Peter Woit has a blog post which says in part: '... Science has a paper by Steinhardt and Turok promoting their cyclic cosmological model as explaining the small value of the cosmological constant, together with an article by Vilenkin criticizing them and promoting the anthropic point of view.'

On the small positive value of the CC see Phil Anderson’s comment on cosmic variance:

‘the flat universe is just not decelerating, it isn’t really accelerating’ - Prof. Phil Anderson, http://cosmicvariance.com/2006/01/03/danger-phil-anderson/#comment-10901

The point is that general relativity is probably not a complete theory of gravity, as it doesn’t have quantum field theory in it.

Assume Anderson is right, that gravity simply doesn’t decelerate the motion of distant supernovae.

What value of the CC does this predict quantitatively? Answer: the expansion rate without gravitational retardation is just Hubble’s law, which predicts the observed result to within experimental error! Hence the equivalent CC is predicted ACCURATELY.

(Although Anderson’s argument is that no real CC actually exists, a pseudo-CC must be fabricated to fit observation if you FALSELY assume that there is a gravitational retardation of supernovae naively given by Einstein’s field equation).

Theoretical explanation: if gravity is due to momentum from gauge boson radiation exchanged from the mass in the expanding universe surrounding the observer, then in the observer’s frame of reference a distant receding supernova geometrically can’t be retarded much.

The emphasis on theoretical predictions is important. I've shown that the correct quantum gravity dynamics (which predict G accurately) give the effective or AVERAGE radius of the gravity-causing mass around us (ie, the average range of the receding mass which is causing the gravity we experience) is (1 - e^-1)ct ~ 0.632ct ~ 10,000 million light-years in distance, where t is age of universe. Hence a supernova which is that distance from us, approximately 10,000 million light years away, is not affected at all by gravitational retardation (deceleration), as far as we - as observers of its motion - are concerned. (Half of the gravity-causing mass of the universe - as far as our frame of reference is concerned - is within a radius of 0.632ct of us, and half is beyond that radius. Hence the net exchange radiation gravity at that distance is zero. This calculation already has the red-shift correction built into it, since it is used to determine the 0.632ct effective radius.) This model in a basic form was predicted in 1996, two years before supernovae data confirmed it. Alas, bigots suppressed it, although it was sold via the October 1996 issue of Electronics World magazine.

This is a very important difference between the proper mechanism of gravity, which predicts the Einstein's field equation (Newton's law written in tensor notation with spacetime and a contraction term to keep the mass-energy conservation accurate) as a physical effect of exchange radiation caused gravitation!