  The stochastic gravitational wave (GW) background provides a fascinating
window to the physics of the very early universe. Beyond the nearly
scale-invariant primordial GW spectrum produced during inflation, a spectrum
with a much richer structure is typically generated during the preheating phase
after inflation (or after some other phase transition at lower energies). This
raises the question of what one can learn from a future observation of the
stochastic gravitational wave background spectrum about the underlying physics
during preheating. Recently, it has been shown that during preheating
non-perturbative quasi-stable objects like oscillons can act as strong sources
for GW, leading to characteristic features such as distinct peaks in the
spectrum. In this paper, we study the GW production from oscillons using
semi-analytical techniques. In particular, we discuss how the GW spectrum is
affected by the parameters that characterise a given oscillon system, e.g. by
the background cosmology, the asymmetry of the oscillons and the evolution of
the number density of the oscillons. We compare our semi-analytic results with
numerical lattice simulations for a hilltop inflation model and a KKLT
scenario, which differ strongly in some of these characteristics, and find very
good agreement.
