Testing coupled dark energy with large scale structure observation

TL;DR

This work investigates a coupled dark energy model with background energy transfer $Q=3H\xi_x\rho_x$ and a constant equation of state $w_x$, deriving the linear perturbation equations in the rest frame of dark energy and constraining the model using a joint data set that includes Planck+WMAP9 CMB, BAO, SNIa, and redshift-space distortion measurements via $f\sigma_8(z)$. The analysis shows that a small coupling on the order of $\xi_x\sim10^{-3}$ is favored by current observations, while RSD data help rule out larger couplings at $1\sigma$, and the growth history exhibits sensitivity to the interaction through modified $H_{\rm eff}$ and $G_{\rm eff}$. The $f\sigma_8(z)$ measurements prove especially powerful for breaking degeneracies with $w_x$ and distinguishing the coupled model from $\Lambda$CDM, though distinguishing between different momentum-transfer frames remains challenging. Overall, large-scale structure data provide a robust test of interacting dark energy and substantially tighten cosmological constraints, with future work planned to combine RSD with geometry tests in perturbed expansion scenarios.

Abstract

The coupling between the dark components provides a new approach to mitigate the coincidence problem of cosmological standard model. In this paper, dark energy is treated as a fluid with a constant equation of state, whose coupling with dark matter is $\bar{Q}=3Hξ_x\barρ_x$. In the frame of dark energy, we derive the evolution equations for the density and velocity perturbations. 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. The results show the interaction rate in 3$σ$ regions: $ξ_x=0.00328_{-0.00328-0.00328-0.00328}^{+0.000736+0.00549+0.00816}$, which means that the recently cosmic observations favor a small interaction rate which is up to the order of $10^{-2}$, meanwhile, the measurement of redshift-space distortion could rule out the large interaction rate in the 1$σ$ region.

Figures (7)

• Figure 1: The effects on the CMB temperature power spectra (left panel) and matter power spectra (right panel) for the different values of interaction rate $\xi_x$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00328, 0.2$, and $0.5$, respectively; the other relevant parameters are fixed with the mean values as shown in the fourth column of Table \ref{['tab:results-mean-uxpos']}. The gray dashed, dotted-dashed, and dotted lines are the corresponding ones for the coupled model with $Q^{\mu}\parallel u^{\mu}_{(c)}$ ($b=1$).
• Figure 2: Deviations from standard model of the effective Hubble parameter (left panel) and effective gravitational constant (right panel) for $\delta_c$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00328, 0.2$, and $0.5$, 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 fourth column of Table \ref{['tab:results-mean-uxpos']}. The gray dashed, dotted-dashed, and dotted lines are the corresponding ones for the coupled model with $Q^{\mu}\parallel u^{\mu}_{(c)}$ ($b=1$), where $\frac{\mathcal{H}_{eff}}{\mathcal{H}}|_{(b=1)}=1-3\xi_x\frac{\bar{\rho}_x}{\bar{\rho}_c}$ and $\frac{G_{eff}}{G}|_{(b=1)}=1+ 2\xi_x\frac{\bar{\rho}_{tot}}{\bar{\rho}_c}\frac{\bar{\rho}_x}{\bar{\rho}_c} \left[ \frac{\mathcal{H}'}{\mathcal{H}^2}+1-3w_x+3\xi_x\left(1+\frac{\bar{\rho}_x}{\bar{\rho}_c}\right) \right]$.
• Figure 3: The three-dimensional plots of $\ln k$ ($k$ is the wavenumber), $z$ (redshift), $f_m$ (growth rate of matter) for different ranges of the wavenumber. In the two panels, $\xi_x$ and the other relevant parameters are fixed with the mean values as shown in the fourth column of Table \ref{['tab:results-mean-uxpos']}.
• Figure 4: The evolutions for the growth rate of the matter for $k=0.065[hMpc^{-1}]$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00328, 0.2$, 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 fourth column of Table \ref{['tab:results-mean-uxpos']}. The gray dashed, dotted-dashed, and dotted lines are the corresponding ones for the coupled model with $Q^{\mu}\parallel u^{\mu}_{(c)}$ ($b=1$).
• Figure 5: The fitting evolutionary curves of $f\sigma_8(z)$ about the redshift $z$ for varied interaction rate $\xi_x$. The black solid, red thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00328, 0.01$, and $0.02$, respectively; the brown error bars denote the $f\sigma_8(z)$ observations at different redshifts, which are listed in Table \ref{['tab:fsigma8data']}; the other relevant parameters are fixed with the mean values as shown in the fourth column of Table \ref{['tab:results-mean-uxpos']}. The gray dashed, dotted-dashed, and dotted lines are the corresponding ones for the coupled model with $Q^{\mu}\parallel u^{\mu}_{(c)}$ ($b=1$).