If the universe was not expanding, would gravity be stronger? since the expansion happens everywhere and can overcome gravity at long distances? If not, then are there any changes that would happen to the universe if there was no expansion?
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Your question cannot be answered because ultimately it depends on experiment.
In general relativity the gravitational constant, $G$, is assumed constant and the geometry of spacetime is derived on this basis. At the moment observation suggests the metric we obtain using GR is a good description of the universe (provided you believe in dark energy), so the evidence is that the constant $G$ is indeed constant. Your observation:
the expansion happens everywhere and can overcome gravity at long distances
arises naturally from GR and doesn't require us to make $G$ change with time.
John Rennie
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