George,
That is what I don't know. In a recent course I took on tape there were mentioned a gravitational red shift but it was ignored during the part on quasars. In some 40 plus related popular titles that I have read it has never been quantified.
It is a necessary part of the theory of "Black Holes". ie. when the accelerations of gravity equal the speed of light no light, nor consequently energies, can escape; hence a "Black hole".
In 1919 Eddington went on an eclipse viewing trip to South Africa sanctioned by Einstein and reported quite confidently that light was affected by gravity.
There have been a number of other experiments that showed this. Einstein Crosses have been observed. Gravitational lensing of light has been observed. Radio frequencies have been shown to be distorted etc.
I consequently expect that this effect would be quantified in the literature somewhere. Since every photon that impinges on our recepters has in effect been falling towards the Earth, towards the sun, towards the solar system, towards the Milky Way, towards the local galactic group and so into potentially infinity.
In the last second before coming to our observations the light has been "red shifted" about five parts per 300,000,000. 300,000,000m represents the distance that light would travel if unimpeded. 300,000,000m + 5m represents the distance light would travel if 1/2 the accelerations due to Earths gravity were included. I will admit that this is a very rough outline. I need the calculus to work it out exactly.
But IF the light is shifted by this amount can you imagine what will happen if you calculate the total accellerations for the last 15,000,000,000 years.
The law of gravity indicates that the "force" is calculated as the inverse square of the distance. It does diminish rapidly!
This is how I have approached the problem. Figure out the accellerations at each radius. For instance at Earths radius from the sun the accelerations due to the sun is about 1,000,000 miles per day (90 days--90,000,000 miles or about 11 1/2 miles per second. So at midnight star light will have been red shifted to an observer on Earth roughly 11 1/2 parts per 186,000 miles.
Frankly I suspect that somebody more mathematically adept has already done this. If so; I'd like to know where it is published. If not then there is no justification for assuming a "Big Bang".
I could be all wet
but before I get the soap I like to find somebody who KNOWS
Perhaps the guy who adjusted the "fine tuning" on the Apollo missions radio would know. He doesn't seem to be here though
Second part is that if the red shift is gravitationally induced then local variations in the densities of mass would account for the anomalies where the shift is at odds with other measurements. There are plenty of them. Particularly around quasars. The gravitational red shift just works so well it excites my mechanical id