Running coupling: Does the coupling between dark energy and dark matter
  change sign during the cosmological evolution?
  In this paper we put forward a running coupling scenario for describing the
interaction between dark energy and dark matter. The dark sector interaction in
our scenario is free of the assumption that the interaction term $Q$ is
proportional to the Hubble expansion rate and the energy densities of dark
sectors. We only use a time-variable coupling $b(a)$ (with $a$ the scale factor
of the universe) to characterize the interaction $Q$. We propose a
parametrization form for the running coupling $b(a)=b_0a+b_e(1-a)$ in which the
early-time coupling is given by a constant $b_e$, while today the coupling is
given by another constant, $b_0$. For investigating the feature of the running
coupling, we employ three dark energy models, namely, the cosmological constant
model ($w=-1$), the constant $w$ model ($w=w_0$), and the time-dependent $w$
model ($w(a)=w_0+w_1(1-a)$). We constrain the models with the current
observational data, including the type Ia supernova, the baryon acoustic
oscillation, the cosmic microwave background, the Hubble expansion rate, and
the X-ray gas mass fraction data. The fitting results indicate that a
time-varying vacuum scenario is favored, in which the coupling $b(z)$ crosses
the noninteracting line ($b=0$) during the cosmological evolution and the sign
changes from negative to positive. The crossing of the noninteracting line
happens at around $z=0.2-0.3$, and the crossing behavior is favored at about
1$\sigma$ confidence level. Our work implies that we should pay more attention
to the time-varying vacuum model and seriously consider the phenomenological
construction of a sign-changeable or oscillatory interaction between dark
sectors.
