Studying the decay of the vacuum energy with the observed density fluctuation spectrum

One of the major problems in cosmology today is to explain the observed acceleration of the universe. The present observational data are consistent with the simplest solution to this problem, which is based on the vacuum energy. A decaying vacuum energy is a very attractive solution. It could link the value of the present vacuum energy, that is accelerating the universe today, with the value that created the inflationary epoch in the past. We investigate here models that suggest that the vacuum energy decays into cold dark matter (CDM) and show that the density fluctuation spectrum obtained from the cosmic microwave background (CMB) data together with large galaxy surveys (e.g., the Sloan Digital Sky Survey), puts strong limits on the rate of decay of the vacuum energy. CDM produced by a decaying vacuum energy would dilute the density fluctuation spectrum, created in the primordial universe and observed with large galaxy surveys at low redshifts. Our results indicate that the decay rate of the vacuum energy into CDM is extremely small.