Soft synchronous gauge in the perturbative gravity

An attempt to directly use the synchronous gauge ([Formula: see text]) in perturbative gravity leads to a singularity at [Formula: see text] in the graviton propagator. This is similar to the singularity in the propagator for Yang–Mills fields [Formula: see text] in the temporal gauge ([Formula: see text]). There the singularity was softened, obtaining this gauge as the limit at [Formula: see text] of the gauge [Formula: see text], [Formula: see text]. Then the singularities at [Formula: see text] are replaced by negative powers of [Formula: see text], and thus we bypass these poles in a certain way. Now consider a similar condition on [Formula: see text] in perturbative gravity, which becomes the synchronous gauge at [Formula: see text]. Unlike the Yang–Mills case, the contribution of the Faddeev–Popov ghosts to the effective action is nonzero, and we calculate it. In this calculation, an intermediate regularization is needed, and we assume the discrete structure of the theory at short distances for that. The effect of this contribution is to change the functional integral measure or, for example, to add nonpole terms to the propagator. This contribution vanishes at [Formula: see text]. Thus, we effectively have the synchronous gauge with the resolved singularities at [Formula: see text], where only the physical components [Formula: see text] are active and there is no need to calculate the ghost contribution.