Does the Cosmological Principle in any way underpin Big Bang Theory?

Am I correct in thinking that the Cosmological Principle has been derived entirely from observational data, and is in no way an assumption? Does the Cosmological Principle have any role in underpinning Big Bang Theory? Specifically, was the data regarding the redshift/distance relationship used to help establish the principle (in showing that there's no "center" of the Universe, i.e., no place from which all other matter is receding at an equal rate, i.e., where one can say "The Big Bang originated here")? I assume the redshift/distance data show that all galaxies seem to be moving away from each other on average (ignoring local effects, clustering, etc.), i.e., seems to demonstrate spatial expansion (given the Doppler interpretation of the cosmological redshift). I also assume the fact that starlight, and its characteristic elemental emission/absorption spectra, are pretty much the same in whatever direction we look--along with galaxies, their distribution, the CMBR, etc.--also have helped to establish the principle.

hkyriazi said:

... was the data regarding the redshift/distance relationship used to help establish the principle (in showing that there's no "center" of the Universe, i.e., no place from which all other matter is receding at an equal rate, i.e., where one can say "The Big Bang originated here")?

If we assume that the Big Bang was an explosion that occurred at a certain point from which the galaxies departed in all directions at different speeds, then, from that point we would observe that the velocity-distance relationship would be constant. This means that the constant speed-distance relationship alone doesn't allow us to determine that the expansion doesn't have a center.

hkyriazi said:

Am I correct in thinking that the Cosmological Principle has been derived entirely from observational data, and is in no way an assumption? Does the Cosmological Principle have any role in underpinning Big Bang Theory?

The hypothesis of the expansion of the universe is based on two assumptions: the theory of general relativity and the cosmological principle. Subsequently it was determined by observations that, at very large scales, the cosmological principle holds.

So, then, it would be correct to say that the Big Bang Theory does NOT depend---no longer depends---upon our assuming the cosmological principle, because the data (as you say, at large scales) has proven the latter.

hkyriazi said:

So, then, it would be correct to say that the Big Bang Theory does NOT depend---no longer depends---upon our assuming the cosmological principle, because the data (as you say, at large scales) has proven the latter.

What kind of dependency are you referring to? I ask because the Big Bang theory depends on the cosmological principle in the sense that it is based on it.

hkyriazi said:

So, then, it would be correct to say that the Big Bang Theory does NOT depend---no longer depends---upon our assuming the cosmological principle, because the data (as you say, at large scales) has proven the latter.

It's less of an assumption than it was before, it that's what you're asking. At what point something becomes zero-part assumption and all-parts proven is somewhat problematic to answer.

Jaime Rudas said:

What kind of dependency are you referring to? I ask because the Big Bang theory depends on the cosmological principle in the sense that it is based on it.

My main question was about the underlying assumptions of the Big Bang Theory. It's not all of the Cosmological Principle, but just the part about the redshift/distance relationship looking the same from anywhere in the Universe, that underlies it. (Along with the Doppler interpretation of the redshift.) That aspect of the Cosmological Principle has, AFAIK, been upheld by the observational evidence. Before we had all the data from the greatly improved telescopes we've used over the past several decades, I can see that this was once more of an article of faith.

Jaime Rudas said:

If we assume that the Big Bang was an explosion that occurred at a certain point from which the galaxies departed in all directions at different speeds, then, from that point we would observe that the velocity-distance relationship would be constant. This means that the constant speed-distance relationship alone doesn't allow us to determine that the expansion doesn't have a center.

It seems to me that a Universe that began as you described would have a very different appearance than our current Universe. For one, it'd have a huge gaping hole at the origin. For two, there'd be a wall of blackness beyond the distance the furthermost galaxies have moved radially outward. Would there also be differences in the speed galaxies move apart that are side-by-side so to speak (moving away at the same speed and along nearly the same trajectory) vs. ones that have the same trajectory but different speeds? Such features would show up in the detailed data that our most powerful telescopes have gathered. But since no such features exist, it seems that the Cosmological Principle isn't an underlying assumption, but more of an underlying observation.

hkyriazi said:

Before we had all the data from the greatly improved telescopes we've used over the past several decades, I can see that this was once more of an article of faith.

In 1922 Friedmann showed that, if relativity and the cosmological principle are assumed, the Hubble-Lemaître law is fulfilled, that is, that galaxies move away at a speed proportional to the distance at which they are. Does that mean that Friedmann regarded the cosmological principle as an article of faith? Of course not. He simply showed that, mathematically, one thing implies the other.

hkyriazi said:

It seems to me that a Universe that began as you described would have a very different appearance than our current Universe.

Yes, it would look slightly different, but the speed-distance relationship (which is what you were referring to) would be the same.

And no: it wouldn't have a huge hole at the origin and the velocity-distance relationship would remain constant.

Jaime Rudas said:

If we assume that the Big Bang was an explosion that occurred at a certain point from which the galaxies departed in all directions at different speeds, then, from that point we would observe that the velocity-distance relationship would be constant.

What are you basing this on? Do you have a reference? This is the sort of claim that should be based on something in the published literature.

PeterDonis said:

What are you basing this on? Do you have a reference? This is the sort of claim that should be based on something in the published literature.

Doesn't that just follow from the premise? Faster moving objects should be further away at some point in time than slower moving objects. Assuming everything came from one point that would seem to create a case where all objects at the same distance are moving at the same speed outwards. Am I mistaken?

Drakkith said:

Doesn't that just follow from the premise?

Yes, but only if we set the velocities to be constant, something I didn't explicitly state

PeterDonis said:

What are you basing this on?

I accept that I didn't make explicit that I assumed the velocities to be constant, but, under these conditions, the velocity-distance relationship will be the same for all galaxies at a given moment in time and will be equal to the inverse of time.

Jaime Rudas said:

Yes, it would look slightly different, but the speed-distance relationship (which is what you were referring to) would be the same.

And no: it wouldn't have a huge hole at the origin and the velocity-distance relationship would remain constant.

Agreed that there wouldn't necessarily be a big hole at the "center," as one can postulate that some matter was essentially stationary early on. (But, the theory is that there was no actual "explosion" anyway, right? Just space being created between clumps of matter at some minimal distance apart. Fred Hoyle didn't do us any favors with that pejorative titling of the theory. ;-) )

hkyriazi said:

Agreed that there wouldn't necessarily be a big hole at the "center," as one can postulate that some matter was essentially stationary early on.

No, it isn't required that there be stationary matter in the center. It only requires that there be a very large variety of speeds: extremely slow, very slow, slow, neither slow nor fast, fast, very fast, extremely fast, and in between. Under these conditions, the void in the center is more or less of the same order as that between any two galaxies.

Drakkith said:

Doesn't that just follow from the premise? Faster moving objects should be further away at some point in time than slower moving objects. Assuming everything came from one point that would seem to create a case where all objects at the same distance are moving at the same speed outwards. Am I mistaken?

"Faster moving" with respect to what?

vanhees71 said:

"Faster moving" with respect to what?

To the center

There is no "center" due to the cosmological principle. I think there are a lot of misconceptions again in this thread. There is no center by assumption, because the cosmological principle says that space is assumed to be homogeneous and isotropic, which leads to the FLRW spacetime. This in turn implies that the energy-momentum tensor must have the form of a perfect fluid. In standard coordinates it's for a fluid at rest, ##({T^{\mu}}_{\nu}=\mathrm{diag}(\epsilon,P,P,P)##. The resulting Einstein field equations lead to the Friedmann equations for the scale parameter and need to be closed with an equation of state (e.g., for "dust matter", ##P=0## or ultrarelativistic matter/radiation ##\epsilon=3P##).

vanhees71 said:

There is no "center" due to the cosmological principle. I think there are a lot of misconceptions again in this thread. There is no center by assumption, because the cosmological principle says that space is assumed to be homogeneous and isotropic, which leads to the FLRW spacetime.

Yes, that's right, but what is in dispute isn't whether the cosmological principle holds. What is in dispute is whether or not the constancy of the velocity-distance relationship implies the cosmological principle, as seen here:

https://www.physicsforums.com/threa...underpin-big-bang-theory.1055179/post-6926218

Jaime Rudas said:

To the center

No centre.
There is a history of observation, theory, observations, theory and so on.
Have you read how these things developed?
Slipher, Einstein GR, Hubble, Lemaitre, Gamov, Hoyle, CMBR?
A stack of information on over 100 years of observations and Theory.

"If we assume that the Big Bang was an explosion"

It was not an explosion.

"that occurred at a certain point"

Not at a certain point.

"from which the galaxies departed in all directions at different speeds"
A lot happened before that that was theorised and observed.

" then, from that point we would observe that the velocity-distance relationship would be constant. This means that the constant speed-distance relationship alone doesn't allow us to determine that the expansion doesn't have a center."

The universe appears to be the same and the same in all directions. No centre no special place.

https://en.m.wikipedia.org/wiki/Cosmological_principle

pinball1970 said:

No centre.
There is a history of observation, theory, observations, theory and so on.
Have you read how these things developed?

Yes, I have read how these matters developed and it is perfectly clear to me that the universe doesn't have a center.

On the other hand, have you read what the discussion is about? Notice:

https://www.physicsforums.com/threa...underpin-big-bang-theory.1055179/post-6926218

Jaime Rudas said:

I didn't make explicit that I assumed the velocities to be constant

And once you make that explicit, you realize that it is inconsistent with the galaxies having gravity. Their mutual gravity should slow them down. Only if there is zero gravity (or if there is zero matter in the universe--all the galaxies are actually just "test particles" containing no actual matter) will the velocities behave as you describe.

This is why I asked if you had a reference. The possibility you describe was in fact discussed in the literature decades ago, and rejected for the reason I just gave (among other reasons). Look up the "Milne model".

Jaime Rudas said:

Yes, I have read how these matters developed and it is perfectly clear to me that the universe doesn't have a center.

On the other hand, have you read what the discussion is about? Notice:

https://www.physicsforums.com/threa...underpin-big-bang-theory.1055179/post-6926218

Perhaps I am missing the point of this and your other thread.

"Am I correct in thinking that the Cosmological Principle has been derived entirely from observational data, and is in no way an assumption."

This starts in a confusing way to me, the observations AND theory contributed.
What do you think the assumptions were?

Jaime Rudas said:

have you read what the discussion is about? Notice

This is not your thread, and the discussion is not about what you are saying. It's about what the OP of the thread, who is not you, asked about. Your posts are simply attempts to contribute to a discussion of what the OP is saying. And, given my post #23, your attempts are actually not contributing anything substantive, since the original reasoning you gave in your first post in this thread is wrong.

PeterDonis said:

The possibility you describe was in fact discussed in the literature decades ago, and rejected for the reason I just gave (among other reasons).

I totally agree. That is why I didn't present it as a realistic model, but as a (non-realistic) example that the constancy of the velocity-distance relationship doesn't imply that the cosmological principle holds.

Jaime Rudas said:

a (non-realistic) example that the constancy of the velocity-distance relationship doesn't imply that the cosmological principle holds

No, it's not any such example, because it contradicts the laws of physics: it assumes velocities are constant when they can't be because of gravity. An "example" that contradicts the laws of physics can't prove anything.

PeterDonis said:

This is not your thread, and the discussion is not about what you are saying. It's about what the OP of the thread, who is not you, asked about. Your posts are simply attempts to contribute to a discussion of what the OP is saying. And, given my post #23, your attempts are actually not contributing anything substantive, since the original reasoning you gave in your first post in this thread is wrong.

My only intention was to answer the question posed in post #1 about whether the velocity-distance relation data had been used to help establish the cosmological principle by showing that there is no center of the Universe. My answer was no, because the velocity-distance relationship alone does not imply that the universe is centerless.

Jaime Rudas said:

My answer was no

Based on an example that violates the laws of physics, and therefore does not justify a "no" answer, because you can't prove anything with an example that violates the laws of physics.

PeterDonis said:

Based on an example that violates the laws of physics, and therefore does not justify a "no" answer, because you can't prove anything with an example that violates the laws of physics.

I do have to ask what laws of physics are in question.
The cosmological principle is based upon not a single law of physics that I am aware.
Several theories of the universe can satisfy the principle - Steady State, Milne, Newtonian - but are rejected as being suspect from observations, mathematical inconsistencies, or the progression of scientific principles and philosophies. Milne can be said to be delegating special relativity as being global, with special relativity rendered to a being local phenomenon, contrary to Big Bang foundations, notably Lamaitre. Milne himself expressed the view that a cosmological theory worth its salt should conform to the Cosmological Principle.
The cosmological Principle AFAIK does not state that there is not a centre to the universe, only the implication that the universe should appear to be the same for an observer no matter where located.

In any event, it is moot since even if an actual centre does exist, no observer, which is what @Jaime Rudas is eluding to, could be able to ascertain the "centre", since with the Cosmological Principle applied, would not allow them in in way, shape, or form pinpoint its location, since to each observer, they themselves would appear to be at the centre.

256bits said:

what laws of physics are in question

The example I referred to violates the law of gravity.

256bits said:

The cosmological principle is based upon not a single law of physics that I am aware

The post of mine that you quoted was not about the cosmological principle. It was about the specific example proposed by the poster I responded to and the invalid claim he made based on it.

Nobody is claiming that the cosmological principle itself violates any law of physics.

256bits said:

The cosmological Principle AFAIK does not state that there is not a centre to the universe, only the implication that the universe should appear to be the same for an observer no matter where located.

You're contradicting yourself. "There is a center to the universe" means that the universe does not appear the same from everywhere.

256bits said:

if an actual centre does exist

Then the cosmological principle would be false. So your reasoning that follows, which assumes the cosmological principle is true, is obviously wrong.

PeterDonis said:

No, it's not any such example, because it contradicts the laws of physics: it assumes velocities are constant when they can't be because of gravity. An "example" that contradicts the laws of physics can't prove anything.

But if a distribution of dark energy is established such that it counteracts gravity, then it wouldn't be contradicting physical laws.

Jaime Rudas said:

if a distribution of dark energy is established such that it counteracts gravity, then it wouldn't be contradicting physical laws

There is no expanding solution with this property: the solution where dark energy just "counteracts" the gravity of the matter is the Einstein static universe, which does not expand.

Please do not hijack this thread any further with these claims. If you do you will receive a warning and a thread ban.

Jaime Rudas said:

Yes, that's right, but what is in dispute isn't whether the cosmological principle holds. What is in dispute is whether or not the constancy of the velocity-distance relationship implies the cosmological principle, as seen here:

https://www.physicsforums.com/threa...underpin-big-bang-theory.1055179/post-6926218

The cosmological principle is a conjectured. The conceptual problem of cosmology is that you have to work with conjectures, derive predictions for observable effects and compare observations with these predictions, and one should be aware that all our observations are "local", i.e., we can observe only a tiny neighborhood of spacetime around the Earth.

Nevertheless through observing farther and farther away objects or rather the em. waves (and recently also the gravitational waves) we also "look to the past".

The cosmological principle is the statement that on a coarse-grained large-scale level the universe is homogeneeous and isotropic, leading to the Friedmann-Lemaitre-Robertson-Walker spacetime. The Einstein equations then tell us that the energy-momentum tensor of matter and radiation takes the form of an ideal-fluid energy-momentum tensor (+the cosmological-constant term, also dubbed "dark energy"). In standard "co-moving coordinates" with the coordinate time chosen as the proper time of an observer co-moving with this fluid,
$$\mathrm{d}s^2 =\mathrm{d} t^2 -a^2(t) \left [\frac{\mathrm{d} r^2}{1-K r^2} - r^2 (\mathrm{d} \vartheta^2 + \sin^2 \vartheta \mathrm{d} \varphi^2) \right],$$
the spatial coordinate system is chosen similar to spherical coordinates, and this of coarse "hides" the translation invariance of space, but that's only due to the coordinates. The chosen "origin" of these spherical coordinates can be an arbitrary point in this space, because no point is distinguished from any other. The same holds for the "polar axis" of the coordinate system, which can be chosen to point in any direction you like since space doesn't distinguish any direction in this spacetime model.

An observer in the origin at rest wrt. this reference frame (a "fundamental observer") sees the distance between him and a distant galaxy increasing with the scale factor ##a## and he also sees a red-shift of light emitted from a far distant galaxy. As should be clear, the interpretation of this Hubble-Lemaitre redshift as a "Doppler shift" is only approximately right for not too far-distant objects.

For a nice pedagogical paper, see

https://doi.org/10.1119/1.1446856