Comments - Inflationary Misconceptions and the Basics of Cosmological Horizons

[bapowell]

bapowell submitted a new PF Insights post

Inflationary Misconceptions and the Basics of Cosmological Horizons

Continue reading the Original PF Insights Post.

 

[eltodesukane]

The usefulness of comoving coordinates tells me that "expanding space" may be better viewed as "contracting matter", that "receding galaxies" may be better understood as "contracting galaxies".
Those point of view are probably exactly equivalent, but maybe they are not.

 

[Greg Bernhardt]

Fantastic work!

 

[marcus]

Really nice work, Brian. This could be our "go to" essay for a lot of newcomer questions.

 

[marcus]

Brian I was thinking how, when answering a question, I could direct somebody to a specific place in your tutorial---like Figure 6 which shows graphically all the events which can have influenced us by time T, and also all the events which we (or our matter starting in ancient times) can have have influenced by time T. Very interesting sets of events to focus on and think about.

There is a footnote #8 right near that figure 6. I wonder if I could use this link, to direct someone to that part of your essay:

https://www.physicsforums.com/insig...nceptions-basics-cosmological-horizons/#back8

Let me see how that works. Yes that works, it jumps right to Figure 6. So that way I wouldn't have to tell the person to read the whole essay, or to go to the start and scroll down to such and such. I could just say "look at this figure". the proximity of the footnote gives a mark to jump to. there may be other ways I don't know about to jump to a specific passage

 

[bapowell]

Let me see how that works. Yes that works, it jumps right to Figure 6. So that way I wouldn't have to tell the person to read the whole essay, or to go to the start and scroll down to such and such. I could just say "look at this figure". the proximity of the footnote gives a mark to jump to. there may be other ways I don't know about to jump to a specific passage

Thanks Marcus. This is a good idea. I can easily add linkable tags to figures and such if they end up being useful.

 

[timmdeeg]

Great article! Please allow me a remark regarding the balloon analogy. No doubt, it is a very helpful layman's guide but at the same time eventually a source of a common misunderstanding. Saying "the points separate on account of the expanding rubber" possible supports a laymen's notion to understand space as a sort of substance which expands physically. The analogy shows increasing distances perfectly, but perhaps one should clarify the role of the rubber.

 

[Chiclayo guy]

In the introduction you said, “…but my goal is to present the key ideas at a popular level, without assuming any prior understanding of cosmology.” In my view you’ve accomplished that, at least to the degree possible for someone with no physics or math background. My first read has already clarified several concepts for me. Thank you.

 

[bapowell]

Great article! Please allow me a remark regarding the balloon analogy. No doubt, it is a very helpful layman's guide but at the same time eventually a source of a common misunderstanding. Saying "the points separate on account of the expanding rubber" possible supports a laymen's notion to understand space as a sort of substance which expands physically. The analogy shows increasing distances perfectly, but perhaps one should clarify the role of the rubber.

Good point timmdeeg. I've added a footnote warning against this pitfall.

 

[Torbjorn_L]

Very useful, even though I've read D&L (a long time ago). Thanks!

Some typos, the most visible in the equation below fig. 4, and as you note by my circumstantial reference, the equation numbers are missing (re using this article as a reference).

I know this is a matter of taste and hence opinion, but the balloon analogy never did anything for me. The first time I met it it was used to discuss the then unknown topology of the universe and to make away with the question of a boundary. Very confusing at the time, which is why I prefer the 3D risin' raisin bread analogy instead even though the analogy breaks down re boundaries.

 

[phinds]

Great article! Please allow me a remark regarding the balloon analogy. No doubt, it is a very helpful layman's guide but at the same time eventually a source of a common misunderstanding. Saying "the points separate on account of the expanding rubber" possible supports a laymen's notion to understand space as a sort of substance which expands physically. The analogy shows increasing distances perfectly, but perhaps one should clarify the role of the rubber.

You might find it informative to check out the link in my signature

 

[S Buschmann]

Great article! I'm really a novice at this, forgive me. At some point, would the expansion reverse to a contraction?

 

[bapowell]

Great article! I'm really a novice at this, forgive me. At some point, would the expansion reverse to a contraction?

It certainly could, but that does not appear to be on the menu. For the last 9 billion years or so, the universe has been undergoing an accelerated expansion with no change of pace in sight.

 

[timmdeeg]

You might find it informative to check out the link in my signature

Agreed: No Stretching (!)

 

[slatts]

Great article!...If I can just remember where I bookmarked it, it should save PF a few tortuous threads on the relative speeds of objects within colliding bubble universes. (My parenthesizing and underlining fingers thank you, too.)

 

[JohnnyGui]

A very nice and clear article which definitely helps me understand things better.

A small thing that confused me though is the following quote:
"The result d_H > c is the hallmark of decelerated expansion"

Wouldn't an increase of the Hubble radius with ANY velocity, not just > c, mean a decelerating expansion?

I'm a real novice at this.

 

[bapowell]

Thanks for the comment JohnnyGui. If you look at the equation above Fig. 3 (yes, I know, no equation numbers!), \dot{d}_H = c(q+1), where q is the deceleration parameter, you'll see that when -1 < q < 0 -- when the universe is accelerating -- the Hubble scale grows at a rate smaller than c (and conversely). A good way to think about decelerated expansion is that comoving lengths (the size of spacings on an expanding grid) grow more slowly than the Hubble scale (this is identical to the statement that \dot{d}_H > c (since points with r = d_H have v_{rec} = c and the only way for the Hubble scale to overtake them is if it itself is growing at a rate greater than c)). On the other hand, if \dot{d}_H < c, that means that comoving lengths are growing more quickly than the Hubble scale: this is accelerated expansion.

 

[JohnnyGui]

Thanks for the comment JohnnyGui. If you look at the equation above Fig. 3 (yes, I know, no equation numbers!), \dot{d}_H = c(q+1), where q is the deceleration parameter, you'll see that when -1 < q < 0 -- when the universe is accelerating -- the Hubble scale grows at a rate smaller than c (and conversely). A good way to think about decelerated expansion is that comoving lengths (the size of spacings on an expanding grid) grow more slowly than the Hubble scale (this is identical to the statement that \dot{d}_H > c (since points with r = d_H have v_{rec} = c and the only way for the Hubble scale to overtake them is if it itself is growing at a rate greater than c)). On the other hand, if \dot{d}_H < c, that means that comoving lengths are growing more quickly than the Hubble scale: this is accelerated expansion.

I'm probably missing something here, but how can the Hubble radius grow faster than c if its very own limit (d_H) is determined by c?
How I see it, the only way to let the Hubble radius grow at a larger rate is to make the recession velocity (i.e. the growing rate of the comoving distance) of the objects behind it ≤ c but I can't see how that translates into a \dot{d}_H > c. Decelerating an object to ≤ c doesn't make the Hubble radius go any faster than c is what I would think.

Sorry for my misunderstanding.

 

[bapowell]

I'm probably missing something here, but how can the Hubble radius grow faster than c if its very own limit (d_H) is determined by c?

Good question. The key here is that the Hubble radius is not itself a comoving object, receding with the expansion: one does not apply Hubble's Law to the Hubble radius itself. You can think of it merely as a speed limit marker that is moving faster than the speed limit it is imposing on comoving objects.

 

[JohnnyGui]

Good question. The key here is that the Hubble radius is not itself a comoving object, receding with the expansion: one does not apply Hubble's Law to the Hubble radius itself. You can think of it merely as a speed limit marker that is moving faster than the speed limit it is imposing on comoving objects.

Is it correct if I say that relative to Earth (physical distance), the Hubble radius is always traveling/expanding at c? And if the expansion of the universe is decelerating, more objects fall into the Hubble radius while with acceleration objects escape out of the Hubble radius? If so, relative to what does the Hubble radius travel faster than c in a decelerating scenario?

 

[bapowell]

And if the expansion of the universe is decelerating, more objects fall into the Hubble radius while with acceleration objects escape out of the Hubble radius? If so, relative to what does the Hubble radius travel faster than c in a decelerating scenario?

Relative to Earth. But perhaps it's easier to think of decelerated expansion as comoving length scales growing relative to the Hubble scale. That way we avoid worrying about defining relative velocities.

 

[nikkkom]

Typo (first tag should be an opening one):

gets pushed out to [/itex]\tau=−\infty[/itex]

 

[haushofer]

Nice article! One question: why exactly is one allowed to add the two velocities due to own movement and space expansion a la Galilei, i.e. in a linear way?

 

[rede96]

Thanks for the great article. I'm only just an interested layman and not very good with the math, but your article helps to understand a lot of the confusion I found myself in when starting to learn about cosmology.

However there is one thing that is still confusing me which I was hoping you might help clear up:

Because this galaxy and the light it emits are being swept away from us by the expansion of space, it would indeed seem like this galaxy is forever unobservable. But that would be wrong. Many people make this mistake, including many cosmologists.

I've recently been watching the Stanford lectures on cosmology by Leonard Susskind and in those lectures he quite clearly states that once a galaxy starts to recede faster than c then it will be gone forever. In fact he goes on to say the in our very future universe the only light we will see is from our own galaxy, as everything else will be gone.

As I currently understand the expansion rate of the universe, it is accelerating, and it's the rate of acceleration which is decreasing, which will eventually slow to become a constant rate of acceleration. But the expansion rate is always going to be accelerating and never decelerating, at least not in terms where the recession velocity of a given distant galaxy can ever become smaller than it's current value.

So once the rate of expansion of a distant galaxy exceeds c, it will never slow to a recession velocity of less than c. So I am struggling to see how light emitted from a galaxy that is receding from us >c can ever reach us?

 

[alw34]

For the last 9 billion years or so, the universe has been undergoing an accelerated expansion with no change of pace in sight.

Isn't this usually described as 4 or 5 billion years ago...??

 

[alw34]

I've recently been watching the Stanford lectures on cosmology by Leonard Susskind and in those lectures he quite clearly states that once a galaxy starts to recede faster than c then it will be gone forever.

I may be misremembering here, it has been a while, but I think Susskind starts out with a simple model, one that ends up being different than the FLRW cosmological model. If you post a link to the lecture we can take a look.

 

[bapowell]

For the last 9 billion years or so, the universe has been undergoing an accelerated expansion with no change of pace in sight.

Isn't this usually described as 4 or 5 billion years ago...??

Yes, thanks for catching that. Looks like I took the complement.

 

[rede96]

I may be misremembering here, it has been a while, but I think Susskind starts out with a simple model, one that ends up being different than the FLRW cosmological model. If you post a link to the lecture we can take a look.

You might be right, and there are also two sets of lectures. One from 2009 and one from 2013. I'll see if I can find it.

 

[alw34]

I found a few notes I made regarding Susskind lecture:


PS: Oopsy daisy...how did the video actually get posted?

"Newtonian derivation of the FRW cosmological model from energy conservation. A Newtonian Cosmological Model…..Does not have ALL the features of a general relativity derivation….and flat special geometry…..k = 0…..[This is a matter dominated Universe model where the particles in the mass box are slowly moving. Universe behaved this way from about 100,000 years after BB to a few billion years of age..]

So it is a simplified model at least in this lecture...
I do really like Susskind lectures.

 

[rede96]

So it is a simplified model at least in this lecture...

Wow, well found! My notes weren't that good. However I did manage to find at least one of the other references he makes to distant galaxies eventually disappearing and we (our galaxy) are left as an isolated island.

I've put the link below, in which he spends the first 30 minutes or so answering questions, but the some key times are:

At 04:46 He starts to talk about relative velocities being greater than c

At 06:20, He goes on to explain the once something is moving away from you at a velocity > c then it can no longer send a message to you. And that any light traveling in your direction is actually moving away from you and thus never reach you.

At 17:25 he starts to talk about expansion of space and talks about modelling expansion as like little bits of space filling in as space expands

At 22:45 he then explains that distant galaxies will someday pass beyond the Hubble horizon and that the Hubble parameter is tending towards a constant at which point the Hubble horizon will become a fix distance.

At around 22:00 he goes on to say that eventually all galaxies (that aren't gravitationally bound to ours) will pass beyond this horizon and be gone forever and will be left as a truly isolated island with future cosmologist having to rely on history to know that the universe is expanding.

There is another session like this in a later lecture, so it isn't just this one reference.

 

[bapowell]

Nice article! One question: why exactly is one allowed to add the two velocities due to own movement and space expansion a la Galilei, i.e. in a linear way?

Thanks for reading! Is your question why we have v_{tot} = v_{pec} + v_{rec}?

 

[bapowell]

Thanks for the great article. I'm only just an interested layman and not very good with the math, but your article helps to understand a lot of the confusion I found myself in when starting to learn about cosmology.

However there is one thing that is still confusing me which I was hoping you might help clear up:

I've recently been watching the Stanford lectures on cosmology by Leonard Susskind and in those lectures he quite clearly states that once a galaxy starts to recede faster than c then it will be gone forever. In fact he goes on to say the in our very future universe the only light we will see is from our own galaxy, as everything else will be gone.

As I currently understand the expansion rate of the universe, it is accelerating, and it's the rate of acceleration which is decreasing, which will eventually slow to become a constant rate of acceleration. But the expansion rate is always going to be accelerating and never decelerating, at least not in terms where the recession velocity of a given distant galaxy can ever become smaller than it's current value.

So once the rate of expansion of a distant galaxy exceeds c, it will never slow to a recession velocity of less than c. So I am struggling to see how light emitted from a galaxy that is receding from us >c can ever reach us?

Thanks for reading. When the universe is accelerating, there is an event horizon. In this case, there are indeed events (like the emission of a photon from a distant galaxy) that will never be observable by us. The misconception that snares many people is that this is also true during even decelerated expansion as long as the galaxy is receding at superluminal speeds (see Figure 10). I hope I've convincingly argued in the article why that is not the case.

 

[alw34]

So once the rate of expansion of a distant galaxy exceeds c, it will never slow to a recession velocity of less than c. So I am struggling to see how light emitted from a galaxy that is receding from us >c can ever reach us?

Correct.

What changes is the as the 'Hubble constant', where recession v elocity =c. As H stops decreasing over time, which it is doing in the current era, and as Susskind says, approaches it's asymptotic constant limit in the far distant future, then the Hubble distance D = c/H stabilizes and 'things begin to disappear' at great distances as expansion moves beyond. It starts to get 'dark'.
Right now the Hubble distance is growing encompass more and more. After that, in the far ,far distant future, even nearby galaxies that are not gravitationally bound to us will eventually disappear. Even the CMBR dissipates as distances are stretched.

Here are some calculations I saved from and earlier discussion: [perhaps from Marcus]:
You can see in the near future, we actually get to see 'new things' we could not see before, just as in the past.

"The present is year 13.4 billion of the expansion and we are receiving CMB from hot matter that was 42.1 million ly from our matter (“us”) at the time of emission (and the wavelengths have been stretched by a factor of 1090) In year 17 billion we will be receiving CMB stretched by a factor of 1362 from matter that was 44.8 million ly from us at time of emission. In year 19 billion we will be receiving CMB stretched by a factor of 1557 from matter that was 46.1 million ly from us at time of emission.

I think the source was the "ned Wright calculator'
http://www.astro.ucla.edu/~wright/CosmoCalc.html

More recently, a " Jorrie calculator" has been utilized...unsure where that is///

 

[Jorrie]

Yes, thanks for catching that. Looks like I took the complement.

I think with modern parameters, the correct inflection point for changing from decelerating to accelerating expansion is at cosmic time T~7.6 Gy, making it about 6.2 Gy ago. It occurs when $(\Omega_\Lambda - \Omega_m/(2a^3) - \Omega_r/a^4)=0$, giving a~0.605, which happens at T~7.6 Gy in LCDM.

Of no consequence in this discussion though...

 

[haushofer]

Thanks for reading! Is your question why we have v_{tot} = v_{pec} + v_{rec}?

Yes. Intuitively I can see this because one speed involves the expansion of the background, but I'm not sure why we can simply add these velocities. Is it possible to show this by considering the corresponding 4-velocities or something alike?

 

[alw34]

I think with modern parameters, the correct inflection point for changing from decelerating to accelerating expansion is at cosmic time T~7.6 Gy, making it about 6.2 Gy ago.

Good to have an update.
That seems quite different from several years ago when I read here in physics forums.

A search here in the forums brings up Jorrie calculator 1.0...is that the most recent??

 

[Jorrie]

Good to have an update.
That seems quite different from several years ago when I read here in physics forums.

A search here in the forums brings up Jorrie calculator 1.0...is that the most recent??

The most recent release is always in my signature below...

 

[rede96]

Thanks for reading. When the universe is accelerating, there is an event horizon. In this case, there are indeed events (like the emission of a photon from a distant galaxy) that will never be observable by us. The misconception that snares many people is that this is also true during even decelerated expansion as long as the galaxy is receding at superluminal speeds (see Figure 10). I hope I've convincingly argued in the article why that is not the case.

Thanks for the reply. I think so, but you'll have to excuse my lack of understanding. I'm not great with the Math. What I read into that was deceleration implies actual 'slowing down' of expansion, as opposed to a 'slowing' in acceleration we see today, which is different. So in a decelerating universe, galaxies that were receding with speeds > c will eventually slow down to recession speeds less < c. So at this point during this slowing down, any photon's emitted whilst the galaxy was receding > c will now be able to catch up and we will eventually see them whiz past us at c.

Incidentally, if in an expanding universe a photon losses energy, which is transferred to the kinetic energy of expansion, does this mean in a decelerating universe the photon gets back energy from deceleration of the universe?

 

[rede96]

What changes is the as the 'Hubble constant', where recession v elocity =c. As H stops decreasing over time, which it is doing in the current era, and as Susskind says, approaches it's asymptotic constant limit in the far distant future, then the Hubble distance D = c/H stabilizes and 'things begin to disappear' at great distances as expansion moves beyond. It starts to get 'dark'.

Thanks for explanation, that's what I understood but just wanted to check!

 

[George Jones]

Yes. Intuitively I can see this because one speed involves the expansion of the background, but I'm not sure why we can simply add these velocities.

The Milne universe is a portion of Minkowski spacetime in cosmological coordinates. In the Milne universe, what are these velocities in the standard language of special relativity?

 

[haushofer]

The Milne universe is a portion of Minkowski spacetime in cosmological coordinates. In the Milne universe, what are these velocities in the standard language of special relativity?

I'm not so familiar with this Milne-solution, and I'm not sure what you're hinting at. Could you elaborate?

Is it about reinterpreting recessional velocities as peculiar velocities and then add them as you add ordinary 4-velocities in spacetime?

 

[bapowell]

Thanks for the reply. I think so, but you'll have to excuse my lack of understanding. I'm not great with the Math. What I read into that was deceleration implies actual 'slowing down' of expansion, as opposed to a 'slowing' in acceleration we see today, which is different.

Yes, it is different. By "decelerating" I mean a universe whose rate of expansion is decreasing in time.

 

[Rene Kail]

As many readers I share the enthusiasm about your article "Inflationary misconceptions".
While reading I spotted a mistake (not a misconception!) in Fig. 9 illustration and caption on page 10. In deSitter expansion the event horizon = Hubble radius = constant for all times. So both are shrinking in comoving coordinates and the acceleratered expansion
- pushes all galaxies beyond the event horizon (p. 11, OK); and
- all emitted photons will cross the event horizon. You can see this easily in the comoving diagram of Fig. 10 when sending a photon from any conformal time tau to the future.
- All galaxies at the event horizon have infinite redshift.

Also, I see no inconvenience in labelling the discussed horizons as Particle horizon and Event horizon (also called "ultimate lightcone") stressing their very different nature.
Greetings from Switzerland
Rene Kail
rhkail@gmx.net

 

[bapowell]

As many readers I share the enthusiasm about your article "Inflationary misconceptions".
While reading I spotted a mistake (not a misconception!) in Fig. 9 illustration and caption on page 10. In deSitter expansion the event horizon = Hubble radius = constant for all times. So both are shrinking in comoving coordinates and the acceleratered expansion
- pushes all galaxies beyond the event horizon (p. 11, OK); and
- all emitted photons will cross the event horizon. You can see this easily in the comoving diagram of Fig. 10 when sending a photon from any conformal time tau to the future.
- All galaxies at the event horizon have infinite redshift.

Also, I see no inconvenience in labelling the discussed horizons as Particle horizon and Event horizon (also called "ultimate lightcone") stressing their very different nature.
Greetings from Switzerland
Rene Kail
rhkail@gmx.net

Yes, indeed: during de Sitter expansion, the Hubble radius sets the event horizon. Thank you for pointing this out. What I am trying to emphasize in the article (not clearly enough, sadly) is that the event horizon corresponds to the comoving distance beyond which light emitted from Earth will never reach. This comoving distance is set by the Hubble scale at the time the light is emitted. This is what Fig 9 is trying to depict, but you are correct that the red circle is not the event horizon itself, but rather the comoving distance that forever outpaces light emitted in the left-most panel. I will revise the text to more carefully explain this.

 

[bapowell]

Yes. Intuitively I can see this because one speed involves the expansion of the background, but I'm not sure why we can simply add these velocities. Is it possible to show this by considering the corresponding 4-velocities or something alike?

The proper distance to an object is given by x = a x_{\rm com}, where a is the scale factor and x_{\rm com} is the comoving distance. The relative velocity between Earth and this object is \dot{x} = \dot{a}x_{\rm com} + a \dot{x}_{\rm com}. The first term is identified with v_{rec}, because it is the relative velocity due to the expansion of the universe. The second term is the peculiar velocity, v_{pec}, because it measures how the object moves relative to the expansion (via \dot{x}_{\rm com}).

 

[haushofer]

Ah, I see. A "why didn't I thought of that myself"-argument :P Thanks!