Cosmological redshift, how fast can the universe expand?

[P.Bo]

Ok, I'm writing up something and I do something I always hate doing... I start arguing myself into a corner.

The argument of the night is the expansion of the universe and how it applies to redshifts. Which has brought a series of questions which I can't seem to grasp right now.

I) Is it possible that there are parts of the Universe that are expanding at FTL velocity w.r.t. us?

I.a) If not, at what point does the "relativistic" contribution come into play... I use this term tongue in cheek akin to Newtonian kinetic energy changes at really high speed but is a pretty darn good approximation at most speeds not anywhere close to c. Would the expansion of the universe be limited in any fashion (I'm guessing not here due the whole "warp drive" ideas)

I.b) If it is possible, what exactly happens to that light with respect to us? The way I learned is light still travels at speed c through any space, it simply gets stretched (redshift) as the space expands (although the idea of an expanding point source still is fuzzy to me).

I.b.1) If space moves at speed c, has redshift of infinity(?) basically infinite long wavelength or zero energy photon? Then space moving > c, has redshift of... infinity+1 :), imaginary values?, with negative/imaginary energy photons? The source of dark energy?? (Where's my Nobel!)

I.b.1.a) The expansion of space is only relative to any given observer, so a closer observer would see a smaller redshift because the galaxy is receding slower with respect to them. So if there is FTL expansion "way out there" then a "closer" galaxy would see less than FTL expansion, have whatever redshifting of light, then the next one sees that galaxy receding away and would have whatever redshifting of that light, etc etc etc until it gets to us, something akin to a Zeno's paradox... so even though there is a FTL expansion, photons should still be visible (doubling the length of a wavelength... you'll never get an infinite wavelength).

Keep in mind, I realize the largest Z values are the CMBR, but I'm still thinking in the "what if" mindset. So yeah, I start arguing myself down a path now I'm lost :D

 

[Mordred]

Redshift is distance dependant.

The further the distance the greater the redshift. or the greater the recessive velocity. At further parts of the universe we do see FTL recessive velocity. However this does not mean FTL expansion.
I recently have been writing an article covering this page 7

https://www.physicsforums.com/showthread.php?t=678485&page=7

on this thread had the last draft of that article. It should answer all your questions.

 

[P.Bo]

Thanks for the reply, I did skim through the relevant parts of your post before I posted, one thing that was a bit confusing

The current accepted value is 70 kilometers/second per mega parsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light.

in one part you're saying H₀ = 70 km/s/Mpc, then a line later you say H₀ = 4300±400Mpc... which I'm assuming you mean d = 4300 Mpc ... and it simply was a typo in your FAQ.

Either way, from my understanding the farthest thing we've seen is in the 4100 Mpc range, which would make it close, but not FTL recession speeds. I realize it might be moving FTL now (if that is the case) but we're not seeing it now, we're seeing it 13.37 Gyr ago.

This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity. It is precisely analogous to a separation speed. If, in one frame of reference, one object is moving east at .9c, and another west at .9c, they are separating by 1.8c.

I have issues with this as an explanation, while yeah, separation distances can exceed c, from anyone of those observers reference points they will not see any speed > c regardless of separation speeds. I was under the impression it doesn't violate GR because it's not the object that's moving, it's the space the object is in is expanding, and it's just going along for the ride in it. Basically there's no limitation in expansion of space speeds in GR (SR?)

You'll have to forgive me, all my astrophysics and cosmology classes I took were in the late 90s, and I'm sure the state of the art has changed a bit since then.

 

[Chronos]

The modern view is that FTL expansion is perfectly acceptable under GR. Nothing moves FTL in its own inertial reference frame and nothing forbids distance between distant objects from receeding FTL. In fact, we still receive light from bodies that were receeding FTL when those photons were emitted.

 

[P.Bo]

The modern view is that FTL expansion is perfectly acceptable under GR. Nothing moves FTL in its own inertial reference frame and nothing forbids distance between distant objects from receeding FTL. In fact, we still receive light from bodies that were receeding FTL when those photons were emitted.

Yes but the 64 dollar question is will we ever receive photons from those bodies that are now receeding FTL.

If so, then how would they be redshifted?

If not, then why not... since again it's recession speed is relative to distance, and there is a reference frame were the recession where those photons were emited is not FTL(obviously not our reference frame), and through linking with that reference frame those photons will pass through that receding reference frame and eventually get to us wouldn't they?

 

[Chronos]

See Davis and Lineweaver, Expanding Confusion - http://arxiv.org/abs/astro-ph/0310808

 

[Jorrie]

I have issues with this as an explanation, while yeah, separation distances can exceed c, from anyone of those observers reference points they will not see any speed > c regardless of separation speeds. I was under the impression it doesn't violate GR because it's not the object that's moving, it's the space the object is in is expanding, and it's just going along for the ride in it. Basically there's no limitation in expansion of space speeds in GR (SR?)

You must be careful of thinking "expansion of space speeds". Expansion does not really have a speed - it is a % growth per unit time of all large scale distances. That % changes slowly, but at any given time all distance grow with the same % per unit time. Distances presently grow at 1/140 % per million years. This directly causes Hubble's law; the farther, the higher the recession speed from us (change in proper distance per unit time).

We can observe the earliest galaxies that receded at near 4c when the light was emitted, simply because the expansion % has decreased dramatically in early times and the photons that were first 'dragged' away from us, eventually started to make headway towards us. It is pictured in the "teardrop" (light cone) curve of the 'Davis Three-panel Expansion graphs' in my signature below.

 

[Mordred]

Thanks for pointing out the typo. I had meant to cover the Hubble sphere. This is the point where recessive velocity changes from subluminal to FTL. The radius is r_HS=cH_o The second part you mentioned is PAllens contribution for Doppler shift.
Classically redshift is treated as different than redshift. However with proper observer treatment Redshift and Doppler shift can also be treated as one and the same. PAllen is better qualified to describe that relation.
As the others have mentioned recessive velocity has no inertia. The space between two coordinates is simply expanding. the farthur you look the greater the expansion will look.
Redshift is always observer dependant. Study Hubbles law closely to see the distance relation to redshift.

 

[Chalnoth]

Yes but the 64 dollar question is will we ever receive photons from those bodies that are now receeding FTL.

That depends upon how the universe expands in the future. Because the Hubble parameter is likely to decrease in the future, there are some galaxies out there that are currently expanding faster than the speed of light from us, but we will still be able to see their light emitted today.

This will no longer be the case when dark energy dominates the universe, as the Hubble parameter approaches a constant value.

 

[Mordred]

That depends upon how the universe expands in the future. Because the Hubble parameter is likely to decrease in the future, there are some galaxies out there that are currently expanding faster than the speed of light from us, but we will still be able to see their light emitted today.

This will no longer be the case when dark energy dominates the universe, as the Hubble parameter approaches a constant value.

I've always found the statement " There are galaxies out there that are currently expanding faster than the speed of light."
misleading from our observer viewpoint the recessive velocity is FTL. However expansion itself is the same everywhere. It would be better to describe briefly that when we make that statement we should also add an explanation of the distance factor.

In point of fact photons has no problem transversing the regions we describe as FTL as that descriptive is a distance dependant recessive velocity.
described by Hubbles Law: the greater the distance the greater the recesive velocity

At the location of the photon the local spacetime is not expanding FTL. The FTL statement in that above sentence is what leads to the light reaching us confusion. Unfortunately too many pop media articles use that statement.

 

[Chalnoth]

I've always found the statement " There are galaxies out there that are currently expanding faster than the speed of light."
misleading from our observer viewpoint the recessive velocity is FTL. However expansion itself is the same everywhere. It would be better to describe briefly that when we make that statement we should also add an explanation of the distance factor.

You're right, I misspoke. And it's worth adding that the apparent recession faster than light is only based upon convention: the velocities of far-away objects are arbitrary. Differences in velocity are only well-defined at a single point.

At the location of the photon the local spacetime is not expanding FTL.

Well, it doesn't even make sense to talk about expansion faster (or slower) than the speed of light: expansion isn't a speed, it's a rate. It'd be like saying you have a car that can travel faster than 3,000 RPM's. That statement doesn't even make sense.

That said, there probably is a limit on the rate of expansion given by the Planck scale, at about $1.6 \times 10^{63}\mathrm{km/s/Mpc}$, as compared to today's measured expansion rate of roughly 70 in the same units.

 

[Jorrie]

You're right, I misspoke. And it's worth adding that the apparent recession faster than light is only based upon convention: the velocities of far-away objects are arbitrary. Differences in velocity are only well-defined at a single point.

I suppose if we define recession speed as the change in proper distance per unit cosmic time, it is at least well defined, or not? Or shall that be called a recession rate rather than a recession speed?

I agree on expansion rate that must not be confused with recession speed (or rate).

 

[Mordred]

Yeah your right on the speed and rate comparision also being misleading lol.

 

[Mordred]

I suppose if we define recession speed as the change in proper distance per unit cosmic time, it is at least well defined, or not? Or shall that be called a recession rate rather than a recession speed?

I agree on expansion rate that must not be confused with recession speed (or rate).

I would prefer recession rate over recession speed as speed implies inertia, would have been nice if recession velocity in the Hubbles law never used the word velocity lol. same with the big bang term.

How about recession velocity is a measure of the change in proper distance per unit cosmic time where recession velocity is directly proportional to its proper distance.

 

[Chalnoth]

I suppose if we define recession speed as the change in proper distance per unit cosmic time, it is at least well defined, or not? Or shall that be called a recession rate rather than a recession speed?

The problem is that there are other equally-valid definitions one could use. I could just as easily, for instance, use the definition that the speed of the far-away object is the speed we infer from its redshift using the relativistic doppler effect formula.

 

[Mordred]

Yeah that's a good point I looked around for quit a while for an all inclusive definition. Every one was either misleading or left vital details out.

 

[Jorrie]

The problem is that there are other equally-valid definitions one could use.

Doesn't Hubble's law: Vrec = HoD, with D the co-moving (present proper) distance, make Vrec = dD/dt somewhat of a preferred definition, even if it is just conventional?

I guess the SR conversion from redshift could be called an "apparent recession rate", whereas the co-moving definition is more "proper"...