  Oscillons are long-lived, localized excitations of nonlinear scalar fields
which may be copiously produced during preheating after inflation, leading to a
possible oscillon-dominated phase in the early Universe. For example, this can
happen after axion monodromy inflation, on which we run our simulations. We
investigate the stochastic gravitational wave background associated with an
oscillon-dominated phase. An isolated oscillon is spherically symmetric and
does not radiate gravitational waves, and we show that the flux of
gravitational radiation generated between oscillons is also small. However, a
significant stochastic gravitational wave background may be generated during
preheating itself (i.e, when oscillons are forming), and in this case the
characteristic size of the oscillons is imprinted on the gravitational wave
power spectrum, which has multiple, distinct peaks.
