I Any direct measure of Universe expansion via galaxy subtended angles?

[phinds]

... I suggest it might be possible that a measurement across a combination of galaxies in relatively nearby cluster group

Interesting idea. You should check it against the calculations in posts 10 and 15. I think it likely that the numbers will show that it won't work, but I certainly can't say that for sure.

 

[Justin Hunt]

Forgive my ignorance, but wouldn't "gravitational time dilation" be a factor considering the universe billions of years ago was more dense then universe of today?

But, as for a direct observation, I would imagine a change in red shift over time would be a much better value. An object approaching the edge of the observable universe should have it's red shift increase towards infinity as its light intensity approaches zero. This effect should gradually become more extreme the closer and object gets to the edge of the observable universe. The best part of this type of observation would also be that we could use it to determine how much of the red shift value is due to universe expansion and could help refine the hobble value H0.

 

[phinds]

Forgive my ignorance, but wouldn't "gravitational time dilation" be a factor considering the universe billions of years ago was more dense then universe of today?

No. I don't follow why you think it would.

But, as for a direct observation, I would imagine a change in red shift over time would be a much better value.

yes

An object approaching the edge of the observable universe should have it's red shift increase towards infinity as its light intensity approaches zero.

No, it would not.

This effect should gradually become more extreme the closer and object gets to the edge of the observable universe.

since such an effect (approaching infinity) doesn't exist, that makes no sense.

You seem to have some sort of belief that there is something magical about the "edge" of the observable universe. There is not. The objects at the remotest observable point in the observable universe are receding from us at about 3c and their red shift (about 1100) is not approaching infinity except in the most trivial sense that 10 is bigger than 9

 

[Justin Hunt]

@phinds In order for a distance galaxy to be observed, a photon released from said galaxy has to enter a region of space that is not moving away from us >C due to the expansion of space. This is why we have an observable universe that can change in size depending on the rate of expansion. Considering Scientists believe the universe is expanding at an accelerated rate, out observable universe will continue to shrink.

like traveling through a black holes event horizon, there is nothing special about it for the the object. But, observing said object here on Earth there is a distinction.

 

[George Jones]

Considering Scientists believe the universe is expanding at an accelerated rate, out observable universe will continue to shrink.

Actually, this is a myth. If an object is observable (i.e., on our past lightcone), the object will always be on our past lightcone, even in universes that have accelerating expansion. As time passes, some objects that are not our past lightcone move onto our past lightcone, but, once on, no object moves off our past lighcone, i.e., the amount of stuff in the observable universe increases with time.

 

[phinds]

@phinds In order for a distance galaxy to be observed, a photon released from said galaxy has to enter a region of space that is not moving away from us >C due to the expansion of space.

Sure. So what?

This is why we have an observable universe that can change in size depending on the rate of expansion.

No, it is not the reason.

Considering Scientists believe the universe is expanding at an accelerated rate, out observable universe will continue to shrink.

Not only is that wrong, it is backwards. The OU will continue to increase at a very small rate, both in terms of its size and in terms of the amount of stuff in it. It WILL eventually red-shift beyond our ability to detect it, but so what?

like traveling through a black holes event horizon, there is nothing special about it for the the object. But, observing said object here on Earth there is a distinction.

Again, so what? No one is disputing gravitational time dilation if you go near a black hole.

 

[Bandersnatch]

Forgive my ignorance, but wouldn't "gravitational time dilation" be a factor considering the universe billions of years ago was more dense then universe of today?

If everything is equally denser, then there is no gravity well to climb out of.

But, as for a direct observation, I would imagine a change in red shift over time would be a much better value. An object approaching the edge of the observable universe should have it's red shift increase towards infinity as its light intensity approaches zero. This effect should gradually become more extreme the closer and object gets to the edge of the observable universe. The best part of this type of observation would also be that we could use it to determine how much of the red shift value is due to universe expansion and could help refine the hobble value H0.

This does happen, but not with the edge of the observable universe. You need - much like with black holes - an event horizon.
However, that cosmological event horizon is farther away than what is observable. Signals emitted at the event horizon will reach us in the infinite future and will be infinitely redshifted. The longer we wait, the closer from the event horizon the signals will be reaching us, and the more redshifted they'll be. But it won't be possible to observe infinite redshifts until infinite time has passed.

Furthermore, neither the edge of the observable universe nor the event horizon are at the distance where expansion reaches c (aka Hubble radius). This is due to the changing rate of expansion (i.e. the Hubble constant decreasing), which permits light signals emitted from where expansion is >c to enter regions where it is <c - or, in other words, the Hubble radius is expanding and gradually encompasses previously non-approaching light signals.
There is a nice article in the Insights section of the forum discussing this phenomenon, here: https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/. This pedagogical paper covers this as well: https://arxiv.org/abs/astro-ph/0310808 (the light cone graphs are of great help, if you can read them).

 

[Bandersnatch]

The OU will continue to increase at a very small rate, both in terms of its size and in terms of the amount of stuff in it.

While true in terms of the stuff in it (i.e. comoving radius of the past light cone), in terms of its size the rate is not small at all. The size of the OU is the proper distance to the particle horizon, and this increases to infinity in the infinite future.

 

[Justin Hunt]

Except our universe is currently expanding at an accelerated rate. which is covered quite clearly in the insights article Bandersnatch provided above. The OU decreases in those situations. our universe had massive inflation at the beginning and then most of our past history has had the rate of expansion decreasing over time. some time ago until the present, however, the expansion has been accelerating again. It well may be the case that the OU is currently still increasing, I am not expert on this, but if our universe continues to expand at an accelerated rate, the OU will begin shrinking at some point until it is a very lonely universe.

 

[phinds]

Except our universe is currently expanding at an accelerated rate. which is covered quite clearly in the insights article Bandersnatch provided above. The OU decreases in those situations. our universe had massive inflation at the beginning and then most of our past history has had the rate of expansion decreasing over time. some time ago until the present, however, the expansion has been accelerating again. It well may be the case that the OU is currently still increasing, I am not expert on this, but if our universe continues to expand at an accelerated rate, the OU will begin shrinking at some point until it is a very lonely universe.

You are mistaking what CAN be seen with what COULD be seen. The "edge" of the OU is that place where light COULD reach us (and may well do so) but which may have been red-shifted beyond our ability to detect it.

You certainly ARE correct in saying that it's going to be lonely place, since only the local group (at most) will still be visible at some point in the distant future.

 

[Buzz Bloom]

since only the local group (at most) will still be visible at some point in the distant future.

Hi phinds:

Are you saying that galactic groups/clusters in the Virgo Supercluster other than the Local Group are not gravitationally bound to the Local Group?

https://en.wikipedia.org/wiki/Virgo_Supercluster​

I would much appreciate a source clarifying this. The Wikipedia article above does not make this clear.

Regards,
Buzz

 

[phinds]

Hi phinds:

Are you saying that galactic groups/clusters in the Virgo Supercluster other than the Local Group are not gravitationally bound to the Local Group?

https://en.wikipedia.org/wiki/Virgo_Supercluster​

I would much appreciate a source clarifying this. The Wikipedia article above does not make this clear.

Regards,
Buzz

Not positive, but my understanding is that superclusters ARE affected by expansion so only the local group will remain (again, if that).

 

[Bandersnatch]

Except our universe is currently expanding at an accelerated rate. which is covered quite clearly in the insights article Bandersnatch provided above. The OU decreases in those situations.

It doesn't. It doesn't follow that accelerated expansion causes reduction of OU.
To be clear, OU decreasing would mean that the farthest emitters we see today were beyond the farthest emitters observable tomorrow. This never happens in the LCDM model, regardless of accelerated expansion. The fig.1 graphs in the second link show this is the case.
Perhaps you have something else in mind, that you identifying the OU with, and that causes the confusion?

 

[Bandersnatch]

You are mistaking what CAN be seen with what COULD be seen. The "edge" of the OU is that place where light COULD reach us (and may well do so) but which may have been red-shifted beyond our ability to detect it.

No, it's the other way around. The OU is what can be seen right now. It's our past light cone and the edge is its base.
What could reach us (eventually, given enough time, and arbitrary detection abilities) is the event horizon - our past light cone in the infinite future.

 

[Justin Hunt]

@Bandersnatch I suppose I was really talking about the Hubble sphere, but the Hubble sphere has a direct effect on the OU. The OU is just much harder to calculate.

"
Fig. 4 Time sequence of the Hubble sphere (red circle) expanding to overtake a receding galaxy (blue dot) comoving with the expansion in a decelerating universe.

Reference https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/
"

"
Fig. 7 Time sequence of the Hubble sphere (red circle) expanding in an inflating universe. The receding galaxy (blue dot), comoving with the expansion, is pulled outside the Hubble sphere. What does this mean for our observable universe? In the decelerating universe, all objects eventually become visible simply because they are slowing down in their recession and the light they emit is able to find its way into our telescopes. Things are not so simple during inflation: it is easy to imagine a situation where the light emitted towards Earth by a distant galaxy gets overwhelmed by the accelerated expansion, dashing any hope of forward progress.

Reference https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/
"

Due to technology limitations, even in the first case where we could theoretically see the entire universe at some point, what we see would still be limited to our technology. But, in the second case, objects do move from being inside our OU to outside our OU.

 

[George Jones]

But, in the second case, objects do move from being inside our OU to outside our OU.

Again, this is absolutely incorrect.

 

[Justin Hunt]

did you read the article?
"
Fig. 9 Illustration of the event horizon, ℓ, during de Sitter expansion. The gray circle is the Hubble sphere and the red circle is the event horizon. The leftmost frame is today: a photon is just emitted (yellow dot), the Hubble sphere and event horizon coincide. Subsequent frames show times in the future, as the shell of photons moves outwards. The Hubble sphere does not expand since d˙H=0 during de Sitter expansion. The event horizon, the comoving distance (7 units) that coincides with the Hubble scale today (leftmost frame), moves outwards with the expansion. Even if we included many more frames into the future, the photons never reach the receding event horizon. The boundary set by ℓ carves out a region of spacetime containing events that will never influence us: those events beyond ℓ occurring now and forever into the future. For this reason, ℓ is known as our future event horizon, or simply, our event horizon. Contrast this with the particle horizon, our past event horizon, consisting of those events we will never influence (cf. Figure 6 and surrounding discussion). We can draw something like Figure 6 to depict the event horizon, but we can’t ignore the expansion because the event horizon exists only by virtue of the inflating

Reference https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

"

Things outside the event horizon can not be seen.

"
The accelerated expansion “pushes” all comoving objects outwards towards the event horizon, a conveyor belt to the point of no return. What all of this means, of course, is that the inflating universe is a rather lonely place

Reference https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

"

 

[Bandersnatch]

I suppose I was really talking about the Hubble sphere, but the Hubble sphere has a direct effect on the OU. The OU is just much harder to calculate.

Sure, objects are leaving the Hubble sphere. But you can't just wave a hand and call it OU. Or conflate Hubble sphere with event horizon, as you appear to do in your later post - which are equivalent only in the case of a de Sitter expansion. When the article invokes de Sitter expansion, it presents it as an edge case - physical during inflationary epoch, but not in the current universe - which it clearly states.

But, in the second case, objects do move from being inside our OU to outside our OU.

Only in the sense that the objects move farther than they were at the time when they emitted currently observed light, including towards a distance from which no light they emit >now< could ever be observed (i.e. they move beyond the event horizon). But this is not what OU means. If you can see them, they're inside your observable universe. Their light, emitted during their past histories will remain observable, even as their current states may be forever out of reach.

Here's a graph of LCDM model in comoving coordinates (discussed in the Insights article) from the Lineweaver and Davies paper, linked earlier:

The light cone is our OU. The particle horizon is its inverted equivalent (as discussed in the Insights article).
The dotted lines can be treated as galaxies at indicated redshifts. As time progresses towards infinite future, the light cone ascends the graph towards the event horizon. Its base continually expands to encompass more comoving galaxies, increasing the observable universe.
At any given >now< time there are objects (e.g. a galaxy with redshift z=3) that are >now< beyond the current or any possible light cone in the future. But that same galaxy in the past emitted signals that are on the light cone now, and there will always be signals on light cones in the future that were emitted by that galaxy = the galaxy remains observable forever.

 

[George Jones]

@Justin Hunt , let's look at some examples from @Bandersnatch 's most recen post, using the diagram in this post, and let's assume that the universe is transparent through its history (not just after 380000 years).

The worldlines of galaxies that move with the Hubble flow are vertical lines that can be labeled by their comoving coordinate (numbers on the bottom horizontal line).

Consider galaxy P that has comoving coordinate of 21. We can currently see P, as its worldline intersects our past lightcone at a conformal time of about 31. The current conformal time is about 46, so B is currently in our observable universe, and we see it as it was in the past.The event horizon is our past lighcone in the "infinite future". B intersects this light cone at a conformal time of about 42, Consequently: we can now see B, and we can always see B. B never moves out of our observable universe. B does, however, lose causal contact with us us. At (conformal) t = 40, B can fire a death ray us which, in the future (about t = 60 ), destroys us. At t = 45, B can still fire a death ray, but this death ray will never reach us, even in the "infinite future".

Now consider galaxy Q that has a worldline labeled by comoving coordinate 50. Q's worldline does not intersect our current (t = 46) past lightcone, i.e., Q currently is not in the observable universe. Q does intersect our past light cone, starting at t = 50 for us, i.e., at t = 50, Q changes from being not in our observable universe, to being in our observable universe. For the same reasons as P, once P is in our observable universe, P always remains in our observable universe.

Bottom line: anything that is now in our observable universe remains in our observable. Some (but not all) things that are not now in observable will move into our observable universe in the future; once in, always in.

Int terms of comoving coordinte, the size of our unierse increases as time progresses.

On the diagram, wordlines with comoving coordinate greater than about 62 are never in the observable universe.

Inflation doesn't alter this picture.

 

[Justin Hunt]

Thank you for the additional detail. I am seeing your point now. A part that is still not clear to me though, is that my understanding of OU was all that can at some point be seen while Visible Universe (VU) is all that we can currently see. I am not sure if you are talking about OU above or VU. There are many galaxies in our OU that have given off light that has not had sufficent time to reach us here on Earth and so would be in the OU but not the VU. I did not see much distinction in the article between VU and OU.

 

[Bandersnatch]

Thank you for the additional detail. I am seeing your point now. A part that is still not clear to me though, is that my understanding of OU was all that can at some point be seen while Visible Universe (VU) is all that we can currently see. I am not sure if you are talking about OU above or VU. There are many galaxies in our OU that have given off light that has not had sufficent time to reach us here on Earth and so would be in the OU but not the VU. I did not see much distinction in the article between VU and OU.

Judging by the above, I think what you call OU is the event horizon according to standard nomenclature. While your VU would be OU (or past light cone, or particle horizon). VU doesn't function in standard usage. See if the articles and the discussion above make more sense in this light.

 

[phinds]

Thank you for the additional detail. I am seeing your point now. A part that is still not clear to me though, is that my understanding of OU was all that can at some point be seen while Visible Universe (VU) is all that we can currently see. I am not sure if you are talking about OU above or VU. There are many galaxies in our OU that have given off light that has not had sufficent time to reach us here on Earth and so would be in the OU but not the VU. I did not see much distinction in the article between VU and OU.

As far as I am aware "visual universe" is a pop-science term not actually used by physicists but I would expect it to be just the OU by another name.

EDIT: I see Bandersnatch beat me to it. I didn't see his post before posting.

 

[alantheastronomer]

Summary: Is there anyone examining a large sample of galaxies' subtended angles over time, as an independent test of the universe's supposed expansion?

As indicated in the title and summary, I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship, by measuring individual galaxy subtended angles over time. The predicted decreases in size over time should be small, to be sure, but with a large enough sample size and good enough telescopes, may be measurable over a 5-, 10-, or 20-year period.

If you're interested in doing it yourself, you can access data from the Sloan Digital Sky Survey (SDSS) and the 2 Micron All Sky Survey (2MASS)…have at it! - But be forewarned, the limitations that Bandersnatch and Vanadium 50 pointed out will most likely make it futile...

Are you seriously questioning the expansion of the universe?

Even though he said he supposes so, I think he's just proposing an additional method to nail down the expansion rate, in addition to the cosmological distance ladder and the distances to SNIa explosions, if it were only observationally viable!

 

[mfb]

There is one way we can measure the expansion of the universe directly as change over time with near future instruments: We can measure the change of the redshift of a source over time. ELT will be able to do it, although this task will require hundreds or even thousands of observation hours - it is unclear if that much time will be spent on a single project.

 

[Vanadium 50]

Even though he said he supposes so, I think he's just proposing an additional method to nail down the expansion rate

Gosh, I usually go with what someone actually said instead of something else which is almost the opposite of what he actually said.

 

[Buzz Bloom]

I suggest it might be possible that a measurement across a combination of galaxies in relatively nearby cluster group (but not one that we are gravitationally connected with) might have a large enough angle to notice a angular shrinking over say a hundred years.

Well I found it quite difficult, but I will report what I did find out.
First, I confirmed that the local group is not gravitationally bound to M82 group.
The distance from the Earth to the M81 group is given as 1.174 x 10⁷ ly.
The criteria I used is that
(1) at the distance D from the gravitation body (the local group) has an an attraction gravitational acceleration of
[1] A_G = GM/D²,
and at distance D the universe expansion acceleration is
[2] A_H = H₀²D.
The value of D when
[3] A_G = A_H
is the threshold between being gravitationally bound and not.
From [1], [2], and [3], this distance is
[4] D_GB = (GM/H₀²)^1/3.
Converting the units for G from
m² kg^-1 s^-2
to the units
ly³ M_S-1 (solar mass) yr^-2
gives
[5] G = 1.75976 x 10^-17 ly³ M_S^-1 y^-2.
The mass of the local group is
[6] M_LG = 1.03 x 10¹² M_S.
The reciprocal of the Hubble constant is
[7] 1/H₀ = 1.44 x 10¹⁰ y.
From [5], [6] and [7] the following is the calculated value
[8] D_GB = 1.94 x 10⁵ ly.
This is much less than the distance between Earth and M81
[9] D_E-M81 = 1.174 x 10⁷ ly.

OK, now I will discuss two galaxies in the M81 group: M81 and M82.
Galaxies M81 and M82 are 36 arc minutes (= 2160 arc seconds) apart.
[10] α = 2160 arc seconds
The expansion speed at which M81 and M82 are moving away from Earth is
[11] V = H₀ D_E-M81 = 8.15 x 10^-4 ly/yr.
The distance moved in 100 years is
[12] ΔD = 8.15 x 10^-2 ly.
The distance ratio is
[13] ΔD/D = 8.15 x 10^-2 / 1.174 x 10⁷ ly = 6.942 x 10^-9.
This means that after 100 years the angular distance between M81 and M82 will shrink by
[14] Δα = α ΔD/D = 1.76 x 10^-5 arc seconds.

I apologize for not including references. My wide has just told me it is time for us to leave for a previous commitment. I hope to have time to add some more details and references in several days.

Regards,
Buzz

 

[PeterDonis]

The criteria I used is that
(1) at the distance D from the gravitation body (the local group) has an an attraction gravitational acceleration of
[1] AG = GM/D2,
and at distance D the universe expansion acceleration is
[2] AH = H02D.
The value of D when
[3] AG = AH
is the threshold between being gravitationally bound and not.

There are at least two things wrong with this.

First, if we ignore for the moment the effect of dark energy, the correct criterion for whether a pair of objects are gravitationally bound is whether their relative recession velocity is greater than escape velocity. The recession velocity is $V_H = H_0 D$ and the escape velocity is $V_E = \sqrt{2 M / D}$, so $V_E = V_H$ gives

$$
D = \left( \frac{2 M}{H_0^2} \right)^{\frac{1}{3}}
$$

Your formula happens to be within a factor of $2^{1/3}$ of this (once we add back the corrections for using conventional units instead of the "natural" units I used), but that just means you were lucky to get an answer close to the right one using wrong logic.

Second, if we are talking about "universe expansion acceleration", we are talking about dark energy, which adds an extra correction to the above formula. The easiest way to add that correction is to modify the escape velocity formula from the one for Schwarzschild spacetime, which is what we were using above, to the one for Schwarzschild-de Sitter spacetime; that gives us

$$
V_E = \sqrt{\frac{2 M}{D} - \frac{D^2}{\alpha_0^2}}
$$

where $\alpha$ is the distance to the cosmological horizon "now". Plugging that into $V_E = V_H$ gives

$$
D = \left( \frac{2 M}{H_0^2 + \frac{1}{\alpha_0^2}} \right)^{\frac{1}{3}}
$$

As you can see, this decreases $D$ compared to the formula above that ignored dark energy, so for your purposes here the above formula (assuming your math is correct when the factors for conventional units are added back in) is fine. But you still need to use correct reasoning to get to it.

 

[mfb]

M81 and M82 have some relative velocity. All you'll measure by tracking their angular separation is their relative velocity. 1.76 x 10^-5 arc seconds in 100 years at 12 million light years distance is just 3 km/s.

 

[Buzz Bloom]

There are at least two things wrong with this.

Hi Peter:

I do appreciate the time you took to point out my errors about gravitational boundedness relative to the
expanding universe. I find that your corrections raise more questions in my mind which I would like to pursue. However, these questions seem to me to not be related to the topic of this thread, so I plan to start a new thread specifically about gravitational boundedness relative to the expanding universe.

Regards,
Buzz

 

[dabunting]

I appreciate this discussion very much!
Except for those who ask, "Are you seriously questioning...?"
If we're not questioning, we're not scientists.

hkyriazi asked:
"Is there anyone examining a large sample of galaxies' subtended angles over time, as an independent test of the universe's supposed expansion? I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship... A Doppler shift is one interpretation of the redshift/distance relationship. Others are possible. I'd be happy to see any direct confirmation of the expansion..."

There's a lot we don't know about the universe: Is there anything beyond our observed universe? Or do we assume it infinite?
Could the entire observed universe be within the singularity or very tiny space origin of the Big Bang?
Do we make the questionable assumption that we are at the singularity or very tiny space origin of the Big Bang?
The explanation seems very concocted for the observation that the space between galaxies increases and accelerates with time while the size of galaxies (or gravitationally bound space) does not increase or accelerate.
Explanations also seem concocted or non-existent regarding the Great Attractor in the direction of the Shapley Supercluster and the Dipole Repeller, the two comprising the CMB Dipole.
The CMB spectral radiance contains small anisotropies that match what would be expected if small thermal variations generated by quantum fluctuations of matter in a very tiny space had expanded to the size of the observable universe we see today.
I ask again: Is the entire observed universe WITHIN the "very tiny space," or singularity, the origin of the Big Bang?
We postulate or concoct dark matter and energy with peculiar characteristics that conveniently explain(?) all.
But yes...
We question.