We investigate models that suggest that the vacuum energy could decay into cold dark matter (CDM) or into a homogeneous distribution of thermalized cosmic microwave background (CMB) photons. We show that the agreement of the density fluctuation spectra obtained from the CMB and galaxy distribution data puts strong limits on the rate of vacuum energy decay. A vacuum energy decaying into CDM increases the density of the CDM rho, diluting the CDM density fluctuations (<FONT FACE=Symbol>dr</FONT>/rho)². The temperature fluctuations of the CMB photons (deltaT/T)² are approximately proportional to (<FONT FACE=Symbol>dr</FONT>/rho)², at the recombination epoch. We define F as the predicted increase of (<FONT FACE=Symbol>dr</FONT>/rho)² (or (deltaT/T)²) at the recombination epoch. Since the present observed (<FONT FACE=Symbol>dr</FONT>/rho)² derived from the CMB and galaxy distribution data agree to ~ 10%, the maximum value for F is Fmax <FONT FACE=Symbol>@</FONT> 1.1. Our results indicate that the rate of decay of the vacuum energy into CDM or CMB photons is extremely small.
