  One of the best motivated hypotheses in cosmology states that most of the
matter in the universe is in the form of weakly-interacting massive particles
that decoupled early in the history of the universe and cooled adiabatically to
an extremely low temperature. Nevertheless, the finite temperature and horizon
scales at which these particles decoupled imprint generic signatures on their
small scales density fluctuations. We show that the previously recognized
cut-off in the fluctuation power-spectrum due to free-streaming of particles at
the thermal speed of decoupling, is supplemented by acoustic oscillations owing
to the initial coupling between the cold dark matter (CDM) and the radiation
field. The power-spectrum oscillations appear on the scale of the horizon at
thermal decoupling which corresponds to a mass scale of
\~10^{-4}*(T_d/10MeV)^{-3} solar masses for a CDM decoupling temperature T_d.
The suppression of the power-spectrum on smaller scales by the acoustic
oscillations is physically independent from the free-streaming effect, although
the two cut-off scales are coincidentally comparable for T_d~10MeV and a
particle mass of M~100GeV. The initial conditions for recent numerical
simulations of the earliest and smallest objects to have formed in the
universe, need to be modified accordingly. The smallest dark matter clumps may
be detectable through gamma-ray production from particle annihilation, through
fluctuations in the event rate of direct detection experiments, or through
their tidal gravitational effect on wide orbits of objects near the outer edge
of the solar system.
