I Observational Evidence for Metric Expansion of Space?

[kevindin]

Imagine that the CMB did not exist. What observational evidence exists to support the theory of the metric expansion of spacetime, as opposed to having a static spacetime and it's the matter distribution that is expanding - as it would in an explosion?

 

[PeterDonis]

What observational evidence exists to support the theory of the metric expansion of spacetime, as opposed to having a static spacetime and it's the matter distribution that is expanding - as it would in an explosion?

The relationship between observed redshift, apparent brightness, and angular size for all observed galaxies is not consistent with a model in which spacetime is static.

 

[kevindin]

The relationship between observed redshift, apparent brightness, and angular size for all observed galaxies is not consistent with a model in which spacetime is static.

Can you expand on why that is, or can you point me at links? (I have tried to look, but it's not easy separating the wheat from the chaff.) Thanks

 

[Orodruin]

However, it is worth pointing out that you cannot make any local inference to deduce the difference between metric expansion and things just flying apart because on a scale on which curvature is negligible, the two are just different interpretations of the same space-time using different sets of coordinates. You need to make measurements at a scale on which space-time curvature is measurable.

 

[PeterDonis]

Can you expand on why that is, or can you point me at links?

A good quick explanation is in this answer in Ned Wright's cosmology FAQ:

http://www.astro.ucla.edu/~wright/cosmology_faq.html#CC

The entire FAQ and the accompanying tutorial are worth reading; they were done some time ago but are still good introductions to the main concepts, and will help you to learn what to look for in other treatments.

To give my own attempt at a quick explanation: apparent brightness and angular size are two methods of estimating the distance to an object, so let's collapse them into one and talk about the relationship between observed redshift and distance. The key thing to keep in mind is that both of these items are not quantities "now"; they are quantities when the light we are seeing "now" was emitted. So when we look at a lot of different objects, each with different redshifts and different distances, we are also looking at different times (since the light we see "now" from different objects took different amounts of time to get to us), so putting all of this data together tells us how the universe evolved over time. And different models of the universe will predict different evolutions over time, so we can use the data to test different models and rule out the ones that don't make correct predictions.

There is also another consideration: according to the Einstein Field Equation, any matter distribution will curve spacetime. But in the model you refer to in which spacetime is static and the matter distribution is just expanding from an initial explosion, spacetime is not curved; it's flat. So on theoretical grounds we would not expect such a model to match the data.

 

[kevindin]

There is also another consideration: according to the Einstein Field Equation, any matter distribution will curve spacetime. But in the model you refer to in which spacetime is static and the matter distribution is just expanding from an initial explosion, spacetime is not curved; it's flat. So on theoretical grounds we would not expect such a model to match the data.

Can you please explain the "theoretical grounds"? Yes, spacetime is locally curved by the presence of matter. But that's not the same as expanding or contracting - isn't expansion just a theoretical possibility/assumption? And recent observations suggest that spacetime is flat.

 

[PeterDonis]

spacetime is locally curved by the presence of matter. But that's not the same as expanding or contracting

It is for the solutions that describe the universe as a whole.

recent observations suggest that spacetime is flat.

No, they suggest that the universe is spatially flat. More precisely, that spacelike surfaces of constant comoving time--i.e., surfaces of constant time for observers who see the universe as homogeneous and isotropic--are flat. But spacetime as a whole is curved.

 

[kevindin]

It is for the solutions that describe the universe as a whole.

Could you provide references for those assertions please? (Trying to learn here.) If you're referring to the FLWR model, then doesn't that contain theoretical assumptions and approximations? Is there any observational evidence, since Oridruin is saying that it isn't measurable? Thank you.

 

[PeterDonis]

Could you provide references for those assertions please?

Any cosmology textbook.

If you're referring to the FLWR model, then doesn't that contain theoretical assumptions and approximations?

Of course. Every solution does.

Is there any observational evidence

Yes. I already referred to it.

Oridruin is saying that it isn't measurable?

No, he isn't. He's saying it isn't measurable just by looking at a single object, or a small collection of objects that all have similar redshifts. You have to look at a large collection of objects with a large range of redshifts. That is what he meant by saying you have to make measurements at a scale on which spacetime curvature is measurable.

 

[Orodruin]

Is there any observational evidence, since Oridruin is saying that it isn't measurable?

I never said so. I said it is not locally measurable on distances small enough for space-time curvature not to be measurable. As Peter has already pointed out, while hypersurfaces of equal cosmological time are flat to current experimental precision, space-time is not flat.

Edit:

or a small collection of objects that all have similar redshifts

... and that are located in more ore less the same direction from us.

 

[kevindin]

I never said so. I said it is not locally measurable on distances small enough for space-time curvature not to be measurable. As Peter has already pointed out, while hypersurfaces of equal cosmological time are flat to current experimental precision, space-time is not flat.

OK, I did mean "spatially flat" rather than "spacetime is flat" - I understand that matter curves spacetime - that wasn't the main question. What I'm looking for is evidence that space is expanding, and not just changing its shape because of the movement of matter. Redshifts on their own isn't enough?

 

[PeterDonis]

What I'm looking for is evidence that space is expanding, and not just changing its shape because of the movement of matter.

What does "changing its shape because of the movement of matter" mean? How is it different from "expanding"?

I think you are getting yourself confused by using ordinary language instead of math.

 

[kimbyd]

Imagine that the CMB did not exist. What observational evidence exists to support the theory of the metric expansion of spacetime, as opposed to having a static spacetime and it's the matter distribution that is expanding - as it would in an explosion?

Metric expansion and things in the universe are moving apart with recession velocity proportional to distance are statements of the exact same behavior. There is no "or" here: both are descriptions of the exact same thing.

As for an explosion, however, explosions tend to be highly disordered. The expansion of our universe is an extremely orderly process. Simply noting that recession velocity is proportional to distance (e.g. by observing galaxies) eliminates the possibility of the expansion being the aftermath of something that behaved like an explosion. This possibility was ruled out by Hubble's observations nearly a century ago, and has been confirmed by a tremendous number of observations performed since.

 

[Orodruin]

I think you are getting yourself confused by using ordinary language instead of math.

I would concur with this assessment. We can try to relate math to ordinary language explanations and interpretations, but many times those interpretations are based on a particular coordinate system and/or not entirely accurate, which is something you must keep in mind when studying what the theory actually says. What the theory actually says is in the maths and at some point you will not reach a deeper understanding of what is going on without understanding the math and its implications. This understanding will not come easy. Granted, GR is not my field of study, but it is one that I take an active interest in and teach introductory and intermediate courses in and I still continue to discover new things and obtaining a better understanding of what is going on - like a few years back when I actually sat down to do the (frankly quite easy) computations I had not done before that gave me the insights that were the basis for my recent cosmology Insight post.

 

[PeterDonis]

Metric expansion and things in the universe are moving apart with recession velocity proportional to distance are statements of the exact same behavior.

But "things are moving apart" is not the alternative the OP proposed. He specifically proposed that spacetime is static. That's a genuine difference in model, since FRW spacetimes are not static.

 

[Orodruin]

That's a genuine difference in model, since FRW spacetimes are not static.

Not all of them, but some - such as Minkowski space. Of course, Minkowski space is also empty, which violates observations.

 

[PeterDonis]

Not all of them, but some - such as Minkowski space.

Yes, but that's ruled out as a possibility. See below.

Of course, Minkowski space is also empty

Not only that, but an "explosion" in Minkowski spacetime (supposing for the sake of argument that the stress-energy of whatever was exploding was negligible--which as you say it isn't in our actual universe) would show a different relationship between redshift and distance than the one we actually observe (it would be an "expansion" that was neither accelerating nor decelerating, and that would show up in the lack of curvature of the Hubble diagram even at very high redshifts). Basically this "explosion in Minkowski spacetime" model is just the Milne universe, which has been known to conflict with observation for decades.

 

[kevindin]

Any cosmology textbook.

Cosmology textbooks aren't so good at answering 'what if' questions and isolated scenarios - that's why I hoped someone here could help. I'm not suggesting a Milne model, because we obviously do have matter/energy density, etc. What I'm hearing is that we can't currently differentiate between doppler and cosmological redshift without further theoretical assumptions. Does the small Hubble curvature qualify as direct evidence? What other evidence is there that doesn't depend on the CMB?

 

[Orodruin]

Yes, but that's ruled out as a possibility. See below.

Yes, I do not think I ever disputed this.

redshift and distance

I think it should be mentioned that while redshift is directly measurable, distance in this setting is the luminosity distance, i.e., based on the luminosity measurement of a standard candle.

 

[PeterDonis]

I think it should be mentioned that while redshift is directly measurable, distance in this setting is the luminosity distance, i.e., based on the luminosity measurement of a standard candle.

Yes. Also there is angular size distance, which I haven't seen mentioned as much, but which Ned Wright mentions in the cosmology tutorial I linked to. He also mentions that the relationship between angular size distance and luminosity distance is also model-dependent, so the actually observed relationship can be used to test models.

 

[PeterDonis]

Cosmology textbooks aren't so good at answering 'what if' questions

I referred you to a cosmology textbook specifically in response to your asking for references for why "spacetime is locally curved due to the presence of matter" is equivalent to "expanding" (or contracting, in theory, but the expanding models are the ones that match observations) for models of the universe as a whole. Cosmology textbooks generally discuss the Einstein static universe and why it is not a viable solution (because it's unstable, like a pencil balanced on its point); other than that, any solution that is homogeneous and isotropic and has spacetime curvature due to stress-energy will be either expanding or contracting--i.e., not static. This is a simple consequence of the Einstein Field Equation (or the Friedmann equations, which are derived from the EFE) that is discussed in cosmology textbooks, which is why I referred you to them as a reference.

 

[PeterDonis]

What I'm hearing is that we can't currently differentiate between doppler and cosmological redshift without further theoretical assumptions.

No, what you're hearing is that we can't differentiate between these alternatives if redshift is the only piece of data we look at. But it isn't, as has already been explained.

As for "theoretical assumptions", there are always theoretical assumptions; there is no such thing as just "seeing the way the universe is" directly from data without theoretical assumptions. If you don't have some kind of constraint from theory, there are always an infinite number of mathematically possible models that can be made to fit the data. Making reasonable theoretical assumptions is how you narrow that down to a manageable number that can be realistically tested and compared.

 

[Orodruin]

No, what you're hearing is that we can't differentiate between these alternatives if redshift is the only piece of data we look at.

I think you already know my stance on this ... Unless you specifically refer to a particular coordinate system, there is no difference between cosmological redshift and Doppler shift. They can (and should) both be computed in the same way using the inner product of the observer 4-velocity and the 4-frequency. Anything on top of that is just dressing things up in particular coordinates.

However, I would agree with being able to determine from redshift and other observables that we live in a curved space-time that appears very FLRW.

 

[PeterDonis]

Unless you specifically refer to a particular coordinate system, there is no difference between cosmological redshift and Doppler shift.

Yes, fair point. A better way to put it would be that from redshift alone we can't tell what the curvature of spacetime is; we need other data as well.

 

[alantheastronomer]

I agree. I think that the observation that redshifts increase with distance rather than decrease is evidence for an expanding metric.