  We introduce and study a model designed to simultaneously shed light on the
mysteries connected with Baryogenesis, Dark Matter and Dark Energy. The model
describes a self-interacting complex axion field whose imaginary part, a
pseudo-scalar axion, couples to the instanton density of gauge fields including
the hypermagnetic field. This coupling may give rise to baryogenesis in the
early universe. After tracing out the gauge and matter degrees of freedom, a
non-trivial effective potential for the angular component of the axion field is
obtained. It is proposed that oscillations of this component around a minimum
of its effective potential can be interpreted as Dark Matter. The absolute
value of the axion field rolls slowly towards $0$. At late times, it can give
rise to Dark Energy.
