# What does homogeneity mean (in the cosmological context)?

• Lino
In summary, the conversation discusses the concept of homogeneity in the cosmological context. Homogeneity means that the properties of the universe are the same at every point in space, at a given time. This is an intrinsic property of the manifold and does not involve the concept of being embedded in higher-dimensional space. The question is raised whether homogeneity only exists when viewed from within the homogeneous space/time manifold, and if it still holds true when viewed from outside. In general relativity, space-time is not assumed to be embedded in higher-dimensional space and all measurements must be made within the four-dimensional manifold representing the observable universe. The conversation also briefly touches on the possibility of an outside of our universe in string theory, where there could be other directions of
Lino
First, I must stress that I am not asking this question in relation to the proof, or disproof, of any form of rotating Universe. I am only asking in order to understand the meaning of “homogeneity” in the cosmological context.

Secondly, I know that there are many threads that reference homogeneity, some asked by myself, and I thank everyone for your previous comments and answers. However, I don’t think a question from this perspective has been addressed (or at least I couldn’t find it).

Consider a model of the Universe, like a basic spiral galaxy (isotrophic, no black holes, no other complications) – again, I am not suggesting that this model is valid, I just want to use the model to frame a question. From my God-like perspective I can see the centre of rotation and therefore I know that the model is not homogenous. However, if I reside within the model, at any point – centred or off-centre – I see the motion of other objects in the Universe relative to me, so things appear to rotate around me (kind-of-like Earth in pre-Copernican days), and so this is homogenous (I think).

So my question is: which perspective is correct (in relation to the way the word homogenius is used in a cosmological context)?

Thanks, in anticipation, for all your help,

Noel.

Homogeneity means that the properties of the universe are the same at every point in space, at a given time (with time measured this way: https://www.physicsforums.com/showthread.php?t=506990 ).

Rotation in general relativity is different from rotation in Newtonian mechanics. You can have rotation in GR with no center of rotation.

Have you looked at our FAQ on rotation of the universe? https://www.physicsforums.com/showthread.php?t=506988

-Ben

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Thanks Ben.

In relation to rotation, between GR, papers on max value for angular rotation, deSitter space, etc., I still have a lot that I'm trying to get through. I continue to revert to the FAQ to help work through the logic ... and ... I am getting there, but very, very slowly! But all references are, as always, greatly appreciated (thanks again).

In relation to homogeneity, thanks for the reference to the thread on measurement of time / distance, but I'll have to spend some time thinking about this. I was trying to use as simple a model as possible, but obviously, time / distance still have an impact so I will have to work through that.

If you forget about the model that I mentioned, at a very basic level, my question is: when homogeneity is measured ("... properties ... are the same at every point ...") does it matter if the observer is within the space, or not?

Regards,

Noel.

Lino said:
If you forget about the model that I mentioned, at a very basic level, my question is: when homogeneity is measured ("... properties ... are the same at every point ...") does it matter if the observer is within the space, or not?

Regards,

Noel.

Hello Noel,
Is this what you are trying to ask:

Does homogeneity exist only when veiwed from within the homogeneous space/time manifold - by extension if you were to view the space/time manifold not from within itself - would it still be homogeneous and isotropic?

Is that correct?

Lino said:
If you forget about the model that I mentioned, at a very basic level, my question is: when homogeneity is measured ("... properties ... are the same at every point ...") does it matter if the observer is within the space, or not?

Regards,

Noel.

Homogeneity is an intrinsic property of the manifold. The thing is, in GR we don't assume or even think of space - time as being embedded in higher - dimensional space. Any and all measurements must be made in the 4 - manifold in question such as that representing the observable universe. I don't know if this is what you meant by "within space".

WannabeNewton said:
Homogeneity is an intrinsic property of the manifold. The thing is, in GR we don't assume or even think of space - time as being embedded in higher - dimensional space. Any and all measurements must be made in the 4 - manifold in question such as that representing the observable universe. I don't know if this is what you meant by "within space".

I think that's exactly what he meant.

Here's the definition of homogeneity that I like:

There exists a set of observers at different points in space that see the same average properties of the universe (e.g. density, expansion rate).

Thanks everyone.

Cosmo Novice & WannabeNewton, I think that's what I meant ... it sounds right, but I'm afraid I'm not sure that I understand it ... yet. I'll work on it and get there.

Chalnoth, That's exactly the (type of) definition that started me off on this train of thought! I'm trying to work the other elements (mentioned by other people) into this but it seems there are many folds on the journey!

I think that I understand the basics.

GR Homogenity: a set of observers at different points in space that see the same average properties of the universe (e.g. density, expansion rate), an intrinsic property of the manifold ... [not] embedded in higher - dimensional space. Therefore it doesn't make sense to ask the "outside" question. Is that correct?

Are there any non-GR models that allow (?again forgive the clumsy language?) the "outside" question ... just in the theoritical sense?

Regards,

Noel.

Lino said:
Are there any non-GR models that allow (?again forgive the clumsy language?) the "outside" question ... just in the theoritical sense?
Sorta kinda. In string theory, one possibility (among many) is that the 4 dimensions of space-time that we observe are a 4-dimensional brane that moves in some higher-dimensional space. There are, in principle, other directions of motion than forward/backward, up/down, left/right, but we can't move in those directions because we are stuck on this brane. In that sense, there could be a very real "outside" of our universe, it's just that we could never point in that direction (in the same way you can't draw an arrow on a piece of paper that points out of the piece of paper).

This is probably too much to ask but is it possible to write down all the properties of the universe in order that the universe could be decribed as homogeneous (and isotropic)? and perhaps also a range of values for these properties which would still satisfy the definition of homogeneity?

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Tanelorn said:
This is probably too much to ask but is it possible to write down all the properties of the universe in order that the universe could be decribed as homogeneous (and isotropic)? and perhaps also a range of values for these properties which would still satisfy the definition of homogeneity?
Total matter density and spatial curvature. That's about it. There are other things we strongly believe are the same from place to place (e.g. dark energy density, baryon/dark matter ratio, primordial helium abundance), but dark + baryon matter density combined with spatial curvature are the only ones that have much of a chance of actually varying from place to place.

Wow! The last couple of posting are very deep ... and interesting. I'll have to send sometime on it.

In the meantime, thanks again for everyones help.

Regards,

Noel.

Thanks Chalnoth

## What does homogeneity mean in the cosmological context?

In the cosmological context, homogeneity refers to the uniformity of the universe on a large scale. It means that the distribution of matter and energy is the same in all directions and at all locations in the universe.

## Why is homogeneity important in cosmology?

Homogeneity is important in cosmology because it is one of the assumptions of the Cosmological Principle, which states that the universe is both homogeneous and isotropic (meaning the same in all directions). This principle helps us understand the structure and evolution of the universe.

## How is homogeneity measured in the universe?

Homogeneity is measured through observations of the large-scale structure of the universe. This includes studying the distribution of galaxies and clusters of galaxies, as well as the cosmic microwave background radiation. If the universe is truly homogeneous, we would expect to see similar structures and patterns on a large scale.

## What evidence supports the concept of homogeneity in the universe?

One of the main pieces of evidence for homogeneity in the universe is the observed isotropy of the cosmic microwave background radiation. This radiation is nearly the same temperature in all directions, which suggests that the universe is uniform on a large scale. Additionally, studies of the large-scale structure of the universe, such as galaxy surveys, also support the idea of homogeneity.

## Is the universe completely homogeneous?

The concept of homogeneity is a simplification of the actual structure of the universe. While the universe may appear uniform on a large scale, there are still small variations and fluctuations in matter and energy. These variations are important for the formation of structures such as galaxies and galaxy clusters. Therefore, while the universe may be approximately homogeneous, it is not completely so.

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