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The term "Cosmological Principle" is widely invoked in cosmology discussions. I think the basic idea here is that one might guess that the Milky Way is not at a special location in the cosmos as a whole, and one might guess further that each place in the cosmos is much like any other place. This guess is then elevated to the status of "Principle". However it is obvious that some places are unlike others (the centre of a neutron star is unlike a galactic void) so this "principle" is only being invoked as a statement about averages at large scales. So really it is a "principle" which says that after all the stars, galaxies and galaxy-clusters one will eventually arrive at a scale where things are homogeneous on average, and this scale is a good deal smaller than the size of observable universe.

Now it happens that the observable universe is indeed like that (smooth to good approximation on the large scale). However, as far as I am aware there is no principle which says it had to be like that. It is not a principle but an empirical observation. Before looking, we have no a priori justification for expecting homogeneity. The universe might have been structured like a tree, with structure at all scales above some minimum. Indeed, in view of all the other scales of structure, one might guess that it would be quite likely to come out like that.

If the tree-like structure were the case, then one would have the issue whether or not the Milky Way should be located at a special place in such a tree. It is obvious that the answer is yes, up to a point, because it has to be at a place where a galaxy can form.

So you see I begin to doubt that there is any "cosmological principle" in the sense of a principle of logic or of theoretical physics. It is a misnomer for an interesting and important empirical observation.

My question is, then: is there any argument coming either from logic or from physics more generally (not observations such as sky surveys and CMB measurements) which says the cosmos must be expected to be homogeneous? And if it were not homogeneous then is there any argument deserving the name "principle" whose conclusion is that the physical conditions allowing life might be equally well expected at one place as another?

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    $\begingroup$ Which is more likely: (1) you are the only conscious human, or (2) all/most humans are equally conscious? Option 1 requires an explanation of why you are special and different to everyone else; option 2 does not. Same with Earth and the Milky Way. $\endgroup$
    – user253751
    Nov 12 '21 at 12:30
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    $\begingroup$ The center of a neutron star has a different mass distribution than a galactic void; that doesn't mean the place where that mass is concentrated is any different. It's the assumption that the laws of physics are the same in both places that lets us model a neutron star in the first place, without resorting to entirely new physics. $\endgroup$
    – chepner
    Nov 12 '21 at 13:05
  • $\begingroup$ In other posts I have expressed already my modest opinion that the adjective special would be better replace by the fact that is unlike (to be in the center). It seems to me that OP is right. At least modernly, the cosmological principle is derivein reverse. First we observe, than we pose that there is no centre because it is unlikely we are at it. About semantic, I am not sure of what is what. Perhaps principle has not such a strict definition. $\endgroup$
    – Alchimista
    Nov 12 '21 at 13:24
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    $\begingroup$ @user253751 Unfortunately, some philosophers do contend that it is equally likely that everyone else is a zombie, and we have no way to prove otherwise. This is one of the problems with philosophy $\endgroup$
    – gardenhead
    Nov 12 '21 at 16:18
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    $\begingroup$ @gardenhead Not quite, the argument simply highlights that consciousness is not observable. A replica of a human sans consciousness (or sentience or inner mind or whatever you want to call it) could behave mechanically the same (including looking exactly like a human and arguing convincingly for its own sentience), and therefore be indistinguishable from an empirical point of view. So indeed, you can reason about it, but not show it *empirically*/scientifically. $\endgroup$
    – andrepd
    Nov 13 '21 at 22:43
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it happens that the observable universe is indeed like that... there is no principle which says it had to be like that. It is not a principle but an empirical observation.

Right! Physics explains the world with the simplest performant models. Our place is typical until proven otherwise. We don't need to justify its being typical to an armchair philosopher; we need only have explanations that fit the observations so far. You can learn very little without them.

is there any argument coming either from logic or from physics more generally (not observations such as sky surveys and CMB measurements) which says the cosmos must be expected to be homogeneous?

It's interesting you define physics to exclude the observations that test the mettle of its ideas. Ultimately, physicists tried various full-Universe solutions to general relativity, and realized the only tractable ones data didn't quickly refute were homogeneous and isotropic but not static. Ever since then, additional data has largely gone along with these ideas. The tree idea has been less successful.

I'll take "logic" to include philosophical analyses that are plausible but potentially open to empirical refutation, if only because tautologies won't tell us how the Universe looks. There are those who will argue the Copernican principle is a reasonable prima facie starting point (what else would be?), and that it motivates the cosmological principle.

And if it were not homogeneous then is there any argument deserving the name "principle" whose conclusion is that the physical conditions allowing life might be equally well expected at one place as another?

I won't try to decide what should be called a principle, but I can speak to whether inhomogeneity would make life more feasible in some places, provided it's a narrow notion of life. Certain kinds of star, and certain kinds of elemental distributions on planets etc., occur more readily with specific matter distributions, and are crucial to life as we know it. We could be here all day trying to give examples, every single one of which would be very controversial. To sign off with one, it's been conjectured that the crucial role evolution gave phosphorus in Earth's life, despite it being of low abundance, suggests (i) life needs it and (ii) other parts of the galaxy where phosphorus is rarer will have less life if any.

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As far as I can tell, the use of "principle" in physics is largely interchangeable with "postulate". E.g., it's often said that Einstein's two postulates of special relativity were the principle of relativity and the principle of the constancy of the speed of light.

The cosmological principle is a postulate of FLRW cosmology. Its effect is to force the large scale geometry of spacetime to be a FLRW geometry. You could just assume a FLRW geometry instead, but the more abstract idea of homogeneity and isotropy sounds, I suppose, more principled. Principled or not, it's an assumption, not something you could know a priori. It's ultimately justified, like any postulate, by the agreement of the resulting theory with experiment.

I think it's as well justified as any other so-called principle. The principle of relativity has held up well, but it certainly could be wrong. The principle of least action is wrong; it's just an approximation in quantum mechanics. And so on.

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    $\begingroup$ I think it's quite unhelpful phrasing to say that 'the principle of least action is wrong'. It reduces 'does this theory describe reality' down to a binary 'yes/no', which is oversimplified epistemologically. I would rather say, 'the principle of least action is a very good approximation in the classical regime', or 'the least action principle is an approximation which breaks down in quantum mechanics (and is superceded by the path integral)'. $\endgroup$
    – Joe
    Nov 12 '21 at 14:19
  • $\begingroup$ @Joe I think it's wrong as a principle. It's fine as an approximation to reality, and everything is an approximation anyway, but "principle" suggests something stronger than that, and that's what inspired the question. $\endgroup$
    – benrg
    Nov 12 '21 at 22:14
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I think this is very close to a discussion on definitions rather than physics, but I will give it a shot.

First we could argue it was a principle for historical reasons. And the terminology has stuck, so people still call it 'Principle' today.

On the pragmatic point of view it is the simplest possible scenario computation-wise and speaks directly about the simplest approximation you can make if you want to model the universe. And was used in the scientific community way before actual large scale observations.

Now let me argue from the theory side. There is in my opinion two important points. One is Naturality and the other is Symmetry. If you accept to an extent that a universe starting without preferred direction, location or very specific tuning of some quantity is more appealing that one violating any of the aforementioned, you again conclude an isotropic and homogeneous fluid is the simplest thing you can use (which is exactly the Cosmological Principle). We actually observe the laws of physics do not prefer a direction here on earth and observations of different locations seem to indicate location is also not important for fundamental laws, so we extrapolate... Let us say that happens everywhere. We call this zero-th order approximation a "Principle" again due to custom.

Can we check every possible location? No, thus we need to extrapolate. Is it an approximation, yes we know. Have we gone beyond it? Yes we have and perturbations around such are extremely relevant to the CMB, structure formation, and in general the history of the universe.

Will it we be still called a principle...? Probably yes I am afraid

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Not only is the cosmological principle not a logical requirement, but it is actually violated in many cosmological models such as eternal inflation.

However, we only have access to one Universe, so there's a limit on the largest scales we can probe observationally; beyond that you start getting into shouting matches about metaphysical things like how to put a probability measure on an infinitely large space or what counts as science. The cosmological principle seems to work for scales between 100 Mpc and our cosmological horizon.

There are some proposals that we actually do find ourselves in an underdensity of the cosmological fluid, and perhaps this explains the tension between measurements of the Hubble constant with "local" measures like supernova and "distant" measures like the CMB. However as far as I understand, these models would require us to lie very close to the center of the underdensity (if we do lie in one), and so are fine-tuned.

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There's no argument from fundamental physics or logic that the universe must be homogeneous. My basis for making this statement is argumentum ex silentio: if there is such an argument, then it would have been mentioned in this paper, and it isn't.

The name "principle" is sort of a misnomer, because it's not grounded in fundamental physics, and more reflects what we think ought to be true. The principle of relativity (i.e. the idea that the laws of physics must be the same for all observers) is another similarly-named principle. It would be intuitively really weird if the principle of relativity is false, but it is still a falsifiable statement, and we believe it because of empirical justification.

Similarly, there's already another "principle" that was proven incorrect in cosmology - the perfect cosmological principle, so-named because it says that we are not located in a special position in the universe and we are not located in a special time in the universe. It's intuitively appealing, but it was proven incorrect by the observations that led to Big Bang theory.

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Before looking, we have no a priori justificatioon for expecting homogeneity.

We do have justification for taking it as our starting point. It's akin to Occam's Razor: the simplest hypothesis is that everything is the same everywhere. As we get more data refuting that assumption in some particular senses, we come to conclude that the universe is nonhomogeneous in those senses, while keeping homogeneity in other senses our default assumption.

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  • $\begingroup$ Homogeneity as the simplest assumption only works if we use no information of pyhsics whatsoever. The simplest thing we know about and know for long is entropy. Given that, we can not assume that the universe is infinitely old, as then we would have achieved equilibrium. This now means there has to be a start of the universe. Without making additional assumptions then (like inflation), the easiest assumptions then is in fact non homogeneity, as it is again simpler to postulate a process starting at one point instead of everywhere at once, which implies a difference between "core" and "shell". $\endgroup$
    – trikPu
    Nov 12 '21 at 14:01
  • $\begingroup$ Maybe I am missing something in my train of thought there, but I really don't think that it is that simple to assume homogeneity. $\endgroup$
    – trikPu
    Nov 12 '21 at 14:02
  • $\begingroup$ @trikPu Heterogeneity requires an explanation for why some places are special. Homogeneity doesn't require this -- if everything started with a single state during the Big Bang, it's natural for it all to evolve similarly. $\endgroup$
    – Barmar
    Nov 12 '21 at 15:26
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So you see I begin to doubt that there is any "cosmological principle" in the sense of a principle of logic or of theoretical physics. It is a misnomer for an interesting and important empirical observation.

No physical regularities can be derived entirely from logic alone. All physical regularities are ultimately empirical observations. As far as I can tell, a "principle" is simply an empirical regularity that happen to hold over a particularly broad range of regimes and situations. We are blessed to live in a universe that happens to contain empirical regularities, like the Schrodinger equation or the rules of special relativity, that seem to hold in a lot of different regimes. But of course we can't rule out the possibility that we'll eventually come across some patch of space where the Schrodinger equation or special relativity simply don't apply.

But I think the exact cutoff for what counts as a "principle" will always be somewhat subjective, and so I'd question the premise quoted above. It also depends on what you're trying to describe: a deep-ocean marine biologist could reasonably take it as a "principle" that the temperature is always 4 degrees Celsius, but a stellar astrophysicist cannot.

My question is, then: is there any argument coming either from logic or from physics more generally (not observations such as sky surveys and CMB measurements) which says the cosmos must be expected to be homogeneous?

No. It's an empirical observation that cannot be derived from "fundamental" (i.e. microscopic-scale) laws of physics.

And if it were not homogeneous, then is there any argument deserving the name "principle" whose conclusion is that the physical conditions allowing life might be equally well expected at one place as another?

No, I can't think of one.

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