  We calculate the production of a massive vector boson by quantum fluctuations
during inflation. This gives a novel dark-matter production mechanism quite
distinct from misalignment or thermal production. While scalars and tensors are
typically produced with a nearly scale-invariant spectrum, surprisingly the
vector is produced with a power spectrum peaked at intermediate wavelengths.
Thus dangerous, long-wavelength, isocurvature perturbations are suppressed.
Further, at long wavelengths the vector inherits the usual adiabatic, nearly
scale-invariant perturbations of the inflaton, allowing it to be a good dark
matter candidate. The final abundance can be calculated precisely from the mass
and the Hubble scale of inflation, H_I. Saturating the dark matter abundance we
find a prediction for the mass m = 10^-5 eV (10^14 GeV/H_I)^4. High-scale
inflation, potentially observable in the CMB, motivates an exciting mass range
for recently proposed direct detection experiments for hidden photon dark
matter. Such experiments may be able to reconstruct the distinctive, peaked
power spectrum, verifying that the dark matter was produced by quantum
fluctuations during inflation and providing a direct measurement of the scale
of inflation. Thus a detection would not only be the discovery of dark matter,
it would also provide an unexpected probe of inflation itself.
