  The primordial fluctuations on large scales are adiabatic, but on smaller
scales this need not be the case. Here we derive the general analytical
framework to compute the stochastic gravitational wave background induced by
primordial cold dark matter isocurvature fluctuations on small scales. We find
that large isocurvature fluctuations can yield an observable gravitational wave
signal, with a spectrum distinct from the one induced by adiabatic
perturbations, and we provide for the first time the exact analytic expression
of the kernel necessary to compute this signal. We then forecast the
constraining power of future gravitational wave detectors on dark matter
isocurvature on small scales and find they will dramatically improve on
existing constraints.
