  We present the initial conditions for a decaying cosmological perturbation
and study its signatures in the CMB anisotropies and matter power spectra. An
adiabatic decaying mode in presence of components which are not described as
perfect fluids (such as collisionless matter) decays slower than in a
perfect-fluid dominated universe and displays super-Hubble oscillations. By
including a correlated decaying mode with a red or a scale invariant spectrum,
the anisotropy pattern shows super-imposed oscillations before the first
Dopplear peak, while with a blue spectrum the amplitude of the secondary peaks
relative to the first one and the matter power spectrum can be altered. WMAP
first year data constrain the decaying to growing ratio of scale invariant
adiabatic fluctuations at the matter-radiation equality to less than 10%.
