Asymptotically Safe gravity and non-singular inflationary Big Bang with
  vacuum birth
  General non-singular 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 Renormalisation
Group flow of Asymptotic Safety scenario near the ultraviolet fixed point. In
this scenario, 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 allow for particle production and
entropy generation. Alternatively, in the case of non-zero 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.
