Primordial universe with the running cosmological constant
  Theoretically, the running of the cosmological constant in the IR region is
not ruled out. On the other hand, from the QFT viewpoint, the energy released
due to the variation of the cosmological constant in the late universe cannot
go to the matter sector. For this reason, the phenomenological bounds on such a
running are not sufficiently restrictive. The situation can be different in the
early universe when the gravitational field was sufficiently strong to provide
an efficient creation of particles from the vacuum. We develop a framework for
systematically exploring this ossibility. It is supposed that the running
occurs in the epoch when the Dark Matter already decoupled and is expanding
adiabatically, while baryons are approximately massless and can be abundantly
created from vacuum due to the decay of vacuum energy. By using the handy model
of Reduced Relativistic Gas for describing the Dark Matter, we consider the
dynamics of both cosmic background and linear perturbations and evaluate the
impact of the vacuum decay on the matter power spectrum and to the first CMB
peak. Additionally, using the combined data of CMB+BAO+SNIa we find the best
fit values for the free parameters of our model.
