Does the Expansion of the Universe Affect Gravity?

[PeterDonis]

Isn't the size of the observable universe determined by the speed of light, while the entire universe is the size to which we believe it has expanded.

Not in our current model, no. In our current model, the universe is spatially infinite at all times.

This contextual infinite spacetime in which it's expanding is new to me.

That's one reason why I cautioned that most of the connotations of the word "expanding" do not apply. Those connotations don't help with understanding how a spatially infinite universe can be "expanding". But the mathematical model itself is perfectly consistent, and its predictions match our observations.

 

[Chris Miller]

Not in our current model, no. In our current model, the universe is spatially infinite at all times.
That's one reason why I cautioned that most of the connotations of the word "expanding" do not apply. Those connotations don't help with understanding how a spatially infinite universe can be "expanding". But the mathematical model itself is perfectly consistent, and its predictions match our observations.

Interesting! I guess by expanding, we mean only the distances between certain things within this infinite spacetime. Does our current model hypothesize the existence of any sort of matter beyond what the BBs "singularity" has grown to become (proliferated into?)? Like maybe other "universes?"

 

[jbriggs444]

Interesting! I guess by expanding, we mean only the distances between certain things within this infinite spacetime. Does our current model hypothesize the existence of any sort of matter beyond what the BBs "singularity" has grown to become (proliferated into?)? Like maybe other "universes?"

Does tomorrow count as being beyond what has become so far? Then yes, the model hypothesizes that matter will exist tomorrow.

 

[Chris Miller]

Does tomorrow count as being beyond what has become so far? Then yes, the model hypothesizes that matter will exist tomorrow.

No, "so far" excludes tomorrow.

 

[PeterDonis]

by expanding, we mean only the distances between certain things within this infinite spacetime

That's one way of looking at it, yes: "expanding" can be interpreted as "distances between observers who see the universe as homogeneous and isotropic are increasing with respect to proper time along the worldline of anyone of those observers".

Does our current model hypothesize the existence of any sort of matter beyond what the BBs "singularity" has grown to become (proliferated into?)? Like maybe other "universes?"

No. All "multiverse" models are speculative at this point and our best current model does not incorporate any of them.

 

[jbriggs444]

No, "so far" excludes tomorrow.

That's "yes, 'so far' excludes tomorrow"

 

[Benbenben]

Saying:

"...stretching" of space is purely a pop-sci fantasy. Space is just geometry, not "stuff" that can stretch or bend...",

...doesn't fit well with the usual explanation for the apparent discrepancy between the observable universe being ~92 Gly in diameter but only 14.7 Ga old.

If something 14.7 billion years ago were moving away from us at very nearly the speed of light AND space were not something subject to stretching, then the furthest away it could be then, to be seen today, would be 14.7 Gly; and the furthest away it might be today would be about 29.4 Gly.

That's only a little less than 60 Gly diameter for the observable universe. To get 30+ Gly beyond that to the +92 Gly of current models, there MUST be something akin to stretching or expansion of space/spacetime/vacuum.

.

How else could you get to ~92 Gly diameter without violating c in only 14.7 Ga?

 

[PeterDonis]

How else could you get to ~92 Gly diameter without violating c in only 14.7 Ga?

Because spacetime is curved. If spacetime were flat, your reasoning would be correct. But it isn't flat; it's curved. And in a curved spacetime, the intuitive relationship you are assuming between "speed of light" and "distance" no longer works.
.

 

[phinds]

... the apparent discrepancy between the observable universe being ~92 Gly in diameter but only 14.7 Ga old.

You are laboring under a serious misconception. There IS no "discrepancy".

 

[Benbenben]

Phinds, I would only apparently be laboring under such a misconception, if I accepted at true the solution suggested. In actuality you have misunderstood what I was saying.
I don't believe there is a discrepancy, because I believe the expansion of the universe (space and the vaccum) models well the observation that could otherwise present a discrepancy.
.
Phinds, I do appreciate your initiative in correcting any misconceptions I might have. I will suggest that in any similar future attempts you make an effort to go beyond simply stating what you see as wrong, and also detail why you believe it is wrong, and perhaps any related examples that might support your position.

 

[phinds]

Phinds, I would only apparently be laboring under such a misconception, if I accepted at true the solution suggested. In actuality you have misunderstood what I was saying.
I don't believe there is a discrepancy, because I believe the expansion of the universe (space and the vaccum) models well the observation that could otherwise present a discrepancy.
.
Phinds, I do appreciate your initiative in correcting any misconceptions I might have. I will suggest that in any similar future attempts you make an effort to go beyond simply stating what you see as wrong, and also detail why you believe it is wrong, and perhaps any related examples that might support your position.

Yeah, I do get too terse. thanks.

 

[Benbenben]

Because spacetime is curved. If spacetime were flat, your reasoning would be correct. But it isn't flat; it's curved. And in a curved spacetime, the intuitive relationship you are assuming between "speed of light" and "distance" no longer works.
.

Doesn't whether and how the universe is curved depend on whether the density of the universe is at the critical density and if not, how far off it is to which side?
Wouldn't the curvature need to differ by some minimum amount in the correct way (spherical vs hyperboloid) to allow for such a variation (if the stretching or expansion of space is not responsible for the observations being discussed) within that time frame?

 

[Chris Miller]

A little unclear on how something infinite can also be curved. I've always suffered from the assumption that the universe was analogous to the surface of the Earth in that if you traveled in a "straight" line you'd eventually arrive back where you started; if you could travel faster than it was expanding I mean.

 

[jbriggs444]

A little unclear on how something infinite can also be curved. I've always suffered from the assumption that the universe was analogous to the surface of the Earth in that if you traveled in a "straight" line you'd eventually arrive back where you started; if you could travel faster than it was expanding I mean.

Curved does not mean "curved into itself, making a closed, bounded shape". In the case of two dimensions, a saddle shape is both curved and unbounded.

 

[PeterDonis]

Doesn't whether and how the universe is curved depend on whether the density of the universe is at the critical density and if not, how far off it is to which side?

Spatially curved, yes, that depends on the density relative to the critical density, as far as the theoretical model goes. But we can estimate the spatial curvature itself much more accurately than we can estimate the density.

Wouldn't the curvature need to differ by some minimum amount in the correct way (spherical vs hyperboloid) to allow for such a variation (if the stretching or expansion of space is not responsible for the observations being discussed) within that time frame?

I'm not sure what your line of reasoning is here. The universe can expand while remaining spatially flat.

 

[PeterDonis]

I've always suffered from the assumption that the universe was analogous to the surface of the Earth in that if you traveled in a "straight" line you'd eventually arrive back where you started

This is the case of positive spatial curvature--in that case, yes, the universe is spatially finite. However, as @jbriggs444 noted, the case of negative spatial curvature results in a spatially infinite universe. That curvature is harder to visualize.

 

[Chris Miller]

That curvature is harder to visualize.

I'll say! Was also thinking that since the the ratio of the finite volume of the universe which contains matter/energy to the infinite rest (v/∞) approaches zero, and the infinite void portion, because it contains nothing, could be argued to not exist except as a mathematical construct. In other words, the universe does not physically exist until permeated by something.

 

[Chris Miller]

Curved does not mean "curved into itself, making a closed, bounded shape". In the case of two dimensions, a saddle shape is both curved and unbounded.

This shape does not look unbounded to me? https://en.wikipedia.org/wiki/Saddle_point#/media/File:Saddle_point.svg

 

[PeterDonis]

This shape does not look unbounded to me?

That's because it's not an image of all of the negatively curved space, only a portion of it. If you saw an image of a "Euclidean plane" on Wikipedia that didn't look unbounded, would you therefore conclude that the Euclidean plane itself was not unbounded?

You need to look at the actual math of the negatively curved space. The actual math makes it clear that it is unbounded.

 

[PeterDonis]

the finite volume of the universe which contains matter/energy

Huh? Where are you getting that from?

In our best current cosmological model, all of the infinite spatial volume of the universe contains matter/energy, and the average density is the same everywhere (at a given instant of time in standard cosmological coordinates).

It might be helpful at this point for you to say what your sources are for your understanding of cosmology; you appear to have a number of fundamental misconceptions.

 

[Chris Miller]

In our best current cosmological model, all of the infinite spatial volume of the universe contains matter/energy, and the average density is the same everywhere (at a given instant of time in standard cosmological coordinates).

Infinity is an algorithm, or function. So to me this (infinite mass/energy) makes no sense.

It might be helpful at this point for you to say what your sources are for your understanding of cosmology; you appear to have a number of fundamental misconceptions.

Pretty much any site I peruse. E.g., https://people.cs.umass.edu/~immerman/stanford/universe.html suggests some very large, but finite, numbers. I wonder how well accepted (much disputed) the `best current cosmological model` is.

 

[jbriggs444]

Infinity is an algorithm, or function

No, it is not.

A course in real analysis is useful.

 

[PeterDonis]

Pretty much any site I peruse.

In other words, no textbooks or peer-reviewed papers. Then the solution is simple: go read some textbooks or peer-reviewed papers.

E.g., https://people.cs.umass.edu/~immerman/stanford/universe.html suggests some very large, but finite, numbers.

Those numbers are for the observable universe, not the entire universe. The site says so (it uses the term "visible universe", but that's the same thing.)

I wonder how well accepted (much disputed) the `best current cosmological model` is.

It's very well accepted. You are simply misunderstanding what you are reading, an issue which, as noted above, can be solved by learning from textbooks or peer-reviewed papers.

 

[Chris Miller]

In other words, no textbooks or peer-reviewed papers. Then the solution is simple: go read some textbooks or peer-reviewed papers.
Those numbers are for the observable universe, not the entire universe. The site says so (it uses the term "visible universe", but that's the same thing.)
It's very well accepted. You are simply misunderstanding what you are reading, an issue which, as noted above, can be solved by learning from textbooks or peer-reviewed papers.

I think the web can be a good source of info, though you have to be discriminating, and guidance such as I get here (on the web) can help. This site seems to coroborate and explain what you're saying: http://www.dailygalaxy.com/my_weblog/2013/02/the-real-universe-is-250-times-bigger-than-the-visible-hubble-volume-todays-most-popular-1.html The title's misleading, since they do say "infinite" and explain how this conclusion was arrived at (some of which is over my head). Interesting that, according to his biography, when John Nash proposed a flat, infinite universe to Einstein, he was advised to study physics.

 

[PeterDonis]

I think the web can be a good source of info, though you have to be discriminating

If you don't already understand the science from a better source, textbooks or peer-reviewed papers, on what basis are you going to be "discriminating"?

 

[PeterDonis]

This site seems to confirm and explain what you;re saying

But it doesn't give a link to an actual paper. That's always a red flag with me. How do I know the actual research says what the article claims it says? Journalists in general often don't have a very good grasp of the subjects they report on, and science journalists are usually even worse than the average journalist, because the subjects they report on require much more background to understand properly.

 

[Chris Miller]

No, it is not.

A course in real analysis is useful.

Until this infinite universe thing, I would've called infinity a conceptual construct. Still kind of do.

 

[Chris Miller]

If you don't already understand the science from a better source, textbooks or peer-reviewed papers, on what basis are you going to be "discriminating"?

Math and science are way too specialized for anyone to understand as a whole now, and so we must accept the findings and research of those who've gained our trust. I trust you guys.

 

[PeterDonis]

Math and science are way too specialized for anyone to understand as a whole now, and so we must accept the findings and research of those who've gained our trust. I trust you guys.

Thanks for the kudos.

 

[Chris Miller]

Thanks for the kudos.

I'm serious, and you're welcome. I feel I've learned a lot here, and wonder sometimes what you all get out of it.

I appreciate the recommendations that I read (i.e., study) textbooks and peer-reviewed papers. And while I do read and enjoy some of the simpler papers linked to and occasionally authored by some of you here, most serious texts would require a lot of study, exercise, and probably mentoring, for me to properly appreciate.

I must admit that while I try to harbor no beliefs, only hypotheses, the answers provided in this thread have inspired a kind of faith crisis. I've always been taught that the universe began as a very small dense particle that has, over billions of years, expanded into its current 4D shape and size, estimated to be about 90 billion ly in diameter. Now I'm told (I think) that the best current model suggests that this naked singularity I've always thought constituted "everything" occurred and exists within the context of infinite space and matter/energy. I know the math doesn't translate well into written language, and I can almost get my head around an infinite void (i.e., infinite nothing). But are you saying that matter and energy are also infinite? That there are theoretically infinite galaxies now? I've always said that existence as we perceive it is impossible by our understandings. But I guess I wasn't quite ready to have this so well exemplified.

 

[jbriggs444]

Now I'm told (I think) that the best current model suggests that this naked singularity I've always thought constituted "everything" occurred and exists within the context of infinite space and matter/energy.

The singularity does not "exist" at all. It is not something that lives within the model. It is something more like a boundary at the end of an open interval.

The model uses manifolds and manifolds use "open" sets. Open sets do not contain their own boundaries. An infinite line is, for instance, an open set. It does not contain either endpoint "at infinity". It has no endpoints.

 

[Grinkle]

@Chris Miller You only need to change one thing in your visualization. The universe was denser in the past than it is now. Where you are picturing a tiny point, instead picture an infintie universe that is as dense as possible, more dense than we have models or theories to describe. Then picture that universe becoming less dense - this is the big bang / expansion etc. Its not very different from your picture, and to me at least, it makes a lot more sense than your picture. I was also carrying the picture you describe in my head for a long time - and replacing the point with a dense infinite-expanse universe was a big light-bulb moment for me - it resolved my confusion / wondering what the small point was expanding into if it was already everything.

It left me with the problem of needing to grapple with a universe that is infinite in extent somehow becoming larger, but for no good reason that I can articulate that doesn't bother me as much as the expanding point visualization did.

I don't think you need to be having any crisis in faith - just tweak your mental model a bit!

 

[plillies]

Because spacetime is curved. If spacetime were flat, your reasoning would be correct. But it isn't flat; it's curved. And in a curved spacetime, the intuitive relationship you are assuming between "speed of light" and "distance" no longer works.
.

Hmmm! The light from 13.8 billion l-ys. Isn't it just the light from the sphere 13.8 billion l-ys in diameter that started out toward us 13.8 billion years ago? As it traveled those 13.8 billion l-ys, it cooled from 3000 K radiation to 2.7 K radiation.

 

[PeterDonis]

The light from 13.8 billion l-ys. Isn't it just the light from the sphere 13.8 billion l-ys in diameter that started out toward us 13.8 billion years ago?

No. The quote you gave from me already explains why.

To illustrate using the particular example you give, consider a light ray just arriving on Earth now that was emitted 13.8 billion years ago. The point from which that light was emitted is not now 13.8 billion light years away from us. It's much further away than that (about 47 billion light-years). And when the light ray was emitted, 13.8 billion years ago, the point it was emitted from, then, was much closer than 13.8 billion light years to the point where the Earth would have been if it had existed then (and had maintained the same motion from then to now, which of course would not have happened, but we can consider it as an idealized thought experiment).

 

[Chris Miller]

The singularity does not "exist" at all. It is not something that lives within the model. It is something more like a boundary at the end of an open interval.

The model uses manifolds and manifolds use "open" sets. Open sets do not contain their own boundaries. An infinite line is, for instance, an open set. It does not contain either endpoint "at infinity". It has no endpoints.

"The singularity does not "exist"... It is something... a boundary... Open sets do not contain their own boundaries."

You see my confusion?