  In this work, we interpret the 3-3-1-1 model when the B-L and 3-3-1 breaking
scales behave simultaneously as the inflation scale. This setup not only
realizes the previously-achieved consequences of inflation and leptogenesis,
but also provides new insights in superheavy dark matter and neutrino masses.
We argue that the 3-3-1-1 model can incorporate a scalar sextet, which induces
both small masses for the neutrinos via a combined type I and II seesaw and
large masses for the new neutral fermions. Additionally, all the new particles
have the large masses in the inflation scale. The lightest particle among the
W-particles that have abnormal (i.e., wrong) B-L number in comparison to those
of the standard model particles may be a superheavy dark matter as it is
stabilized by the W-parity. The dark matter candidate may be a Majorana
fermion, a neutral scalar, or a neutral gauge boson, which was properly created
in the early universe due to the gravitational effects on the vacuum or the
thermal production after cosmic inflation.
