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We present the class of regular homogeneous T-models with vacuum dark fluid,associated with a variable cosmological term. The vacuum fluid is defined bythe symmetry of its stress-energy tensor, i.e., its invariance under Lorentzboosts in a distinguished spatial direction (p_j=-\rho), which makes this fluidessentially anisotropic and allows its density to evolve. Typical features ofhomogeneous regular T-models are: the existence of a Killing horizon; beginningof the cosmological evolution from a null bang at the horizon; the existence ofa regular static pre-bang region visible to cosmological observers; creation ofmatter from anisotropic vacuum, accompanied by very rapid isotropization. Westudy in detail the spherically symmetric regular T-models on the basis of ageneral exact solution for a mixture of the vacuum fluid and dustlike matterand apply it to give numerical estimates for a particular model whichillustrates the ability of cosmological T-models to satisfy the observationalconstraints.

Regular homogeneous T-models with vacuum dark fluid