General nonsingular accelerating cosmological solutions for an initial cosmic period of pure vacuum birth era are derived. This vacuum era is described by a varying cosmological "constant" suggested by the renormalization group flow of asymptotic safety scenario near the ultraviolet fixed point. In this scenario, a natural exit from inflation to the standard decelerating cosmology occurs when the energy scale lowers and the cosmological constant becomes insignificant. In the following period where matter is also present, cosmological solutions with characteristics similar to the vacuum case are generated. Remarkably the set of equations allows for particle production and entropy generation. Alternatively, in the case of nonzero bulk viscosity, entropy production and reheating is found. As for the equations of motion, they modify Einstein equations by adding covariant kinetic terms of the cosmological constant which respect the Bianchi identities. An advance of the proposed framework is that it ensures a consistent description of both a quantum vacuum birth of the universe and a subsequent cosmic era in the presence of matter.
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