Hubble expansion & Structure Formation in Time Varying Vacuum Models
  We investigate the properties of the FLRW flat cosmological models in which
the vacuum energy density evolves with time, $\Lambda(t)$. Using different
versions of the $\Lambda(t)$ model, namely quantum field vacuum, power series
vacuum and power law vacuum, we find that the main cosmological functions such
as the scale factor of the universe, the Hubble expansion rate $H$ and the
energy densities are defined analytically. Performing a joint likelihood
analysis of the recent supernovae type Ia data, the Cosmic Microwave Background
(CMB) shift parameter and the Baryonic Acoustic Oscillations (BAOs) traced by
the Sloan Digital Sky Survey (SDSS) galaxies, we put tight constraints on the
main cosmological parameters of the $\Lambda(t)$ scenarios. Furthermore, we
study the linear matter fluctuation field and the growth rate of clustering of
the above vacuum models. Finally, we derived the theoretically predicted
dark-matter halo mass function and the corresponding distribution of
cluster-size halos for all the models studied. Their expected redshift
distribution indicates that it will be difficult to distinguish the closely
resembling models (constant vacuum, quantum field and power-law vacuum), using
realistic future X-ray surveys of cluster abundances. However, cluster surveys
based on the Sunayev-Zeldovich detection method give some hope to distinguish
the closely resembling models at high redshifts.
