Comments - Inflationary Misconceptions and the Basics of Cosmological Horizons

[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!