  Recently, a new minimal extension of the Standard Model has been proposed,
where a spontaneously broken, flavor-dependent global U(1) symmetry is
introduced. It not only explains the hierarchical flavor structure in the quark
and lepton sector, but also solves the strong CP problem by identifying the
Nambu-Goldstone boson as the QCD axion, which we call flaxion. In this work, we
consider supersymmetric extensions of the flaxion scenario. We study the CP and
flavor violations due to supersymmetric particles, the effects of R-parity
violations, the cosmological gravitino and axino problems, and the cosmological
evolution of the scalar partner of the flaxion, sflaxion. We also propose an
attractor-like inflationary model where the flaxion multiplet contains the
inflaton field, and show that a consistent cosmological scenario can be
obtained, including inflation, leptogenesis, and dark matter.
