  The flavor symmetry-breaking scale in the Froggatt-Nielsen (FN) mechanism is
very weakly constrained by present experiments, and can lie anywhere from a few
TeV to the Planck scale. We construct two minimal, non-supersymmetric,
ultraviolet (UV) complete models that generate the FN mechanism, with a global
$U(1)_{\rm{FN}}$ flavor symmetry and a single flavon field. Using the one-loop
finite temperature effective potential, we explore the possibility of a strong
first order phase transition (SFOPT) induced by the flavon. We show that if the
flavor symmetry-breaking occurs at intermediate scales $\sim 10^4-10^7$ GeV,
then in certain regions of the parameter space, the associated stochastic
gravitational wave (GW) background is strong enough to be detected by second
generation GW observatories such as the Big Bang Observer (BBO), the Deci-hertz
interferometer Gravitational Observatory (DECIGO), the Cosmic Explorer (CE) and
the Einstein Telescope (ET). We identify viable regions of the parameter space
for the best detection prospects. While both models of flavor can produce a
detectable GW background, the GW signature cannot be used to discriminate
between them.
