  We investigate models that suggest that the vacuum energy decays into cold
dark matter (CDM) and into a homogeneous distribution of a thermalized cosmic
microwave background (CMB), which is characteristic of an adiabatic vacuum
energy decay into photons. We show that the density fluctuation spectrum
obtained from the CMB and galaxy distribution data agreement put strong limits
on the rate of decay of the vacuum energy. A vacuum energy decaying into CDM
increases its total density \rho, diluting (\delta \rho/\rho)^2. The observed
temperature fluctuations of the CMB photons (\delta T/T)^2 are approximately
proportional to CDM density fluctuations (\delta \rho/\rho)^2. In both case,
when evaluating (\delta \rho/\rho)^2 at the recombination era, its present
measured value must be increased by a factor F. Since the (\delta \rho/\rho)^2
derived from the CMB and galaxy distribution data agree to \sim 10%, the
maximum value for F is F_{\rm max}\aprox 1.1. Our results indicate that the
rate of the decay of the vacuum energy into CDM and CMB photons are extremely
small.
