Coupled dark energy with perturbed Hubble expansion rate

TL;DR

This work investigates a phenomenological coupling between dark energy and dark matter where the energy transfer scales with the Hubble rate and dark-energy density, incorporating perturbations to the expansion rate via $H=\bar{H}+\delta H$. The authors derive the full background and perturbation equations in the rest frames of the dark components, and perform a joint Planck+WMAP9, BAO, SNIa, and RSD likelihood analysis using CAMB/CosmoMC. They find the interaction rate $\xi_x$ is tightly constrained to the $\mathcal{O}(10^{-3})$ level for both rest-frame choices, with perturbed-$H$ effects contributing negligibly to the parameter space. The growth-rate observable $f\sigma_8(z)$ is particularly sensitive to $\xi_x$, helping to break degeneracies, though distinguishing the perturbed-$H$ scenario from the unperturbed one remains difficult in practice.

Abstract

The coupling between dark sectors provides a possible 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 proportional the Hubble parameter and energy density of dark energy, that is, $\bar{Q}=3ξ_x\bar{H}\barρ_x$. Particularly, we consider the Hubble expansion rate to be perturbed in the perturbation evolutions of dark sectors. Using jointing data sets which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and redshift-space distortions, we perform a full Monte Carlo Markov Chain likelihood analysis for the coupled model. The results show that the mean value with errors of interaction rate is: $ξ_x=0.00305_{-0.00305-0.00305-0.00305}^{+0.000645+0.00511+0.00854}$ for $Q^μ_A\parallel u^μ_c$; $ξ_x=0.00317_{-0.00317-0.00317-0.00317}^{+0.000628+0.00547+0.00929}$ for $Q^μ_A\parallel u^μ_x$, which means that the recently cosmic observations favored small interaction rate which is up to the order of $10^{-3}$. Moreover, in contrast to the coupled model with unperturbed expansion rate, we find perturbed Hubble expansion rate could bring about negligible impact on the model parameter space.

Figures (5)

• Figure 1: (a). The effects on CMB temperature power spectra for different values of interaction rate $\xi_x$ ($Q^{\mu}_A\parallel u^{\mu}_c$). The black solid, cyan thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00305, 0.1$, and $0.2$, respectively; the other relevant parameters are fixed with the mean values as shown in the third column of Table \ref{['tab:results-mean-ucdh']}; the three thin red solid lines are the corresponding ones for the coupled model with unperturbed $H$ for $Q^{\mu}\parallel u^{\mu}_{(c)}$; (b). The corresponding evolutions for $Q^{\mu}_A\parallel u^{\mu}_x$, the relevant values of parameters is from Table \ref{['tab:results-mean-uxdh']}; the three thin red lines correspond to ones for the coupled model with unperturbed $H$ for $Q^{\mu}\parallel u^{\mu}_{(x)}$.
• Figure 2: (a). The effects on matter power spectra for different values of interaction rate $\xi_x$ ($Q^{\mu}_A\parallel u^{\mu}_c$). The black solid, cyan thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00305, 0.1$, and $0.2$, respectively; the other relevant parameters are fixed with the mean values as shown in the third column of Table \ref{['tab:results-mean-ucdh']}; the three thin red solid lines are the corresponding ones for the coupled model with unperturbed $H$ for $Q^{\mu}\parallel u^{\mu}_{(c)}$; (b). The corresponding evolutions for $Q^{\mu}_A\parallel u^{\mu}_x$, the relevant values of parameters is from Table \ref{['tab:results-mean-uxdh']}; the three thin red lines correspond to ones for the coupled model with unperturbed $H$ for $Q^{\mu}\parallel u^{\mu}_{(x)}$.
• Figure 3: (a). The fitting evolutionary curves of $f\sigma_8(z)$ about the redshift $z$ for varied interaction rate $\xi_x$ ($Q^{\mu}_A\parallel u^{\mu}_c$). The black solid, cyan thick dashed, green dotted-dashed, and blue dotted lines are for $\xi_x=0, 0.00305, 0.01$, and $0.02$, respectively; the gray error bars denote the observations of $f\sigma_8(z)$ at different redshifts are listed in Table \ref{['tab:fsigma8data']}; the other relevant parameters are fixed with the mean values as shown in the third column of Table \ref{['tab:results-mean-ucdh']}; the three thin red solid lines are the corresponding ones for the coupled model with unperturbed $H$ for $Q^{\mu}\parallel u^{\mu}_{(c)}$; (b). The corresponding evolutions for $Q^{\mu}_A\parallel u^{\mu}_x$, the relevant values of parameters is from Table \ref{['tab:results-mean-uxdh']}; the three thin red lines correspond to ones for the coupled model with unperturbed $H$ for $Q^{\mu}\parallel u^{\mu}_{(x)}$.
• Figure 4: For the case of $Q^{\mu}_A\parallel u^{\mu}_c$, the 1D marginalized distributions on individual parameters and 2D contours with 68% C.L., 95 % C.L., and 99.7% C.L. between each other using the combination of the observed data points from the CMB from Planck + WMAP9, BAO, SNIa, and RSD data sets.
• Figure 5: For the case of $Q^{\mu}_A\parallel u^{\mu}_x$, the 1D marginalized distributions on individual parameters and 2D contours with 68% C.L., 95 % C.L., and 99.7% C.L. between each other using the combination of the observed data points from the CMB from Planck + WMAP9, BAO, SNIa, and RSD data sets.