Red shift and the maths for gravity

[trevor white]

I have looked but do not seem to be able to pin down how Hubble's Constant deals with Gravity. Is it considered as Newtonian or Einstein special theory?

 

[Bandersnatch]

It's unclear on what level you want the answer. You've selected 'A', but the wording of your question suggests you're new to the subject.

Anyway, Friedmann equations are derived from Einstein's field equations (so they're general relativistic). With some fudging they can be derived using Newtonian mechanics. Details here:
http://diposit.ub.edu/dspace/bitstream/2445/59759/1/TFG-Arnau-Romeu-Joan.pdf

 

[trevor white]

that was interesting and you are right should not have been A. Although maybe not as that was part of the answer I was looking for. The assumption in this maths appears to indicate a bias towards an expanding universe which though interesting brings me to my next question. This does not appear to treat gravity as a compounding factor in the red shift of light. would that be a correct assumption?

 

[berkeman]

(Changed thread prefix from A=Advanced/PhD level to I=Intermediate/Undergrad level)

 

[Bandersnatch]

The assumption in this maths appears to indicate a bias towards an expanding universe

I don't think that's a fair representation of what's going on in there.
You could say that there are two assumptions used in the derivation: 1) that General Relativity is to a good approximation an accurate theory of gravity, and 2) that the large scale universe is homogeneous and isotropic.
Both assumptions are well-founded in observations, so it's not like we've got much choice there.

Solving the relativistic equations for a homogeneous and isotropic distribution of energy, it is found that there are no static solutions, so the universe has to either expand or contract. Expansion leads to redshift, contraction leads to blueshift.
Again, observations constrain our choices in this matter.

So I'm not sure I know what you mean by bias. Expansion is the conclusion resulting from application of existing knowledge. If you still disagree, please be more specific and point out where you see the bias.

This does not appear to treat gravity as a compounding factor in the red shift of light.

Compounding in what way? Since redshift is a necessary result of expansion, and expansion (or contraction) is the large-scale behaviour of matter whose dynamics are governed by gravity, then one could say with some degree of accuracy that redshift is the result of gravity. I.e., gravity is why there's the redshift in the first place.

Unless you mean here local effects of gravity, such as gravitational redshift e.g. when light has to climb out of a gravity well or the Integrated Sachs-Wolfe effect. Then no, these are not included, due to the assumption of homogeneity that was used in the derivation.
However, the former doesn't contribute, due to symmetry of the effect, while the latter is taken into account in more detailed treatments (it's also tiny in magnitude when compared to cosmological redshift).