  We present a novel mechanism for gravitational wave generation in the early
Universe. Light spectator scalar fields during inflation can acquire a
blue-tilted power spectrum due to stochastic effects. We show that this effect
can lead to large curvature perturbations at small scales (induced by the
spectator field fluctuations) while maintaining the observed, slightly
red-tilted curvature perturbations at large cosmological scales (induced by the
inflaton fluctuations). Along with other observational signatures, such as
enhanced dark matter substructure, large curvature perturbations can induce a
stochastic gravitational wave background (SGWB). The predicted strength of SGWB
in our scenario, $\Omega_{\rm GW}h^2 \simeq 10^{-20} - 10^{-15}$, can be
observed with future detectors, operating between $10^{-5}$ Hz and 10 Hz. We
note that, in order to accommodate the newly reported NANOGrav observation, one
could consider the same class of spectator models. At the same time, one would
need to go beyond the simple benchmark considered here and consider a regime in
which a misalignment contribution is also important.
