I've taken a shot at checking whether a matter-only, flat FRW model with variable gravitational constant G(t) = G(to) (t / to) can match observations of luminosity distance DL versus redshift z.

As far as I could check, the prediction of the model works quite well:

DL = RH(to) (1 + z) Ln(1 + z)

where RH(to) = c / H(to) is the current Hubble radius, 4222 Mpc for H(to) = 71 km/(s Mpc)

Another advantage of the model is that it is based on setting the Hubble constant H(t) = 1 / t. Therefore it matches current observations that H(to) to = 1.

Details in

http://vargfrw.blogspot.com/