Running cosmological constant with observational tests
  We investigate the running cosmological constant model with dark energy
linearly proportional to the Hubble parameter, $\Lambda = \sigma H +
\Lambda_0$, in which the $\Lambda$CDM limit is recovered by taking $\sigma=0$.
We derive the linear perturbation equations of gravity under the
Friedmann-Lema\"itre-Robertson-Walker cosmology, and show the power spectra of
the CMB temperature and matter density distribution. By using the Markov chain
Monte Carlo method, we fit the model to the current observational data and find
that $\sigma H_0/ \Lambda_0 \lesssim 2.63 \times 10^{-2}$ and $6.74 \times
10^{-2}$ for $\Lambda(t)$ coupled to matter and radiation-matter, respectively,
along with constraints on other cosmological parameters.
