Expansion of the Universe and the cosmological principle

[Madeleine Birchfield]

TL;DR Summary

Is the expansion of the universe due to the assumption of homogeneity and isotropy in the FLRW metric?

Wikipedia states the following in their article about the expansion of the universe:

In 1912, Vesto Slipher discovered that light from remote galaxies was redshifted,[3][4] which was later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used Einstein field equations to provide theoretical evidence that the universe is expanding.[5]

Swedish astronomer Knut Lundmark was the first person to find observational evidence for expansion in 1924. According to Ian Steer of the NASA/IPAC Extragalactic Database of Galaxy Distances, "Lundmark's extragalactic distance estimates were far more accurate than Hubble's, consistent with an expansion rate (Hubble constant) that was within 1% of the best measurements today."[6]

In 1927, Georges Lemaître independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented observational evidence for a linear relationship between distance to galaxies and their recessional velocity.[7] Edwin Hubble observationally confirmed Lundmark's and Lemaître's findings in 1929.[8] Assuming the cosmological principle, these findings would imply that all galaxies are moving away from each other.

If the cosmological principle was discovered to be false in our universe, i.e. our universe was discovered to be inhomogeneous or anisotropic or both on very large scales and the FLRW metric does not hold for our universe, is it still the case that our universe could be said to be expanding?

 

[Ibix]

If the cosmological principle was discovered to be false in our universe, i.e. our universe was discovered to be inhomogeneous or anisotropic or both on very large scales and the FLRW metric does not hold for our universe, is it still the case that our universe could be said to be expanding?

We can see cosmological redshift, so it appears to be expanding independent of theoretical reasons to expect it. We might have to revise our explanations, but the observations of increasing velocity with distance would remain.

 

[PeterDonis]

Is the expansion of the universe due to the assumption of homogeneity and isotropy in the FLRW metric?

No. A human theoretical assumption can't cause anything.

Wikipedia

...is not always a reliable source and should be used with caution.

If the cosmological principle was discovered to be false in our universe, i.e. our universe was discovered to be inhomogeneous or anisotropic or both on very large scales and the FLRW metric does not hold for our universe, is it still the case that our universe could be said to be expanding?

Yes. Even apart from observational evidence, there are known theoretical models that are expanding but not homogeneous or isotropic.

 

[Madeleine Birchfield]

No. A human theoretical assumption can't cause anything.

Yes. Even apart from observational evidence, there are known theoretical models that are expanding but not homogeneous or isotropic.

That's what I thought, but I've recently been arguing with somebody who says that if the cosmological principle is falsified then the big bang theory will fall apart, so it is good to get confirmation otherwise.

 

[PeroK]

That's what I thought, but I've recently been arguing with somebody who says that if the cosmological principle is falsified then the big bang theory will fall apart, so it is good to get confirmation otherwise.

Established theories rarely fall apart. Instead, they tend to be generalised. Newtonian physics didn't fall apart when SR came along. Far from it. Instead, we learned that it is only a good approximation in many cases. The same is true of classical EM, which didn't fall apart when QM came along.

One reason is that these theories are grounded in experimental evidence (first and foremost). If the Big Bang were a speculative theory that couldn't seriously be tested experimentally, then it would be more likely to fall apart when the evidence is found.

There is perhaps a strong possibility that the Big Bang is not the last word in cosmology, but I'd expect it to remain part of the overall picture. It has so much experimental evidence in its favour.

 

[Ibix]

That's what I thought, but I've recently been arguing with somebody who says that if the cosmological principle is falsified then the big bang theory will fall apart, so it is good to get confirmation otherwise.

If the cosmological principle were to be falsified then we would certainly need to revisit the theory side of the big bang. However, we can see increasing redshift with distance, and the CMB, and proportions of elements in the early universe (mostly) fit the expectation of nucleosynthesis in the big bang, and we can see large scale isotropy. That's all observational evidence that can't be wished away.

As PeroK says, we may one day improve on the current big bang theory - but any new theory would have to explain the same evidence so would have to look very like the big bang theory.

 

[Madeleine Birchfield]

Established theories rarely fall apart. Instead, they tend to be generalised. Newtonian physics didn't fall apart when SR came along. Far from it. Instead, we learned that it is only a good approximation in many cases. The same is true of classical EM, which didn't fall apart when QM came along.

One reason is that these theories are grounded in experimental evidence (first and foremost). If the Big Bang were a speculative theory that couldn't seriously be tested experimentally, then it would be more likely to fall apart when the evidence is found.

There is perhaps a strong possibility that the Big Bang is not the last word in cosmology, but I'd expect it to remain part of the overall picture. It has so much experimental evidence in its favour.

If the cosmological principle were to be falsified then we would certainly need to revisit the theory side of the big bang. However, we can see increasing redshift with distance, and the CMB, and proportions of elements in the early universe (mostly) fit the expectation of nucleosynthesis in the big bang, and we can see large scale isotropy. That's all observational evidence that can't be wished away.

As PeroK says, we may one day improve on the current big bang theory - but any new theory would have to explain the same evidence so would have to look very like the big bang theory.

I suppose another question is that - if a cosmological model which is not FLRW still implies the metric expansion of the universe, would it make sense to call the model a "big bang theory"? Or does the term "big bang theory" solely refer to theories which have the FLRW metric in it, or even more narrowly, the current concordance model which also has the cosmological constant and cold dark matter?

In particular, does Alexandre Deur's gravitational self-interaction cosmological model count as a "big bang theory"? It is non-FLRW but still implies the metric expansion of the universe.

 

[Ibix]

The metric expansion of the universe, run backwards, implies a hot dense state in the past. And we can see the glow from that (it's what the Cosmic Microwave Background is). So any model that doesn't include a hot dense state in the past needs a really good explanation for what it is we're looking at.

As far as I'm aware Deur is proposing that we don't need dark matter to describe the rotation of galaxies - basically that the effects attributed to dark matter are actually a mathematical error. I don't think it changes the larger scale significantly, or at least I'm not aware of any such implication. So (if he's correct, which I don't think there's any consensus on) he's modifying our models on a galactic scale, not on the really large scales we're talking about here. If your friend has a reference to where he/she thinks Deur (or other credible sources, rather than some dude on YouTube) said otherwise I'm happy to take a look.

 

[Madeleine Birchfield]

The metric expansion of the universe, run backwards, implies a hot dense state in the past. And we can see the glow from that (it's what the Cosmic Microwave Background is). So any model that doesn't include a hot dense state in the past needs a really good explanation for what it is we're looking at.

As far as I'm aware Deur is proposing that we don't need dark matter to describe the rotation of galaxies - basically that the effects attributed to dark matter are actually a mathematical error. I don't think it changes the larger scale significantly, or at least I'm not aware of any such implication. So (if he's correct, which I don't think there's any consensus on) he's modifying our models on a galactic scale, not on the really large scales we're talking about here. If your friend has a reference to where he/she thinks Deur (or other credible sources, rather than some dude on YouTube) said otherwise I'm happy to take a look.

Sure, his latest preprint on the arXiv: https://arxiv.org/pdf/2301.10861.pdf

The conclusion of that paper states:

Our results show that the Hubble tension may be resolved if one accounts, when quantifying the evolution of the universe, for the self-interaction of gravitational fields, a feature of General Relativity ordinarily neglected. In the cosmological model used in this article, as in the previous studies using that model, the effects of self-interaction are contained within a depletion function which effectively relaxes the traditional assumptions of the Cosmological Principle—isotropy and homogeneity of the evolving universe.

 

[Ibix]

Thanks.

Notice that the paper is talking about the Hubble constant, which is a measure of the expansion rate of the universe, and talks about the Cosmic Microwave Background, but doesn't comment that these things have non-standard interpretations in his model. That implies he's talking about an "expanding space" model, the same as everyone else.

In fact, I think he's talking about something that's true in regular cosmology as well. The original FLRW model assumes perfect homogeneity, which manifestly isn't correct on the small scale but does appear to be correct on the large scale. Simple calculations for redshifts and distances just assume homogeneity at all scales and assume that neglecting small scale homogeneity only causes small corrections. More complicated models that include small scale inhomogeneity are a more recent (compared to the century old FLRW model) development, but they don't change anything about the early universe when inhomogeneity truly was tiny. That inclusion of inhomogeneity is the "relaxation of the cosmological principle" that Deur is talking about. He is just saying that people neglect it or do not handle it correctly in their calculations. Again, I don't think there's an agreed view on whether Deur has a point.

So Deur's model is different in details from naive FLRW, but small scale inhomogeneity is already studied in standard cosmology and doesn't change the implication of a Big Bang. Deur (if correct) is actually strengthening the case for the Big Bang model by solving an outstanding problem with the model.

The kind of failure of the cosmological principle that would force a re-evaluation of the big bang would be if we could see significantly more galaxies in one half of the sky than the other. That's not what Deur is talking about.