Post-$Planck$ constraints on interacting vacuum energy

TL;DR

This work tests whether a covariant interacting vacuum energy model, effectively a decomposed generalized Chaplygin gas with a single interaction parameter $α$ and zero DM sound speed, can reconcile Planck CMB observations with low-redshift measurements. The background evolution mirrors GCG dynamics, while perturbations are engineered to avoid DM instabilities by enforcing geodesic DM flow. Using Planck+WP, WMAP9, SN Ia Union2.1, BAO, and RSD data, the study finds that CMB data alone poorly constrain $α$ due to degeneracies, but the inclusion of growth measurements drives a negative $α$ at about the 2σ level when all data are combined, with planck+WP+Union2.1+BAO+RSD yielding $α=-0.043^{+0.019}_{-0.020}$ (1σ) and $α\in[-0.083,-0.006]$ (95% CL). While negative $α$ can alleviate RSD–$\Lambda$CDM tensions, it does not resolve the Planck–HST $H_0$ discrepancy, indicating only modest departures from $\Lambda$CDM are favored. The results highlight the potential for interacting-vacuum models to modify structure growth while leaving background dynamics largely similar to $\Lambda$CDM.

Abstract

We present improved constraints on an interacting vacuum model using updated astronomical observations including the first data release from Planck. We consider a model with one dimensionless parameter, $α$, describing the interaction between dark matter and vacuum energy (with fixed equation of state $w=-1$). The background dynamics correspond to a generalised Chaplygin gas cosmology, but the perturbations have a zero sound speed. The tension between the value of the Hubble constant, $H_0$, determined by Planck data plus WMAP polarisation (Planck+WP) and that determined by the Hubble Space Telescope (HST) can be alleviated by energy transfer from dark matter to vacuum ($α>0$). A positive $α$ increases the allowed values of $H_0$ due to parameter degeneracy within the model using only CMB data. Combining with additional datasets of including supernova type Ia (SN Ia) and baryon acoustic oscillation (BAO), we can significantly tighten the bounds on $α$. Redshift-space distortions (RSD), which constrain the linear growth of structure, provide the tightest constraints on vacuum interaction when combined with Planck+WP, and prefer energy transfer from vacuum to dark matter ($α<0$) which suppresses the growth of structure. Using the combined datasets of Planck+WP+Union2.1+BAO+RSD, we obtain the constraint on $α$ to be $-0.083<α<-0.006$ (95% C.L.), allowing low $H_0$ consistent with the measurement from 6dF Galaxy survey. This interacting vacuum model can alleviate the tension between RSD and Planck+WP in the $Λ$CDM model for $α<0$, or between HST measurements of $H_0$ and Planck+WP for $α>0$, but not both at the same time.

Figures (12)

• Figure 1: The time evolution of the effective EoS of dark energy for different $\alpha$ values.
• Figure 2: The time evolution of $f_{\rm \textcolor{black}{m}}$ for different $\alpha$ values, with the same value of $\Omega_m$ today.
• Figure 3: Upper panel: time evolution of $f_{\rm \textcolor{black}{m}}(z)\sigma_8(z)$ for different values of $\alpha$, with the same value of $\Omega_m$ today. The points with error bars are the observational data Percival:2004JunBlake:2011AprSamushia:2011FebReid:2012MarBeutler:2012Apr, summarized in Ref. Samushia:2012Jun; Lower panel: predictions for $\sigma_8$ with the interaction parameter, $\alpha$, at the given redshifts.
• Figure 4: Upper panel: CMB TT(top), EE(middle) and TE(bottom) power spectra for $\alpha=0.3$ (blue) and $\Lambda$CDM (black) models; Lower panel: the ratio of $\theta_{\ast}$ between the $\Lambda$CDM model and interacting vacuum model as a function of $\alpha$.
• Figure 5: The 1D marginalized distributions of $H_0$ for the $\Lambda$CDM model and interacting vacuum (represented by "IV" for short in the plot) model from the constraints of only CMB data: WMAP9 and Planck+WP. The grey band corresponds to the direct measurement of $H_0$ from HST at the 68% C.L. The cyan band is the $1\,\sigma$ range of $H_0$ measured by 6dF Galaxy Survey.