  In our previous paper, we have presented a covariant BRST quantization of
unimodular gravity which may account for the smallness of the cosmological
constant, and have shown that the physical degrees of freedom in the theory are
the same as general relativity. The formulation has been given by using rank-2
antisymmetric tensor fields for both ghosts and antighosts. Here we give an
alternative formulation using a vector field for the antighost but keeping the
same structure for the ghosts. This gives a significantly simpler covariant
quantization with less ghosts and no tripole modes in the ghost sector. We show
that this also gives only two physical transverse modes as in general
relativity.
