Probing the Coupling between Dark Components of the Universe

TL;DR

This work investigates a possible coupling between dark energy and dark matter by confronting two phenomenological models with current observations. It develops analytic background evolutions for a constant coupling ${\delta}$ and a redshift dependent coupling ${\delta}(z)$ controlled by a parameter ${\xi}$ via ${\rho_X}/{\rho_m} \propto a^{\xi}$, and then performs a joint likelihood analysis using 71 SNLS SNe Ia, the CMB shift parameter ${\cal R}$, and the BAO amplitude ${A}$. The results constrain the coupling strongly, with ${-0.08 < {\delta} < 0.03}$ for constant coupling and ${-0.4 < {\delta_0} < 0.1}$ for the varying case at 95% CL, while the best-fit tends toward negative coupling with ${w_X<-1}$; nevertheless the uncoupled ${\Lambda}$CDM model remains a good fit. The findings highlight that high redshift data, especially the CMB, are crucial to ruling out substantial energy transfer between dark sectors and suggest a mild preference for phantom-like behavior when coupling is allowed. These constraints can guide future work on dark sector interactions and inform upcoming surveys on their potential to tighten limits via perturbations.

Abstract

We place observational constraints on a coupling between dark energy and dark matter by using 71 Type Ia supernovae (SNe Ia) from the first year of the five-year Supernova Legacy Survey (SNLS), the cosmic microwave background (CMB) shift parameter from the three-year Wilkinson Microwave Anisotropy Probe (WMAP), and the baryon acoustic oscillation (BAO) peak found in the Sloan Digital Sky Survey (SDSS). The interactions we study are (i) constant coupling delta and (ii) varying coupling delta(z) that depends on a redshift z, both of which have simple parametrizations of the Hubble parameter to confront with observational data. We find that the combination of the three databases marginalized over a present dark energy density gives stringent constraints on the coupling, -0.08 < delta < 0.03 (95% CL) in the constant coupling model and -0.4 < delta_0 < 0.1 (95% CL) in the varying coupling model, where delta_0 is a present value. The uncoupled LambdaCDM model (w_X = -1 and delta = 0) still remains a good fit to the data, but the negative coupling (delta < 0) with the equation of state of dark energy w_X < -1 is slightly favoured over the LambdaCDM model.

Figures (5)

• Figure 1: Probability contours from the SNLS data only at 68.3%, 95.4% and 99.7% confidence levels in the ($w_X, \delta$) plane marginalized over $\Omega_{X0}$ with priors $\Omega_{X0}=0.72 \pm 0.04$ and $\delta<3$ in the constant coupling models. The horizontal and dashed lines represent the uncoupled "XCDM" models and the coupled $\Lambda$CDM models respectively, and their crossing point corresponds to the standard $\Lambda$CDM model. In this case we have the constraint $-1.78 <\delta<3$ (95% CL).
• Figure 2: Probability contours from the SNLS and BAO data in the ($w_X, \delta$) plane marginalized over $\Omega_{X0}$ without a prior for $\Omega_{X0}$ and with a prior $\delta<3$ in the constant coupling models. In this case we have the constraint $-1.73 < \delta <3$ (95% CL).
• Figure 3: Probability contours from the combination of SNLS, BAO and CMB data in the constant coupling models. The left panel shows observational contours in the ($w_X, \delta$) plane marginalized over $\Omega_{X0}$ without a prior for $\Omega_{X0}$, whereas the right panel shows contours in the ($\Omega_{X0}, \delta$) plane marginalized over $w_X$ with no prior for $w_X$. The best-fit model parameters correspond to $\delta=-0.03$, $w_X=-1.02$ and $\Omega_{X0}=0.73$ with $\chi^2=60.94$. In this case we have the constraint $-0.08 < \delta < 0.03$ (95% CL).
• Figure 4: Probability contours from the joint analysis of the SNLS, BAO and CMB data in the varying coupling models. The left panel shows observational contours in the $(w_X, \delta_0)$ plane marginalized over $\Omega_{X0}$ without prior for $\Omega_{X0}$, whereas the right panel shows contours in the ($\Omega_{X0}, \delta$) plane marginalized over $w_X$ without prior for $w_X$. The best-fit parameters correspond to $\delta=-0.11$, $w_X=-1.03$ and $\Omega_{X0}=0.73$ with $\chi^2=60.94$. In this case we have the constraint $-0.4 < \delta_0 < 0.1$ (95% CL).
• Figure 5: Probability contours in the varying coupling models in the $(w_X, \xi)$ plane marginalized over $\Omega_{X0}$. The line $\xi=-3w_X$ corresponds to the uncoupled models. In this case we have the constraint $2.66 < \xi < 4.05$ (95% CL).