general relativity - Friedmann Equations with varying G?

If Newton's constant $G$ actually varies with cosmological time $t$ would a suitably modified form of the Einstein field equations:

$$G_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G(t)}{c^4} T_{\mu \nu},$$

together with the standard cosmological assumptions, lead to equations that look like the standard Friedmann equations but with the varying function $G(t)$ in place of the constant $G$?