Holographic Dark Energy with Cosmological Constant
  Inspired by the multiverse scenario, we study a heterotic dark energy model
in which there are two parts, the first being the cosmological constant and the
second being the holographic dark energy, thus this model is named the
$\Lambda$HDE model. By studying the $\Lambda$HDE model theoretically, we find
that the parameters $d$ and $\Omega_{hde}$ are divided into a few domains in
which the fate of the universe is quite different. We investigate dynamical
behaviors of this model, and especially the future evolution of the universe.
We perform fitting analysis on the cosmological parameters in the $\Lambda$HDE
model by using the recent observational data. We find the model yields
$\chi^2_{\rm min}=426.27$ when constrained by $\rm Planck+SNLS3+BAO+HST$,
comparable to the results of the HDE model (428.20) and the concordant
$\Lambda$CDM model (431.35). At 68.3\% CL, we obtain
$-0.07<\Omega_{\Lambda0}<0.68$ and correspondingly $0.04<\Omega_{hde0}<0.79$,
implying at present there is considerable degeneracy between the holographic
dark energy and cosmological constant components in the $\Lambda$HDE model.
