  We study the cosmological signatures of Invisibly Annihilating Dark Matter
(IAnDM), where DM annihilates into dark radiation particles that are decoupled
from the Standard Model (SM). In the simple benchmark model we consider here,
such invisible annihilation determines the relic abundance of DM via dark
thermal freeze-out. We demonstrate that IAnDM may reveal itself through
observable, novel signatures that are correlated: scale-dependent $\Delta
N_\text{eff}$ (number of extra effective neutrinos) in the Cosmic Microwave
Background (CMB) spectrum due to DM residual annihilation, while the phase of
acoustic peaks shifts towards the opposite direction relative to that due to SM
neutrinos, resembling the effect due to scattering (fluidlike) thermal dark
radiation; in addition, IAnDM induces modifications to the matter power
spectrum that resemble those due to warm dark matter. Current data are
sensitive to IAnDM with masses up to $\sim200$ keV, while future observations
will improve this reach, especially if the late-time DM annihilation cross
section is enhanced relative to the standard thermal value, which can be
realized in a variety of scenarios. This work also demonstrates a new
possibility of realizing thermal sub-MeV DM with observable signals.
