On 10/1/12 2:17 AM, Phillip Helbig---undress to reply wrote:

H^2 = \frac{8\pi G\rho}{3}

Thus the critical density is, by definition, 3H^2/(8\pi G) since the
value of the density is always the critical density in the Einstein-de
Sitter universe. So H(z) is proportional to the square root of the
density. (If lamnda and/or k are not zero, then the expression for H(z)
is of course more complicated.)

In a purely mathematical sense
critical density rho_c is proportional to H^2/G
and
critical density rho_c is proportional to H^2
if G is a constant.
but alternatively
critical density rho_c is proportional to H
if H/G is a constant.

As previously posted by Jonathan Thornburg,
lunar ranging in our local bound system indicates
(d^2G/dt^2)/G = (4 ± 5) * 10^{-15}/year^2
but this does not negate
a delta G in galactic cluster systems
in near equilibrium with expanding critical density rho_c.

http://arxiv.org/abs/1106.4052
states the traditional physics:

critical density rho_c is proportional to H^2
with G constant

but no attempt is made
in using this relationship
to dimensionally explain the Table C1 data
represented by the slope 1.91 ~ 2
graphed in Figure C1

that can be dimensionally explained by:

critical density rho_c is proportional to H
with H/G constant.