# Measuring the Expansion of space

1. Apr 9, 2009

### robousy

We can measure the expansion of space via the galactic redshifting.

Please for now excuse my order of mag. estimate, but in mks units, Hubble's constant is roughly:

$$H=2\times 10^{-18} {\rm m/s/m}$$

If this exapansion was much larger. Say $$H'=2\times 10^{-10} {\rm m/s/m}$$

Could a 'table-top' device with impeccable sensitivity measure the expansion of space.

I'm not an experimentalist, but perhaps using lasers, interferometers perhaps??

Any thoughts on how this could be done, or if it is fundamentally possible....

2. Apr 9, 2009

### marcus

The length or width of the table top is determined by molecular bonds, which do not change size.

Or crystal lattice bonds if it is a metal table. Or the bonds in rock if it is a tectonic plate.

Distances anchored to a bonded material system, like rock or the solar system, or the galaxy, are not expanded.

The distances which are affected are, for instance, distances between widely separated observers both of whom are stationary with respect to the CMB. You know what I mean by at rest w.r.t. CMB----it means doppler-neutral, no dipole hotspot/coldspot.

BTW this suggests an alternative way of looking at the cosmogical expansion. You could think of expansion as a property of the CMB.

Let me know if thinking of it as something intrinsic to the CMB (rather than directly involving galaxies, for example) interests you and you want to discuss it. I'd be up for it if you want. In some sense the CMB represents for us the ancient matter of the universe when it was in a roughly uniform comparatively unclumped distribution. Being at rest w.r.t. CMB is in a certain way like being at rest with respect to the distribution of ancient matter.

Last edited: Apr 9, 2009
3. Apr 9, 2009

### marcus

Robousy, that is actually a really nice question!

The mental model is interferometry on a table top---or radar ranging on a solid platform at slightly larger scale.

The answer is actually YES if you can make the CMB your table top.

You propose a thought experiment. The current expansion rate is 1/140 of a percent per million years. Basically you say what if it was a million times faster! What if it was 1/140 of a percent per year? How would you set up an experiment to measure this?

That is an interesting thought experiment.

One consideration is how accurately can one establish CMB rest. With current instruments it is better than 1/1000 of a percent. CMB temperature mapping is about this precise, detecting temperature fluctuations of that magnitude.

So one stations the observers out in intergalactic space (so the gravitational field of the galaxy will not perturb the CMB significantly.) And one makes the separation be, say, 140 lightyears. That means the distance between the two observers will be increasing at one percent of the speed of light.

The key thing, since expansion is essentially a property of the CMB, is to get both observers to be at rest with respect to CMB. So they each must measure the temperature in all directions and make sure there is no significant hotspot. Only small fluctuations of the usual sort. Then they can use Doppler radar to measure the rate of increase of distance between them. They should find that the redshift z = 0.01.

4. Apr 9, 2009

### robousy

Thanks Marcus, and I'm glad you posted a response as I put a lot of value on what you say.

Let me entertain you for a few moments and tell you where I'm really coming from.

The energy density of the universe is (again, excuse my approximations)

$$\rho=10^{-47}GeV^4$$

and we know from GR that in an FRW universe:

$$H \propto \sqrt{\Lambda}$$

I've been thinking recently about Petawatt lasers and the energy density of such lasers is on the order of $$10^{9}W/m^3$$.

Now, obviously the laser is focused in a very tight beam, but within that beam the energy density of space would be vast and, via the formula above, the expansion of the universe along that laser beam, would also have increased.

I've done some back of the envelope calculations and I've got a figure of around $$10^{-5}m/s/m$$. (excuse my obtuse use of different units throughout this post - especially for Hubbles constant in m/s/m).

So this is what I'm wandering could be measured...

Do you have any thoughts on this?

Rich

Last edited: Apr 9, 2009
5. Apr 9, 2009

### robousy

I would...let me think about what you've said for a little while so that I can offer an intelligent question...

Last edited: Apr 9, 2009
6. Apr 9, 2009

### marcus

Sure, and I don't guarantee a correct response either. It's just that for me it's a novel way to look at expansion and for that reason I'm glad another person wants to take a look at it that way as well.

I guess one should note that according to the current standard LCDM model the bulk of the ancient matter was actually Dark Matter and the baryonic matter's role is more like a tracer that is intermixed, coextensive, evenly distributed along with the DM. So when the baryonic ancient matter radiates what becomes CMB that is a fair indicator of how the main bulk is distributed. But according to LCDM the baryonic is only 1/6 or 1/7 of the total at that time.

7. Apr 9, 2009

### marcus

Ordinary energy density gravitates, makes parallel lines curve in, and so on.
Dark energy is a special exception, which has to do with its equation of state, or the parameter w you often see referred to---the ratio of pressure to energy density.

For light (like from your laser) w = +1
A box full of light is going to act more or less like a box full of mass, with equivalent density.

Typically for dark energy (so far just postulated, a theoretical construct) w = -1

If you can find a good exposition of the Friedman equations (there are two) it will show the role that w, the equation of state, plays and why you only get accelerated expansion with negative w.

I'd rather not focus on the laser experiment. I want to think about the other thing we talked about. Using the CMB as a lab bench to measure expansion (as in the title of your thread.)
It is an intriguing thought experiment.

8. Apr 10, 2009

### Carid

marcus

You said

Is coextensivity of the baryonic and dark matter at the time of the CMB formation an hypothesis or are there observations to support this?

9. Apr 10, 2009

### marcus

I believe it's an assumption--a simple one, moreover. Modeling early universe structure formation is (to my knowledge--I'm just a spectator without special expertise) a fairly recent development. What I've seen doesn't even bother with the baryonic component at first, since it is a small minority in the mix.

It models how a clustery cobwebby structure of DM emerges from an initially almost uniform DM distribution (which of course fills all of space---space and matter are always assumed to be coextensive, you know the standard homogeneous-isotropic deal.)

The amazing thing is how in a computer model the DM entirely by itself condensing by its own gravity generates a structure very much like what we see at large scale----filaments, blobs, voids of various sizes. You can see how the overall largescale layout of groups of galaxies could have originated.

I'm thinking of the short computer-generated movies that George Smoot showed in his TED talk. Google "Smoot TED", the first hit is:
http://www.ted.com/index.php/talks/george_smoot_on_the_design_of_the_universe.html

Here are links directly to some of the animations:
http://cosmicweb.uchicago.edu/filaments.html
http://cosmicweb.uchicago.edu/group.html

Last edited: Apr 10, 2009
10. Apr 12, 2009

### Redbelly98

Staff Emeritus
Hey, I really like this explanation. I have always been bothered when I read about the "expansion of space itself", or words similar to that. Maybe it sounds too much like the aether theory to me. But thinking about the expansion of, say, a collection of observers, all at rest w.r.t. their own local CMB, is much more palatable to me.

11. Apr 13, 2009

### robousy

Hey, sorry for the delay in getting back to you Marcus. I'm on vacation in Utah with my wife so I'm not in front of the computer as much as usual.

Going back to your thought experiment with two observers separated by 140 ly, you mentioned the observers could use a doppler radar to measure the expansion rate between them. What is the role of the CMB here? I'm not sure I'm following how it comes into play.

Rich

12. Apr 14, 2009

### Redbelly98

Staff Emeritus
Hi Rich,

If the observers are to measure Doppler shifts between themselves, they need to each pick an appropriate inertial reference frame to be in. The local CMB determines what that frame is; each observer needs to adjust their velocity so that the CMB spectrum is the same in all directions.

In general, we observe the CMB to be blue-shifted along one direction, and red-shifted in the opposite direction, relative to the average over all directions. This indicates we are in motion relative to the preferred local frame; if we could adjust our velocity accordingly the CMB spectrum would become uniform in all directions. This neglects the small-scale fluctuations in the CMB that can not be "smoothed out" simply by changing the velocity of our observing frame.

Hope that helps.

Regards,

Mark

13. Apr 18, 2009

### robousy

Thanks for clarifying Mark. Thats crystal clear!

Really neat idea, to use the CMB as an inertial frame. Is this idea new to this thread...I'm guessing probably not.

Rich

14. Apr 18, 2009

### wolram

Every one forgets that the cmb may be some relic, of unknown phenomena, it is a perfect gate way to the cosmologist, yet it may be false, it is to perfect to fit into the ambiguity of cosmology

15. Apr 18, 2009

### Redbelly98

Staff Emeritus
Marcus could better answer that, but I also suspect not.

16. Apr 18, 2009

### Redbelly98

Staff Emeritus
I'm afraid I don't understand the last part of what you said? The CMB spectrum fits very well with what would be emitted by normal matter at one time in the distant past.

17. Apr 20, 2009

### yogi

Getting any skiing - I will be there next week - still any good snow?

18. Apr 20, 2009

### marcus

Yes, and Mark's (Redbelly's) concise explanation makes it consideraby clearer. About newness, I also suspect not.

19. Apr 21, 2009

### robousy

...probably. We've been hiking in Bryce and Zion and it's getting fairly warm now. I'm sure that the ski resorts still have lots of snow though!

20. Apr 22, 2009

### wolram

Surly every one realises by now that there is no rigid ruler in today's cosmology, people can spout hypothetical measures till the cows come home but are they right?