B Does the Expansion of the Universe Affect Gravity?

[Chris Miller]

This is irrelevant. We have a model of the entire universe which is spatially infinite. That's the only tool we have to even talk about concepts like "the total energy of the universe". If we're not allowed to use models that extrapolate beyond what we can directly observe, this whole discussion is pointless since it is based on nothing.

Been reading through this thread: https://www.physicsforums.com/threads/infinite-versus-finite-space.924230/ which has helped a little. Seems like what's called spacetime is a theoretical context for the big bang and the current known universe. By "known" I don't mean observable, but the universe that is expanding within this infinite hypothetical context. When I read that each cubic m of space contains 10^-10 joules of dark energy, it can't be referring to an infinite amount of space, can it? But only the space within the 90 billion ly's across of universe that is expanding.

 

[PeterDonis]

Seems like what's called spacetime is a theoretical context for the big bang and the current known universe.

"Spacetime" is a general term in relativity; it refers to any 4-dimensional geometry that is a solution of the Einstein Field Equation.

Our current cosmological model uses a particular solution of the EFE--i.e., one particular spacetime geometry out of an infinite number of possible ones--to describe our universe.

the universe that is expanding within this infinite hypothetical context

This is fine as long as you understand that the statement "the universe is expanding" means nothing more than "the particular spacetime geometry our current model uses to describe the universe has a particular 4-dimensional shape". In other words, most of the connotations of the word "expanding" do not apply. That's one reason why physicists use math to do physics, not ordinary language; ordinary language is too vague and misleading.

When I read that each cubic m of space contains 10^-10 joules of dark energy, it can't be referring to an infinite amount of space, can it?

Yes, it can. That's what our current cosmological model says.

 

[jbriggs444]

but the universe that is expanding within this infinite hypothetical context

The hypothetical infinite thing is the entire universe, observable and not. It can be thought of as a completed four-dimensional whole (a "block universe"). It is not a context within which something else expands.

Edit: @PeterDonis explained it better, it seems.

 

[Chris Miller]

There was no universe at $t = 0$. The "instant" $t = 0$ is not part of the model; it's a limit point that doesn't actually exist.

Of course, I meant approaching t=0.

The observable universe is not the same as the entire universe. All of the discussion in Carroll's article that you linked to refers to the entire universe, not just the observable universe. So the fact that the observable universe has a finite size is irrelevant here.

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

 

[phinds]

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.

Only if the entire universe is finite. The current consensus seems to be that it is most likely infinite in extent. Personally, I have a hard time getting my head around the concept that the universe is infinite in extent (and therefor of course has ALWAYS been infinite in extent] but I also have a hard time getting my head around the concept of a finite universe because then you have to worry about what shape it is and other things. Basically, I have a hard time getting my head around any of this. I have a small head.

 

[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"?