Cosmological constraints on interacting dark energy with redshift-space distortion after Planck data

TL;DR

The paper investigates an interacting dark energy model with a constant equation of state $w_x$ and a coupling $Q=3H\xi_x\rho_x$ to address the coincidence problem. By deriving the background and perturbation equations in a general gauge and implementing a stability criterion via the doom factor, the authors couple theory with observations using Planck+WMAP9, BAO, SNLS3, and redshift-space distortion data to constrain the model with an MCMC approach. They show that the coupling imprints on CMB and growth observables and, crucially, that redshift-space distortion data tighten the constraints on $\xi_x$, yielding a mean value around $\xi_x \approx 0.00372$ and disfavouring large interactions at 1$\sigma$. The results demonstrate the importance of combining geometry and large-scale structure data to probe dark sector interactions and set the stage for constraining other forms of dark energy–dark matter couplings. $Q=3H\xi_x\rho_x$ with $\xi_x>0$ remains compatible with current data but favors only a small coupling, highlighting the potential of $f\sigma_8(z)$ measurements in reducing parameter degeneracies.

Abstract

The interacting dark energy model could propose a effective way to avoid the coincidence problem. In this paper, dark energy is taken as a fluid with a constant equation of state parameter $w_x$. In a general gauge, we could obtain two sets of different perturbation equations when the momentum transfer potential is vanished in the rest frame of dark matter or dark energy. There are many kinds of interacting forms from the phenomenological considerations, here, we choose $Q=3Hξ_xρ_x$ which owns the stable perturbations in most cases. Then, according to the Markov Chain Monte Carlo method, we constrain the model by currently available cosmic observations which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and $fσ_8(z)$ data points from redshift-space distortion. Jointing the geometry tests with the large scale structure information, the results show a tighter constraint on the interacting model than the case without $fσ_8(z)$ data. We find the interaction rate in 3$σ$ regions: $ξ_x=0.00372_{-0.00372- 0.00372-0.00372}^{+0.000768+0.00655+0.0102}$. It means that the recently cosmic observations favor a small interaction rate between the dark sectors, at the same time, the measurement of redshift-space distortion could rule out a large interaction rate in the 1$σ$ region.

Figures (8)

• Figure 1: The effects on CMB temperature power spectra for the different values of interaction rate $\xi_x$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00372, 0.4$, and $2.0$, respectively; the gray vertical line is used to clearly look into the shift tendency of the first peak; the other relevant parameters are fixed with the mean values as shown in the fifth column of Table \ref{['tab:results-mean-pos']}.
• Figure 2: The evolutions for the ratio of dark fluid and radiation $\Omega_m/\Omega_r$ when the parameter $\xi_x$ is varied. The different lines correspond to the cases of the Fig. \ref{['fig:CMBpower-pos']}; 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 fourth column of Table \ref{['tab:results-mean-pos']}.
• Figure 3: The effects on matter power spectra for the different values of interaction rate $\xi_x$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00372, 0.4$, and $2.0$, respectively; the other relevant parameters are fixed with the mean values as shown in the fifth column of Table \ref{['tab:results-mean-pos']}.
• Figure 4: Deviations from standard model of the effective Hubble parameter (left panel) and effective Newton constant (right panel) for $\delta_c$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00372, 0.4$, and $2.0$, respectively; $\xi_x=0$ corresponds to the case of $\Lambda$CDM model; the other relevant parameters are fixed with the mean values as shown in the fifth column of Table \ref{['tab:results-mean-pos']}.
• Figure 5: The evolutions for the growth rate of dark matter. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00372, 0.2$, and $0.5$, respectively; $\xi_x=0$ corresponds to the case of standard model; the other relevant parameters are fixed with the mean values as shown in the fifth column of Table \ref{['tab:results-mean-pos']}.