Differentiating the gravitational redshift and the cosmological redshift?

Question

If general relativity accounts for a redshift, independent of inflation, how can we still know that inflation is viable? Moreover, how do we differentiate the the gravitational redshift and the cosmological redshift observationally?

Answer 1

The cosmologial redshift only requires expansion, not inflation.

There is no way to distinguish just from observing the light of a single object how much of the shift is cosmological, gravitational or Doppler (peculiar motion).

However, given that in all directions the red shift is increasing rather uniformly with distance, expansion seems like the only explanation. To be all gravitational, the objects would need to be uniformly at lower gravitation potential as distance from Earth increases.

See this Stanford link for more infomation: http://einstein.stanford.edu/content/relativity/a11859.html

Answer 2

Back of the envelope calculation for others to check: z= ∆U/c^2 (https://en.wikipedia.org/wiki/Gravitational_redshift), U is the gravitational potential energy. Since ∆U=gh, where h is the distance/height from a massive body, we get; z = (g/c^2) h. To translate to the Hubble form, use Fizu-Doppler formula; z=v/c, and get the recession-phase shift(due to gravity) relation; v = (g/c) h; giving a Hubble constant; H0=g/c. That is the phase shift due to gravity is proportional to the distance away from a mass- to first approximation and similar to what Hubble found. Using the universe values of M=1.5e53 kg, and r=4.4e26 m; we have g=5.168e-11 m/s^2. Divide by c as in the formula and get; H0=1.7239e-19 /s- the same order as the experimental value of the constant. That is to say; a more travelling distance causes more energy loss due to the potential climbing against the pull of all the masses in the universe. I am treating massless photons like normal massive particles in the present case. This can be concluded from Galileo Pisa tower experiment showing that acceleration is independent of mass which is in effect the equivalence principle. This can then be extended down to massless particles. So that photons bend when passing the sun, and get red shifter when leaving earth and blue shifted when the come down. This is also the basis used by Newton to calculate light beam bending by massive objects.