  The trace-free version of the Einstein Gravitational equations, essentially
equivalent to unimodular gravity, can solve the troubling issue of the huge
discrepancy between quantum field theory estimates of the vacuum energy density
and the astronomically observed value of the cosmological constant. However it
has been suggested that this proposal cannot work because it prevents the
inflaton potential energy from driving inflation. It is shown here that that
concern is unjustified: inflation proceeds as usual if we adopt the trace free
gravitational equations.
