Can vacuum decay in our Universe?
  We take a phenomenological approach to study the cosmological evolution of decaying vacuum cosmology ($\Lambda(t)$CDM) based on a simple assumption about the form of the modified matter expansion rate. In this framework, almost all the current vacuum decaying models can be unified in a simple manner. We argue that the idea of letting vacuum decay to resolve the fine-tuning problem is inconsistent with cosmological observations. We also discuss some issues in confronting $\Lambda(t)$CDM with observation. Using the effective equation of state formalism, we indicate that $\Lambda(t)$CDM is a possible candidate for phantom cosmology. Moreover, confronted with a possible trouble of effective equation of state formalism, we construct the effect dark energy density. Finally, we discuss the evolution of linear perturbation. 
Peng Wang, Xin-He Meng (Nankai U.)