Observational constraint on the interacting dark energy models including the Sandage-Loeb test

TL;DR

This work investigates two phenomenological interacting dark energy models—the constant coupling model with a fixed δ and the varying coupling model with δ(z)—by combining SNIa, OHD, and CMB data with simulated Sandage-Loeb (SL) redshift-drift measurements to extend constraints to the high-redshift window z ≈ 2–5. The SL test markedly tightens parameter contours, reducing the allowed interaction strength and sharpening the reconstruction of δ(z); in the constant-coupling case, the interaction shifts toward a small negative value and remains close to zero at high z, while in the varying-coupling case δ(z) remains negative at low z and vanishes as z → ∞, with ξ around 3.1. Across both models, ΛCDM continues to fit the data well, but the coincidence problem remains severe, and phantom-like dark energy (w_X < -1) is slightly favored when SL data are included. The results demonstrate the critical role of high-redshift probes like the SL test for breaking degeneracies and tracking the evolution of dark-sector interactions.

Abstract

Two types of interacting dark energy models are investigated using the type Ia supernova (SNIa), observational $H(z)$ data (OHD), cosmic microwave background (CMB) shift parameter and the secular Sandage-Loeb (SL) test. We find that the inclusion of SL test can obviously provide more stringent constraint on the parameters in both models. For the constant coupling model, the interaction term including the SL test is estimated at $δ=-0.01 \pm 0.01 (1σ) \pm 0.02 (2σ)$, which has been improved to be only a half of original scale on corresponding errors. Comparing with the combination of SNIa and OHD, we find that the inclusion of SL test directly reduces the best-fit of interaction from 0.39 to 0.10, which indicates that the higher-redshift observation including the SL test is necessary to track the evolution of interaction. For the varying coupling model, we reconstruct the interaction $δ(z)$, and find that the interaction is also negative similar as the constant coupling model. However, for high redshift, the interaction generally vanishes at infinity. The constraint result also shows that the $Λ$CDM model still behaves a good fit to the observational data, and the coincidence problem is still quite severe. However, the phantom-like dark energy with $w_X<-1$ is slightly favored over the $Λ$CDM model.

Figures (7)

• Figure 1: Transition redshift $z_t$ at different interaction term $\delta$ with fixed $\Omega_{X0}=0.724$ and $w_X=-1.14$ for the constant coupling model.
• Figure 2: Transition redshift $z_t$ at different parameter $\xi$ for the varying coupling model.
• Figure 3: Comparison between the simulated $\Delta v$ over 10yr observational time and theoretical expectations of the evaluated (a) constant coupling model and (b) varying coupling model for different parameters. For the model (a), we change the interaction term $\delta$ and fix other parameters under best estimation by Guo et al. guo2007probing. For the model (b), we change the parameter $\xi$ and fix other parameters as best estimation by Cao et al. cao2011testing. The simulated data points with error bars are estimated by the equation (\ref{['velocity error']}) in the fiducial model.
• Figure 4: Contours correspond to 68.3%, 95.4% confidence levels and the marginalized probability distribution of $\delta$ with different data sets for the constant coupling model.
• Figure 5: Same as Figure \ref{['constant contour1']} but for different data sets.