Post-$Planck$ constraints on interacting vacuum energy
  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, $\alpha$, 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
($\alpha>0$). A positive $\alpha$ 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 $\alpha$.
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
($\alpha<0$) which suppresses the growth of structure. Using the combined
datasets of Planck+WP+Union2.1+BAO+RSD, we obtain the constraint on $\alpha$ to
be $-0.083<\alpha<-0.006$ (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 $\Lambda$CDM model for $\alpha<0$,
or between HST measurements of $H_0$ and Planck+WP for $\alpha>0$, but not both
at the same time.
