= Solution
\b[Yes.] <Synchronous gauge in cosmology> uses freely falling time lines and sets the lapse and shift perturbations to zero, so no gravitational-potential force appears explicitly in this component of momentum conservation. Metric perturbations still affect the other field equations, the evolution of matter variables, and the relation between coordinate-dependent variables and gauge-invariant observables; synchronous gauge also retains residual gauge modes.
In <Newtonian gauge in cosmology>, the time-time metric perturbation is a Newtonian gravitational potential. Its spatial <gradient> therefore appears explicitly as a force term in the <Euler equations for an inviscid fluid>[Euler equation]. The difference is a coordinate representation of the same covariant conservation law.
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