A Mechanism for Cosmological Redshift.

Fascinating stuff, and very elegant in its simplicity. I was suspicious of the maths at first but using your approach I come out with 1.136X10^30m. I suppose the only area I'd be concerned with is G which has been the subject of intense experimental testing recently, with variations of up to 0.7%, not significant enough to make a major difference in the result though. One question - is the assumption of 1/f^3 tying in with 3-dimensionality valid (i.e. beyond an intuitive assumption)? Also, okay, two questions(!), has the 1/f noise inherent in the detection equipment been cancelled out (not sure if this would impact on the actual data?)?

If the density of the universe is 1 proton per cubic meter all the mass is in stars and galaxies. The IGM is much denser than this. Lyman Alpha Forest models have the density at ~100,000 p/m3 or so.

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I suppose the only area I'd be concerned with is G which has been the subject of intense experimental testing recently, with variations of up to 0.7%, not significant enough to make a major difference in the result though.
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This must be important per se. It demonstrates that GR is a p*ss-poor model of reality because the "spacetime" readily falls apart.
Yet I have a suspicion that the greater the masses - the more constant G might become (at least as partial dependence). While there's no quantification of the effect within a (non-existent yet) theory, I use whatever we've got.
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One question - is the assumption of 1/f^3 tying in with 3-dimensionality valid (i.e. beyond an intuitive assumption)?
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I infer 1/f^3 from the graphs I see.
Intuition further goes like this - consider two dust particles suspended in hot gas, the distance between them grows as sqrt(time), average momentum contained in a thin cylindric volume connecting them grows as <b>sqrt(time)</b>, average momentum contained in a circular plate defined by them (as centre and radius) grows as <b>(time)</b>, average momentum contained in a sphere defined by them (as centre and radius) grows as <b>(time)^3/2</b>. The average non-balance energy derived from that random momentum fluctuation grows as momentum squared, thus that energy density grows as <b>(time)^3</b>, hence it's spectral density must be <b>1/f^3</b>.
That's how I intuitively connect dimensionality and the power index of 1/f.
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...has the 1/f noise inherent in the detection equipment been cancelled out (not sure if this would impact on the actual data?)?
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The cosmic noise at low frequencies is really strong, furthermore the equipment noise is 1/f rather than 1/f^3, and it's easy to calibrate out by shielding the antenna.
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[from Jim]
If the density of the universe is 1 proton per cubic meter all the mass is in stars and galaxies. The IGM is much denser than this. Lyman Alpha Forest models have the density at ~100,000 p/m3 or so.
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The 10^5 factor you quote is not enough to provide a gravitational redshift close to the necessary figure, yet absorption and scattering would be huge. Though, I can imagine some very special matter distributions that would do the trick. Yet I think those models must work mostly for the internal redshifts of the relevant sources (like quasars).

One more idea for non-constancy of G -
Most of those measurements use torsion pendulum oscillating schemes to calculate G from the period of oscillations. This means that the "rate" of time is involved in deriving the result. So we have gravity and time intertwined through "spacetime" concept and elasticity of the suspension of torsion pendulum that is not so "rate-of-time"-dependent. If we assume a possibility of random very slowly changing potential (massive) field permeating our space, we'd get exactly the kind of effect observed. Thus, by extending the "non-thermal cosmic background" radiation 1/f^3 component to the ULF/ELF/VLF band and below, we get exactly the field capable to account for the result.

The gravity required for the observed redshift is one nanometer per second per second and how much matter is needed to get that?

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The gravity required for the observed redshift is one nanometer per second per second and how much matter is needed to get that?
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About 10^27 protons per m^3 assuming even distribution and 10^26 m visible universe. The formula for radius is <b>R=sqrt[(3c^2)/{4(pi)G(rho)}]</b>, where (rho) is density.