I will talk about the cosmological consequences of Weyl anomalies arising from the renormalization of composite operators in a theory of gravity with a cosmological constant. Near two dimensions, the relevant anomaly can be computed explicitly using results from Liouville theory and leads to a non-local quantum effective action. The resulting quantum energy momentum tensor is also non-local and leads to a decaying vacuum energy in a homogeneous and isotropic expanding universe. I will discuss a generalization of these results to four dimensions and possible implications for inflation and de Sitter spacetime.