Hubble Constant am I gettting this right?

[Loki180]

Hi guys, I am in a state of slight confusion! I need to know if I am getting this information right, or I have gotten something wrong somewhere!

It is to do with the Hubble constant and the Hubble law.

So 1920 Edwin Hubble estimated that the Universe was 14 Billion years Old but new estimations put it at 13.75 Billion years old? So does this change the Hubble Constant? From the 1920 42 miles per sec to the now 45 miles per sec?

To make sure that I have this down,

A star within the milky way is 3 Megaparsec away. So at that distance, would it be correct by saying it was moving away at a rate of 125 miles per sec?

The Hubble rule as far as I am getting it, is that a star is moving away at the rate of 45 miles per sec per Megaparsec?

Could this be put into an mathematical equation?

I hope this makes sense!

Thanks for the help guys.

 

[mfb]

The age of the universe depends on the current Hubble constant and its value in the past. The original estimate of the Hubble constant was not as precise as measurements today, of course.

A star within the milky way is 3 Megaparsec away. So at that distance, would it be correct by saying it was moving away at a rate of 125 miles per sec?

3 Mpc are not enough to neglect the motion of individual stars and galaxies. If there would be no local structures in the universe, this would be true (but 3*45=135).

 

[Loki180]

Ahh I did not see that error before posting. 3 Mpc = 135 Miles per Sec.

3 Mpc are not enough to neglect the motion of individual stars and galaxies. If there would be no local structures in the universe, this would be true (but 3*45=135).

So if I am reading it right, 3 Mpc is not far enough?

What about if a star or Galaxy was

7 Mpc away, 7*45=315 miles per sec?

So a Galaxy or Star that is 7 Mpc away from Earth would be moving at a rate of 315 miles Per Sec?

Thanks for the help by the Way!

 

[jambaugh]

You are using the implied assumption that the Hubble expansion has been constant over the history of the universe since the Big Bang. Keep in mind that the Hubble Constant can be empirically determined (with some wide error bars). The updated estimates of the age of the universe can involve either updated empirical determinations of Hubble's constant or updated theories of the universe's expansion. For example the current astrophysical postulates of an inflationary period would truncate the extrapolation of uniform expansion back to the BB revising the age to a smaller value. This doesn't change the current Hubble constant but rather is a modification of the constant expansion assumption I mentioned.

There are also more involved modeling taking into account cosmological constant (an acceleration factor added into Einstein's equations) and the effects of gravitation (Einstein's equations) which treat the Hubble expansion as non-linear. These of course depend on assumptions about the material density of the universe and you get a lotta talk about dark matter and dark energy when reconciling theory, assumptions, and observations.

 

[cepheid]

Welcome to PF Loki180,

There's quite a few things wrong with what you're saying. First of all, Edwin Hubble did not determine that the age of the universe was 14 billion years. It's true that he discovered that it is expanding, and that he got an estimate for the value of the constant that we now call the Hubble constant. However, the age of the universe depends on this constant and on other cosmological parameters in our mathematical models of the universe, and for a long time (most of the 20th century) there was simply too much *uncertainty* in the values of these parameters for us to be able to say so definitely what the age of the universe was. We certainly didn't know it to 10% precision or better like we do now, and I don't think it would be an exaggeration to say that people really couldn't say definitively whether it was 5 billion years or 20 billion years. In fact, for a long time, it was a problem with the prevailing/favoured cosmological model that it predicted an age of the universe that was younger than the ages we estimated for the oldest stars we could observe (e.g. stars in globular clusters). It wasn't until the late 90s and early 2000s, thanks to a number of pioneering ground-based and sub-orbital experiments to measure fluctuations in the Cosmic Microwave Background (CMB) radiation (e.g. BOOMERANG), that we were able to determine the values of these parameters with any precision. These early results ushered in the era of precision cosmology, and were later confirmed to exquisite precision using telescopes such as the WMAP satellite (launched 2001), and now the Planck satellite (launched 2009), along with non-CMB data, all thanks to which we now have the presently-accepted value of 13.7 billion years. Just a decade before WMAP, we did not think we would ever be able to get such precise answers to questions like "what is the age, geometry, and mass-energy content of the universe?"

Another problem is your conception of distances. 3 megaparsecs (Mpc) is 3 million parsecs, or approximately 10 million light years, which is a tremendously large distance. It is much larger than the size of our Milky Way galaxy, which is only about 100,000 light years, or around 30 kiloparsecs (kpc) across. So it makes absolutely no sense to talk about a star in our galaxy that is 3 Mpc away, because that distance puts us well outside of our galaxy. Once you get in the Mpc range, you're talking about the scales of galaxy clusters, rather than individual galaxies. Note that stars within our own galaxy are not expanding away from us, because our galaxy is a gravitationally-bound object, so the local effects of gravitation dominate over expansion. This is true of individual clusters of galaxies as well. The individual galaxies within a galaxy cluster are gravitationally-bound to each other and hence do not expand away from each other. However, once you get to distances on the scale of the distances between galaxy clusters (like, maybe 10 Mpc or larger), then you find that these individual clusters are moving away from each other in a manner described by Hubble's law. I'm not going to deal with Imperial units (that would just be silly ), but using a sort of fairly standard value for the Hubble constant of 70 (km/s)/Mpc, you'd find that the nearest galaxy clusters, which are of order 10 Mpc away from us, would be receding away from us a at speed of [70 (km/s)/Mpc]*[10 Mpc] = 700 km/s.

 

[marcus]

EDIT: OOPS! I didn't see that so many other people had answered. Maybe I should erase my answer because it just adds to the overload, but I'll leave it for now, just in case there's something useful that wasn't already covered
=========================
Hi Loki,
it's rather hard to understand the expanding separation between regions of space as "motion THRU space". Uniform Hubble-law expansion pattern isn't like familiar motion, nobody GETS anywhere by it, everybody, all regions of space, just become more widely separated. Yes this is unintuitive, we are used to fixed rigid local geometry and largescale geometry is dynamic.

It's good to do arithmetic exercises with small distances like
"What about if a star or Galaxy was 7 Mpc away, 7*45=315 miles per sec? "
but they don't correspond to concrete reality. A galaxy 7 Mpc away would still be in our local neighborhood and subject to the gravity attraction that tends to hold local structures together. So the distance to it would not be increasing precisely at Hubble law rate. Indeed it might not be increasing at all. Things have their own individual local random motion often with speeds of a few hundred miles per second. So Hubble law distance growth gets WASHED OUT at that scale, by the random individual motion thru local space.

A better way to think of it uses the Hubble radius (14 Gly) as a distance scale. Hubble radius is defined as the proper distance which is increasing at speed of light. Most of the galaxies which we can see are beyond that distance from us. It is a convenient distance scale to use in thinking about cosmology (as distinct from the astronomy of our local group of galaxies, which is held together by its own gravity.) Cosmology is on a different scale from local astronomy so it's helpful to get an appropriate perspective.

Proper (in this context) means instantaneous, at a given moment in universe time, as if you could freeze the expansion process long enough to make a conventional measurement and then let the process resume. Gly is short for billion lightyears. Rigorously speaking the Hubble law is about proper distance between stationary observers ( objects which are at so-called CMB rest, not moving relative to the microwave background).
At large distances it works, practically speaking, applied to galaxies because we can NEGLECT their individual random motion and the gravitational attraction that holds clusters of galaxies together.

 

[Jorrie]

... A better way to think of it uses the Hubble radius (14 Gly) as a distance scale. Hubble radius is defined as the proper distance which is increasing at speed of light. Most of the galaxies which we can see are beyond that distance from us. It is a convenient distance scale to use in thinking about cosmology. (rather than the astronomy of our local group of galaxies, which is held together by its own gravity.) Cosmology is on a different scale from local astronomy so it's helpful to get an appropriate perspective.

Proper (in this context) means instantaneous, at a given moment in universe time, as if you could freeze the expansion process long enough to make a conventional measurement and then let the process resume. ...

I've seen this definition of the Hubble radius (the proper distance which is increasing at speed of light) a number of times in threads on PF, but I'm wondering if it is a good one. It needs a lot of extra qualifiers like, "proper distance" at the time applicable, which is usually taken as "now", but it could be a any time in the past or future. Is it not better to simply define Hubble distance as R_H(t)=c/H(t)?

 

[marcus]

H(t) is defined in terms of proper distance between CMB stationary observers at a given moment in universe time.

To say rigorously what H(t) is a ratio of takes a lot of extra qualifiers. So if you start with H(t) and don't explain that, confusion can certainly creep in somewhere down the line.

I think it's somewhat a matter of taste, Jorrie.

 

[marcus]

This raises an interesting topic of discussion, we might need to start a separate thread. In concrete terms I think of it as "how would I explain expansion cosmology to a nephew or niece some afternoon in summer vacation, if they were curious?"

Hubble law is the key pattern and it is formulated in terms of universe time (that is the dt, not some moving observer's time) and freeze-frame distance, frozen at some universe-wide moment of universe time. But that's too technical to start with, for my nephew.

I have to introduce Hubble law, however. So what shall I confront right away and what difficulties shall I ignore at first and have to attend to later?

I think (and it may just be a matter of taste) that what I want to do up front is to acknowledge that the vast majority of the galaxies we can see are receding faster than speed of light. For me that gets right away to the heart of the matter. It's not like ordinary motion thru space. It is dynamic geometry.

And the distance increase is roughly the same in all directions. There is a critical distance which is increasing at c, and anything beyond that distance *in any direction* is receding faster.

This is taking the bull by the horns so to speak, and saying something important and true about the vast majority of the galaxies visible to us. It is a prime fact about how the universe looks. but if you start with "megaparsecs and kilometers per second" you are at the wrong scale, where practically speaking the Hubble law IS NOT EVEN TRUE, and you have to do a lot of algebra before you even get to the main business, which is at Hubble radius scale. You postpone the nephew or niece realizing the essential character of what we are talking about.

So of course it's a personal preference issue, how one feels like explaining the expansion cosmology idea. What *mental images* one thinks are important for the beginners to get in their heads. I'm telling you my personal inclination.

Either way you are eventually going to have to talk about universal (Friedman) time and CMB rest and proper distance. But you best leave out those technicalities at the start (maybe I should have spared Loki them in this thread!)

 

[Loki180]

Hey guys, Thanks so much for the help! So much information that I have over looked. I think I have gotten some wrong information from somewhere or miss understood it! I was also under the impression that one Mpc is 3.3 Million LY it is rather bigger than I thought!

I will continue to read through all yours posts no doubt I will keep coming back to them! Some of the best information I have read in a long time!

Thanks again all of you

 

[cepheid]

Hey guys, Thanks so much for the help! So much information that I have over looked. I think I have gotten some wrong information from somewhere or miss understood it! I was also under the impression that one Mpc is 3.3 Million LY it is rather bigger than I thought!

I will continue to read through all yours posts no doubt I will keep coming back to them! Some of the best information I have read in a long time!

Thanks again all of you

1 Mpc IS 3.3 million light years. That's not the mistake that you made. The mistake that you made was saying that something that is 3 Mpc away would be inside of our own galaxy, when in fact it would be at a distance 100 times the diameter of our galaxy.

 

[Mordred]

Hey guys, Thanks so much for the help! So much information that I have over looked. I think I have gotten some wrong information from somewhere or miss understood it! I was also under the impression that one Mpc is 3.3 Million LY it is rather bigger than I thought!

I will continue to read through all yours posts no doubt I will keep coming back to them! Some of the best information I have read in a long time!

Thanks again all of you

well your in luck we happen to have tons of related info in recent threads lol.

https://www.physicsforums.com/showthread.php?t=685265

this thread has some useful info which includes a related article written by PF members. Its a lengthy read but useful

this sitr has a decent write up on radial commoving, angular commoving and proper distances

http://galacticfool.com/scale-factor/

this I also found to be a handy site

http://www.physics.fsu.edu/users/ProsperH/AST3033/Cosmology.htm

after reading all that you will have a decent knowledge of expansion and hubbles constant.
As well a different distance measures.

Good luck in your studies feel free to ask away if you run into problems

 

[Naty1]

Loki posts:

Could this be put into an mathematical equation?

Trying to sort through 'cosmological expansion' is confusing at first for most people. So hang in there!


cephid posted:

...using a sort of fairly standard value for the Hubble constant of 70 (km/s)/Mpc, you'd find that the nearest galaxy clusters, which are of order 10 Mpc away from us, would be receding away from us a at speed of [70 (km/s)/Mpc]*[10 Mpc] = 700 km/s.

so that seemed to answer your immediate question.

It took me a while to understand the Hubble parameter [H] is related to the scale factor referred to as a[t]. A next step for you might be to go here,

http://en.wikipedia.org/wiki/Scale_factor_(cosmology )


but it may be a lot to swallow depending on your math background. What is significant for now is that the Hubble parameter H, is defined as H = a'[t]/a[t] where a'[t] is the derivative of the scale factor, a[t], indicating the rate of change of the scale factor. Right there you can tell that it's likely the Hubble parameter varies over time since the scale factor a[t] does. [This has been noted already. [Wiki says it's 'dynamic'. ] This scale factor is a measure of proper distance as Marcus described above.

H₀ is often used to denote the Hubble parameter NOW taken to be a constant [for now].

If you know a bit about Newtonian kinetic and potential energy Leonard Susskind has a video on you tube {Cosmology video #3, Leonard Susskind} where he derives the scale factor without tensors, without vectors, without calculus...

He explains the scale factor a[t] is the variable [separation] distance between adjacent coordinates.

gotta go now..a little more later...

 

[Naty1]

That prior post of mine should have referenced Susskind Cosmology lecture #2...not #3...
The distance 'formula' [calculkation by cephid shows Hubble relationships now, not in the past.

To see what the scale factor [expansion distance] looks like over time, in the past and the future, scroll down to the second diagram here:

http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll8.html

[This is a reliable source often linked to from these forums.]
From such scale factor functions of time one can derive the Hubble parameter H at different times.
But these do NOT go all the way back to the big bang, t = 0.


Susskind does a nice job explaining this factor over cosmological history.

Just above the diagrams are equations 8.36, the FRW equation, and this is what Leonard Susskind derives in the Cosmology lecture in an easy to follow manner.

Equation 8.37 is the H = a'[t]/a[t] I posted but with a different notation...

 

[Naty1]

cephid posted:

Note that stars within our own galaxy are not expanding away from us, because our galaxy is a gravitationally-bound object, so the local effects of gravitation dominate over expansion. This is true of individual clusters of galaxies as well. The individual galaxies within a galaxy cluster are gravitationally-bound to each other and hence do not expand away from each other.

I no longer consider this the best way to think about the lack of local expansion. But such a description seems a popular introductory approach.


There is a description of the sort I now prefer here:

Expanding Space: the Root of all Evil?
http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.0380v1.pdf

The authors make the point that it is the assumption of homogeneous and isotropic space, an approximation to our lumpy universe, that leads to cosmological expansion. That model does not apply to 'lumpy' galaxies nor galaxy clusters. [Nor suburban bedrooms!]

We should not expect the global behavior of a perfectly homogeneous and isotropic [FLRW] model to be applicable when these conditions are not even approximately met. The expansion of space fails to have a ‘meaningful local counterpart’ [locally] …..because the physical conditions that manifest the effects described as the expansion of space are not met in the average suburban bedroom.

The classic thought experiment used is the “tethered galaxy” problem (Harrison 1995). In this, a test galaxy in an expanding universe is held at rest with respect to the origin at a cosmological distance. By Hubble’s law, we would expect this galaxy to be receding, however we prevent this, artificially holding the test galaxy in place. The question is, when the galaxy is released, what does it do? In fact, what the particle does once being released depends on the acceleration of the universe. If the scale factor is accelerating the particle moves away but if it is decelerating the particle moves towards the origin [see Barnes et al. (2006) for the full details].

 

[Mordred]

I've read that article a few times, I'm not sure I personally would advocate some of the views he has in the article.

On the point of expansion. Yes a lumpy universe makes for an inhomogenous and anistrophic expansion rates. However this view tends to lead to misundertandings on the cosmological constant. Which is also considered homogenous and isotropic.
Take a De-sitter universe matter removed in that condition expansion is indeed homogenous and isotropic. Both the cosmological constant and expansion are in this model.

So what does this mean? If we try to teach that expansion is not homogenous and isotropic due to the lumpy nature of the universe then we wuld have to separate all the various De-Sitter models (single and multi component FLRW models) state in those models that it is homogenous and isotropic. However in non De-Sitter models its isn't.

However if you stick with it easy homogenous and isotropic however its easily overpowered by gravity.
The latter descriptive I feel is the more accurate due to the various Models that one should learn to understand the FLRW metrics.

the other point is the term homogenous and isotrpoic is seldom true on small scales its nearly never true on those scales. However on large enough scales the inhomogenous areas average out by large scales I'm talking 100 Mpc or greater. Any good cosmology textbook quickly points this out

However that's just my take on it.

 

[marcus]

Hi Naty, I never set much store by that "root of evil" paper. Seemed more attention-getting than educational. Their version of what people mean by "expanding space" may have been a straw man. I personally talk about Hubble law as pattern of expanding distances--avoid talking about "space" as if it were a substance.

Don't see the educational point of this quote: " If the scale factor ... is decelerating the particle moves towards the origin."

This is easy to understand in the expanding distance picture that most of us use. It is exactly what one would expect.
So the example does not serve to undermine the expanding distances way of thinking, in any sense.

You might be amused by the "roast galaxy" scenario. You tether a galaxy with a very long tether, nearly equal to the Hubble radius, so the galaxy is traveling thru its locale at nearly c. So the CMB it is receiving from the direction it is traveling is very HOT. In fact it is getting cooked with X-rays, similar to the light in the core of a star. Several million degrees kelvin, say. this is a nice way to roast a galaxy if you like them roasted. You just need a really strong string to use as tether.

 

[Naty1]

I only intended to reference the authors point that expansion does not apply to galaxies and galaxy clusters. I agree, but I am not a subject matter expert.
.
I quoted their language on that one issue because it was nicely phrased, but especially because it follows the conclusions I reached from a long thread with Wallace [of these forums] a practicing cosmologist..and a number of 'experts'.

I don't remember if there was broad consensus or not, but I'll see if I can find the link to that thread. I have it in my notes somewhere...

Yes a lumpy universe makes for an inhomogenous and anistrophic expansion rates.

That is NOT my understanding. My understanding is that once homogeneity and isotropicism is abandoned, nobody has yet numerically solved the EFE. There is no model for expansion in a lumpy environment. Here is how Wallace addressed the issue of galactic expansion: [I don't have a link to the thread]

Wallace: #60:
Ouch! I have to step into disagree with you here oldman…
“ If anything there is a vanishingly small FRW element to the metric of bound structures. If the FRW metric ‘prevail(ed) on all scales and everywhere, even inside gravitationally bound structures or within atoms’ then why do galaxies maintain a constant size as the distance between them expands? Commonly we are told that the local mass concentration ‘overcomes’ the expansion preventing this from occurring. This is one of the worst and most fallacious explanations you could possibly give someone! What really happens then?

The FRW metric is the inevitable result of the cosmological principle, CP, which is that the universe is homogeneous and isotropic. The metric is only valid if these principles hold. [see general form of the FLRW metric, pg 28, these notes]
Consider now a galaxy, solar system or planet. Does the CP hold? No. Is it a remotely useful approximation? Not at all! Unsurprisingly then the dynamics of bodies in these systems and on these scales bears no resemblance to the dynamics of galaxies. So for instance, there is no redshift of light due to a(t) when we observe light from the other side of our galaxy, or from say Andromeda. The FRW metric simply is not valid on these scales.

found the thread:

https://www.physicsforums.com/showthread.php?t=162727&highlight=current+flow&page=4

Marcus participated too...The above quote is on page 4 of 11.

Marcus:

You might be amused by the "roast galaxy" scenario. You tether a galaxy with a very long tether, nearly equal to the Hubble radius, so the galaxy is traveling thru its locale at nearly c. So the CMB it is receiving from the direction it is traveling is very HOT. In fact it is getting cooked with X-rays, similar to the light in the core of a star. Several million degrees kelvin, say. this is a nice way to roast a galaxy if you like them roasted. You just need a really strong string to use as tether.

Now that is an image! I understand the concepts...And it is not the craziest thing I have come across in these forums. Thank you, that will stick with me a while!

edit: I read that 2007 thread several times several years ago...and do NOT plan again..but if anybody has individual posts to discuss, great...My notes do not mention other viewpoints; I guess I really liked Wallace's ...

 

[Mordred]

Yes a lumpy universe makes for an inhomogenous and anistrophic expansion rates.

you needed to read the last paragraph, so I'll make it clearer.

Yes a lumpy universe makes for an inhomogenous and anistrophic expansion rates, on scales below 100 Mpc due to gravitationally bound regions. Above 100 Mpc the expansion is considered homogeneous and isotropic. Though in light of recent findings I've seen references that use a large value of 120 to 150 Mpc depending on the author.

 

[Naty1]

Yes a lumpy universe makes for an inhomogenous and anistrophic expansion rates.

Can you provide a brief quote or reputable on line reference??
Wallace in the thread I linked I believe referred to a text by Peacock supporting his post that expansion does not apply to galaxies.

 

[Naty1]

Hi Mordred: I understand what you wrote, I said I disagreed...but see below...

I checked ned wrights UCLA tutorial and found this reference:


Why doesn't the Solar System expand if the whole Universe is expanding? 1998
http://www.astro.ucla.edu/~wright/cosmology_faq.html#SS

...For the technically minded, Cooperstock et al. computes that the influence of the cosmological expansion on the Earth's orbit around the Sun amounts to a growth by only one part in a septillion over the age of the Solar System.

However when one goes to the Cooperstock paper, it turns out he has only addressed a TWO BODY problem.

http://xxx.lanl.gov/abs/astro-ph/9803097

Following renewed interest, the problem of whether the cosmological expansion affects the dynamics of local systems is reconsidered.

Here are a few excerpts:

Thus, the cosmological metric alone does not dictate a
scale for expansion and in principle, it could be present at the smallest practical scale
as real– as opposed to pseudo–expansion, and observable in principle... in this debate, we are in agreement with Anderson (1995) that it is most reasonable to assume that the expansion does indeed proceed at all scales...there is a certain ironical quality
attached to the debate in the sense that even if the expansion does actually occur at all
scales, we will show that the effects of the cosmological expansion on smaller spatial and
temporal scales would be undetectable in general in the foreseeable future and hence
one could just as comfortably hold the view that the expansion occurs strictly on the
cosmological scale...The recurrent attention paid to this issue indicates that to this
point a definitive answer is still lacking. However, it is our sense that the prevalent
perception is that the physics of systems which are small compared to the radius of
curvature of the cosmological background is essentially unaffected by the expansion of
the universe...Thus, the effect of the cosmological
expansion is seen to be negligible locally and grows in significance with distance, reaching
full import on the cosmological scale. This conclusion is qualitative, and is certainly
well–known to most relativists but, to the best of the authors’ knowledge, has yet to be
well–formulated quantitatively. In earlier treatments, the coordinate systems adopted
do not correspond to those used by a physical observer...The purpose of the present paper is to provide a clear quantitative answer to the problem...

Discussion and conclusions:

...In the non–spherical case, it is generally recognized that the expansion
of the universe does not have observable effects on local physics, but few discussions
of this problem in the literature have gone beyond qualitative statements... A serious
problem is that these studies were carried out in coordinate systems that are not easily
comparable with the frames used for astronomical observations and thus obscure the
physical meaning of the computations...The numerical estimates
obtained in Sec. 3 suggest that the correction is extremely small and unobservable for
galaxy clusters, galaxies and the solar system, and negligible for smaller systems such
as stars and even more so for molecules and atoms (cf. Anderson 1995). When the
cosmological correction to the local equations of motion is applied to the Newtonian
two–body problem, the evolution equations for the perturbation of the orbit can be
solved.

So there is enough here for both of us to latch on to...I'm not going to pursue other references because I think I understand the issues...any newer work would of course be interesting...so if you have a reference I'd be interested in your supporting quotes. cheers...

 

[Mordred]

Actually looks like were saying the same thing but in different ways lol.
Judging from the last set of links if I am understanding correctly you agree expansion is homogeneous and isotropic. However the issue seems to be on the gravitationally bound statement implying that expansion does not effect those regions. If that's so then again we are in agreement.
In some ways the gravitationally bound statement does incorrectly imply this.

An alternative expression could be that local energy densities of expansion and gravity influence the amount
expansion that occurs in a
region.

 

[ImaLooser]

You might be amused by the "roast galaxy" scenario. You tether a galaxy with a very long tether, nearly equal to the Hubble radius, so the galaxy is traveling thru its locale at nearly c. So the CMB it is receiving from the direction it is traveling is very HOT. In fact it is getting cooked with X-rays, similar to the light in the core of a star. Several million degrees kelvin, say. this is a nice way to roast a galaxy if you like them roasted. You just need a really strong string to use as tether.

Someone told me that in this scenario the CMB was insignificant compared with the effect of the rarified matter in "empty" space.

 

[Naty1]

Judging from the last set of links if I am understanding correctly you agree expansion is homogeneous and isotropic.

yes. but that is because we adopt the cosmological principle... homogeneous and isotropic spacetime...as a model assumption. So of course the result follows the model.

H&I is one of the basic assumptions of the FLRW cosmological model and that with the EFE is what leads to uniform expansion; if the cosmic fluid model is not H&I, and a galaxy is not, then how do we conclude a galaxy is subject to expansion effects. That is what Wallace posted.
Obviously 'expansion' does not apply to a block of say iron. [or pick any material with a uniform lattice..] then consider a 'cosmic' fluid, say water, mercury and lumps of metal...would THAT be modeled by the H&I assumptions?? I don't know what criteria to use. Neither does anybody else AFAIK.

However the issue seems to be on the gravitationally bound statement implying that expansion does not effect those regions.

Depends what you mean: if expansion effects small regions, say galaxies or a 'suburban bedroom' , gravitational and EM forces overwhelm any effects...1 part in a trillion or gazillion..or whatever...too small to observe. The issue is whether the cosmological expansion of almost flat space, based on H&I, even exists in gravitationally bound galaxies and bedrooms...with curved spacetimes.

We don't have a model for such lumpiness and we don't have a mathematical solution. Maybe I missed it, but as I skimmed the Cooperstock paper I did not see a rationale for applying the cosmological principle to a two body system.

edit: I just went back and looked...all Cooperstock does is use dx,dy,dz as equal space components just like the FLRW model does..he uses the FLRW metric...I don't know all the math well enough to know what happens when dx,dy,dz are NOT all the same...or if Cooperstock made any calculational modifications...when do such non H&I effects negate the H&I assumption?? Somehow a sensitivity analysis is required.

 

[Naty1]

Someone told me that in this scenario the CMB was insignificant compared with the effect of the rarified matter in "empty" space.

CMBR is not more rarefied there than here...it's ubiquitous...it's everywhere...
neither is matter believed to be 'more rarified'...but that is immaterial anyway.

When you move at near lightspeed, low energy CMBR at our observed 3 degrees K or so would appear as high energy radiation, that is, it's frequency would be greatly foreshortened.

 

[Mordred]

The Cooperstock article is a decent one, I prefer it as a reference to "expansion root of all evil"

For one the Cooperstock article isn't trying to use problems with expansion to push his own theories which the root of evil does on the Ekryptic theory (hopefully i spelled that right lol).

I also like his straightforward manner of defining expansion.