B How do we know that the rate of expansion of the Universe was slowing down

[photonkid]

I've read that until 5 billion years ago the rate of expansion of space was decreasing. How do we know that it was slowing down?

Does the uniformity of the CMB mean that the rate of expansion is identical throughout the entire universe - or does it just mean that the average rate of expansion over a sufficiently large amount of space is identical?

If the density of matter is the reason for the change in the rate of expansion then why isn't the rate of expansion different at different places in the universe?

 

[phinds]

Does the uniformity of the CMB mean that the rate of expansion is identical throughout the entire universe - or does it just mean that the average rate of expansion over a sufficiently large amount of space is identical?

expansion is a large-scale phenomenon and is uniform outside of bound systems such as galactic clusters.

If the density of matter is the reason for the change in the rate of expansion then why isn't the rate of expansion different at different places in the universe?

expansion is a large-scale phenomenon and on large scales the universe IS uniform (see The Cosmological Principle). The density you are talking about is large scale density. On small scales the universe is not uniform.

 

[PeterDonis]

How do we know that it was slowing down?

The same way we know that for the past few billion years it has been speeding up. We look at the relationship between redshift, apparent brightness, and angular size for objects at a wide range of redshifts, which means we are looking at a wide range of times during the evolution of the universe. Basically this gives us a curve describing how the Hubble constant has changed over time, and that tells us the behavior of the expansion.

 

[photonkid]

expansion is a large-scale phenomenon and is uniform outside of bound systems such as galactic clusters.

expansion is a large-scale phenomenon and on large scales the universe IS uniform (see The Cosmological Principle). The density you are talking about is large scale density. On small scales the universe is not uniform.

Thanks. I had never heard of the cosmological principle before. On wikipedia it says

it is statistically homogeneous on scales larger than 250 million light years

and

In September 2016, however, studies of the expansion of the Universe that have used data taken by the Planck mission show it to be highly isotropical, reinforcing the cosmological principle

I'm still not understanding how matter (mass) can affect the rate of expansion and do it uniformly. e.g. suppose in the future the universe has expanded to the point that all galaxies apart from our own cluster are outside the observable universe, is the rate of expansion still identical everywhere in the observable universe? Is the rate of expansion in "our part of the universe" affected by matter that is outside the observable universe.

Is the rate of expansion (thought to be) precisely identical everywhere in the universe to umpteen decimal places?

Perhaps another way of asking my question is - why do we think the density of matter affects the rate of expansion?

 

[PeterDonis]

Is the rate of expansion (thought to be) precisely identical everywhere in the universe to umpteen decimal places?

The short answer is no. The somewhat longer answer is that it isn't a matter of "rate of expansion", it's a matter of spacetime geometry. When we talk about the universe being homogeneous and isotropic, we are saying that its spacetime geometry is uniform (same curvature--actually it's more complicated than that, but that will do for now since this is a "B" level thread) to some approximation. Obviously it isn't uniform to umpteen decimal places, because you and I and the planet we live on and other stars and planets are a lot more dense than the average density of the universe, and the spacetime geometry in our vicinity changes accordingly.

In other words, the actual spacetime geometry of the universe is not uniform everywhere; it's just uniform on average, but there are local bumps and wiggles where there are concentrations of matter. It's no different from the fact that the geometry of the Earth's surface is not a perfect oblate spheroid: it's an oblate spheroid on average, but there are local bumps and wiggles.

why do we think the density of matter affects the rate of expansion?

Because the density of matter is part of the stress-energy tensor, and the stress-energy tensor affects the spacetime geometry through the Einstein Field Equation.

 

[photonkid]

ok, so it's fairly complex. Thanks for answering.

 

[photonkid]

I have another related question. I've been reading articles on the internet like this one
https://medium.com/starts-with-a-ba...iverse-is-expanding-why-arent-we-71b46b5e9974
but so far I'm unable to tell whether space between say, two stars in our galaxy, is actually expanding but gravity pulls the two stars back together, or whether there's actually no expansion of space in the region of the milky way galaxy and our local group.

So my question is - suppose there's a cubic region of empty space one billion light years by one billion by one billion - i.e. in the centre of this cube the expansion of space is running at maximum speed. I'm going to call this the "empty space expansion rate". So now suppose we have two points in empty space (x1, x2), 100 million light years apart and the space between those two points is expanding at the "empty space expansion rate". Now I take another two points (y1, y2) in space 100 million light years apart, but this time, a straight line between those two points passes right through the center of our local group of galaxies. Most of the space between y1, y2 is empty except for the 10 million or so light years where our local group is. Question 1 - Does the distance between y1, y2 increase at the same rate as between x1, x2? If the answer to question one is no, then how different are the two rates - is the y1 y2 rate roughly 90% of the x1 x2 rate?

I chose a distance of 100 million ly because I've read that over that distance, the expansion of space is more powerful than gravity but over a distance of 10 million ly (where our local group is) gravity is stronger and our local group of galaxies will eventually merge into one single galaxy.

Another way of asking my question might be - suppose I take 100 sets of point pairs (A1/B1 ... A100/B100) at random places in the observable universe, where An/Bn are 100 million light years apart for all n. How much variation in the expansion rate between the two points in each pair could there be?

 

[PeterDonis]

in the centre of this cube the expansion of space is running at maximum speed

"Expansion of space" is not what's going on, and it doesn't have a "speed". It's unfortunate that so many sources, including the article you linked to, talk about "the fabric of space expanding", or something else that gives the (wrong) impression that there is a "thing" which is "expanding", and which invites the natural (wrong) inference that this thing which is expanding must be exerting a force on objects that "tries" to make them expand as well.

All that we really mean by "the universe is expanding" is "galaxies and galaxy clusters which are not gravitationally bound to each other are moving apart, on average". The average is over large distance scales (roughly 100 million light years and larger). But "moving apart" is all that it means. It doesn't mean there is any "expansion of space" that is "trying" to make things move apart. They are moving apart now because they started out moving apart at the Big Bang. That's really all there is to it.

 

[photonkid]

If that's all there is to it then why is the CMB and radiation from distant stars red-shifted due to the expansion of space?

Could you please try to answer the question that I asked - "Does the distance between y1, y2 increase at the same rate as between x1, x2?

Also, is the light that we receive from another star in our galaxy (or from the Andromeda galaxy) red-shifted due to the expansion of space?

 

[phinds]

If that's all there is to it then why is the CMB and radiation from distant stars red-shifted due to the expansion of space?

Could you please try to answer the question that I asked - "Does the distance between y1, y2 increase at the same rate as between x1, x2?

Also, is the light that we receive from another star in our galaxy (or from the Andromeda galaxy) red-shifted due to the expansion of space?

I think if you reread carefully all of the answer so far, you'll see that all of these questions have been answered.

 

[PeterDonis]

If that's all there is to it then why is the CMB and radiation from distant stars red-shifted due to the expansion of space?

It isn't. It's redshifted due to the geometry of spacetime.

Does the distance between y1, y2 increase at the same rate as between x1, x2?

The question has no meaning because "points in space" are an abstraction; they're part of our model, not part of reality. To really understand what's going on, you need to think in terms of concrete objects: our galaxy, other galaxies, galaxy clusters, etc.

For example, suppose we reformulate your question this way: consider four planets, each of which is moving in such a way that observers on those planets see the universe as homogeneous and isotropic. In other words, observers on all four planets are "comoving" observers (this is the usual term used in cosmology). The four planets are divided into two pairs; each pair is separated by the same proper distance at a given instant of time, but what is between them differs:

Pair x1, x2 are separated by nothing but empty space.

Pair y1, y2 are separated by mostly empty space, but about halfway between them is our Local Group of galaxies, the total size of which is a small fraction of the overall proper distance between the pair.

How will the rate of increase of proper distance between the two pairs compare?

The answer, I believe, is that they will be the same. However, there are a couple of caveats. First, proper distance can't be directly measured. We can only directly measure redshift, apparent luminosity, and apparent angular size for distant objects. (We'll assume that the observers on each planet have telescopes powerful enough to do this.) We estimate distance from these data (actually from the last two--redshift itself tells us something different).

Second, we observe distant objects not as they are right now, but as they were when the light we are seeing now was emitted. And because of the presence of a gravitationally bound object between y1, y2 but not x1, x2, the travel of light between them will not be the same; the light rays between y1 and y2 will have their spatial paths bent (gravitational lensing) and will be time delayed (Shapiro time delay) as compared to light rays between x1 and x2. So any comparison between the two pairs will have to correct for that.

is the light that we receive from another star in our galaxy (or from the Andromeda galaxy) red-shifted due to the expansion of space?

No. Nothing is redshifted due to the expansion of space. See above.

A better way of asking the question would be, is the light we receive from another star in our galaxy, or from the Andromeda galaxy, redshifted due to the average geometry of spacetime caused by the average density of matter and energy in the universe as a whole? Then the answer is no, it isn't. All of the observed redshift (or blueshift--note that light reaching us from the Andromeda galaxy is blueshifted) from objects in our galaxy or our Local Group of galaxies--i.e., within the same gravitationally bound system as we are--is going to be due to the local spacetime geometry of that gravitationally bound system, plus the relative motion of the objects (the latter is why light from the Andromeda galaxy is blueshifted--that galaxy is moving towards ours at several hundred kilometers per second).

 

[photonkid]

ok, thanks for answering.