  We show that observations of primordial gravitational waves of inflationary
origin can shed light into the scale of flavor violation in a flavon model
which also explains the mass hierarchy of fermions. The energy density stored
in oscillations of the flavon field around the minimum of its potential
redshifts as matter and is expected to dominate over radiation in the early
universe. At the same time, the evolution of primordial gravitational waves
acts as bookkeeping to understand the expansion history of the universe.
Importantly, the gravitational wave spectrum is different if there is an early
flavon dominated era compared to radiation domination expected from a standard
cosmological model and this spectrum gets damped by the entropy released in
flavon decays, determined by the mass of the flavon field $m_S$ and new scale
of flavor violation $\Lambda_{\rm FV}$. We derive analytical expressions of the
frequency above which the spectrum is damped, as-well-as the amount of damping,
in terms of $m_S$ and $\Lambda_{\rm FV}$. We show that the damping of the
gravitational wave spectrum would be detectable at BBO, DECIGO, U-DECIGO,
$\mu-$ARES, LISA, CE and ET detectors for $\Lambda_{\rm FV}=10^{5-10}$ GeV and
$m_S=\mathcal{O({\rm TeV})}$. Furthermore, the flavon decays can source the
baryon asymmetry of the universe. We identify the $m_S-\Lambda_{\rm FV}$
parameter space where the observed baryon asymmetry $\eta \sim 10^{-10}$ is
produced and can be tested by gravitational wave detectors like LISA and ET. We
also discuss our results in the context of the recently measured stochastic
gravitational background signals by NANOGrav.
