  A consistency condition of general relativity as an effective field theory in
Minkowskian background uniquely fixes the value of the cosmological constant.
In two-loop calculations, including the interaction of gravitons with matter
fields, it has been shown that this value of the cosmological constant leads to
vanishing vacuum energy, under the assumption that the energy-momentum tensor
of the gravitational field is given by the pseudotensor of Landau-Lifshitz's
classic textbook. Here, we demonstrate that this result also holds when the
self-interaction of a scalar field is taken into account. That is, our
two-loop-order calculation suggests that in an effective field theory of metric
and scalar fields, one arrives at a consistent theory with massless gravitons
if the cosmological constant is fixed from the condition of vanishing vacuum
energy. Vice versa, imposing the consistency condition in Minkowskian
background leads to a vanishing vacuum energy.
