/DIC value within the range $[-2,0)$ indicates weak evidence in favor of the model, a value within $[-6, -2)$ indicates positive evidence in favor, a value within $[-10, -6)$ indicates strong evidence in favor, and a value less than $-10$ indicates very strong evidence in favor. The order of models from left to right is arranged according to the interaction form.