Is the inverse-square law valid for all cosmological distances?

StateOfTheEqn

Among the three Friedmann models k=-1,0,+1, the only model in which the inverse-square law is valid at all distances is that for k=0. In other words, its validity depends on the flatness of space. It is easy to show using the R-W metric with k=+1 that objects get magnified and that effect increases with distance. The magnification not only affects the apparent size but also affects the brightness of 'standard candles'.

Two questions:

(1)Is the value for k=0 in the current consensus model calculated assuming the validity of the inverse-square law? That would obviously create a circular argument.

(2)By affecting the brightness of distant standard candles, can a failure of the inverse-square law account for the apparent acceleration in the expansion of the universe by underestimating the distance of those galaxies producing red-shifts greater than that predicted by the Hubble relation?

Chalnoth

Nope. The measurements we use take General Relativity fully into account. There is no reduction to a Newtonian approximation for cosmological observations.

It may potentially be the case that if we modify gravity beyond General Relativity, we might be able to explain the cosmic acceleration. Nobody has yet put forward a compelling model for doing so that also fits observation, however. Nevertheless, one of the potential benefits of future weak lensing surveys is that they may be able to distinguish between some sorts of modified gravity and some sort of dark energy.

IsometricPion

I was under the impression that [tex]\Lambda[/tex]CDM (which is just GR with non-zero cosmological constant, [tex]\Lambda[/tex], and appropriate mass-energy boundary conditions) adequately fits the cosmological data gathered so far.

Chalnoth

Yes. This is accurate. Some people (unreasonably, I feel) don't like the cosmological constant, and so attempt to propose ways of explaining the acceleration without it.

StateOfTheEqn

I have attempted to do something of a literature review on the various distance measurements used in cosmology that depend on the inverse-square law. It is often difficult when looking at an equation to see the assumptions contained within. So far, the most enlightening paper I have found is at
http://www.ssl.berkeley.edu/~mlampto...ngDistance.pdf

It seems the inverse-square law is deeply embedded in much of the methodology of current cosmology. To me, that seems to be hanging a very heavy weight on a very weak hook.

Chalnoth

Why? General Relativity is exceedingly well-tested, and in cosmological studies, many sorts of deviations from General Relativity have been investigated. They simply don't explain any of the apparent observational discrepancies, so as yet there is no reason whatsoever to believe that they are valid.

StateOfTheEqn

The question I was trying to address is this: Could the apparent acceleration in the expansion result from the failure of the inverse-square law to give correct standard-candle distances? In other words, is the acceleration real or the product of false assumption(s) about the validity of the inverse-square law?

StateOfTheEqn

The cosmological equations derived from GR cover three cases:k=-1,0,+1. The only one consistent with the inverse-square law at all distances is k=0.

To question the validity of the inverse-square law is not the same as challenging the validity of GR.

Chalnoth

Well, yes, many modifications of gravity to explain the apparent acceleration have been attempted. The ones that are most strongly theoretically-motivated (and they're still pretty speculative even then) don't fit the data.

Our best bet at really examining this in detail is by examining the growth of structure in the universe by use of weak gravitational lensing surveys. If reality is described by General Relativity + dark energy (either cosmological constant or something else), then there are certain relationships that the growth of structure must necessarily follow. Violation of these relationships will be evidence for some sort of deviation from General Relativity.

In general, however, the theoretical bias is strongly against this sort of deviation from General Relativity. We generically expect that General Relativity should be modified at high energies, not low energies: it is extraordinarily difficult to produce a theory of gravity that is modified at low energies (long length scales) without violating solar system tests of gravity.

XilOnGlennSt

This has worried me too. The different values for k in the Friedman equations would certainly affect light luminosity at distance, but it seems that there are many other possible factors that could affect light over such long distances, quite outside GR. If there have been any empirical verifications of the inverse-square law at cosmological distances, I would like to know about it.

For that matter, isn't it also possible that red shifting of light could be affected by great distance?

Regarding the need to revise the standard cosmological models; what about the introduction the expansion phase, or the need to introduce dark matter and dark energy. These all smell like fudge factors to me.

Please enlighten me, if you think it possible.

Chronos

Assuming the laws of physics are time invariant, how would redshift be affected by distance? That appears to invoke a 'special' reference frame.

clamtrox

So this may be a stupid question... but what is the inverse-square law everyone talks about?

Chalnoth

Gravity, as described by Newton, reduces in strength proportional to the inverse square of the distance between objects. General Relativity, the theory of gravity first produced by Einstein, doesn't quite follow this rule for very small or very large distances.

Chalnoth

It's not blasphemous. It's just against the evidence. GR describes remarkably well the large-scale evolution of the universe, and modifications of GR that change how GR behaves on large scales tend to fail to do so.

Whovian

But GR, as stated already, doesn't actually exhibit the inverse square law for a "nonflat" Universe. So my point was, why would questioning the inverse square law be ... oh ... I absolutely failed, missing the word "not" in the post I quoted. Editing. So I was arguing against my own opinion (for lack of a better word, there are reasons opinion is completely unsuitable here.)

Chalnoth

I'm going to assume that your first sentence here still stands :)

The thing to bear in mind is that for most scales of interest here, the inverse square law holds in General Relativity because the spatial curvature and dark energy contributions are small. It is only at very large scales that there is a noticeable departure. On the scales of galaxies and galaxy clusters, the inverse square law holds exceedingly well.

clamtrox

So I think they are talking about light intensity decreasing as the inverse of r squared, but I'm not completely sure what the point is there. I think the point missed by original poster is that in GR, there is no well-defined universal length measure. The inverse-square law holds for a certain distance measure, defined precisely to be such that it holds.