Nonsingular vacuum cosmologies with a variable cosmological term

We present a class of nonsingular cosmological models with a variable cosmological term described by the second-rank symmetric tensor Lambda(mu)(nu), evolving from Lambdadelta(mu)(nu) to lambdadelta(mu)(nu) with lambda < Lambda. All Lambda(mu)(nu)-dominated cosmologies belong to Lemaitre type models for an anisotropic perfect fluid. The expansion starts from a nonsingular non-simultaneous de Sitter bang, with A on the scale responsible for the earliest accelerated expansion, which is followed by an anisotropic Kasner type stage. For a certain class of observers these models can also be identified as Kantowski-Sachs models with regular R regions. For Kantowski-Sachs observers the cosmological evolution starts from horizons with a highly anisotropic 'null bang' where the volume of the spatial section vanishes. We study in detail the spherically symmetric case and consider the general features of cosmologies with planar and pseudospherical symmetries. Nonsingular Lambda(mu)(nu)-dominated cosmologies are Bianchi type I in the planar case and hyperbolic analogues of the Kantowski-Sachs models in the pseudospherical case. At late times all models approach a de Sitter asymptotic with small lambda.