# Hubble Constant am I gettting this right?

1. Apr 21, 2013

### 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.

2. Apr 21, 2013

### Staff: Mentor

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.

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).

3. Apr 21, 2013

### Loki180

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

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!

4. Apr 21, 2013

### 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.

5. Apr 21, 2013

### cepheid

Staff Emeritus
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 :tongue:), 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.

Last edited: Apr 21, 2013
6. Apr 21, 2013

### 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.

Last edited: Apr 21, 2013
7. Apr 21, 2013

### Jorrie

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 RH(t)=c/H(t)?

8. Apr 21, 2013

### 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.

9. Apr 21, 2013

### 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!)

10. Apr 21, 2013

### 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

11. Apr 21, 2013

### cepheid

Staff Emeritus
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.

12. Apr 21, 2013

### Mordred

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

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 [Broken]

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

Last edited by a moderator: May 6, 2017
13. Apr 21, 2013

### Naty1

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

cephid posted:

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 [Broken])

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...

Last edited by a moderator: May 6, 2017
14. Apr 22, 2013

### 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....

Last edited: Apr 22, 2013
15. Apr 22, 2013

### Naty1

cephid posted:

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!]

16. Apr 22, 2013

### 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 seperate 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 text book quickly points this out

However thats just my take on it.

Last edited: Apr 22, 2013
17. Apr 22, 2013

### 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.

18. Apr 22, 2013

### 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....

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]

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

Marcus:
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 .....

19. Apr 22, 2013

### 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.

20. Apr 23, 2013

### Naty1

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.