Expansion drains momentum from massive objects

[marcus]

Nobel laureate Steven Weinberg has written a new Cosmology textbook. Some folks might be interested. I don't have it yet (too stingy.) I have only second hand info.

One of the things he explains is how the expansion of the universe slows down the local motion of things.
In the early universe there would have been produced a hot cloud of neutrinos (particle-antiparticle pairs) all traveling very fast. The momentum of these particles would have decreased as the scalefactor increased.

So at some time the neutrinos are 3000 kelvin (similar but not exactly same as CMB photons) and since that time the universe has expanded by a factor of 1000, so then the momentum of each individual is 1/1000 what it used to be. Expansion makes the neutrinos more sluggish/

(note, i am not talking about recession speeds away from some distant observer. I am talking about their speed compared with a nearby photon traveling in same direction).

Galaxies would have been slowed down too, just like neutrinos, except that they were never traveling very fast (relative to CMB) in the first place. But in principle any massive object from a neutrino to a galaxy.

I expect you might like to see a mathematical explanation of this effect, and there is one by Hongbao Zhang that he published because it is an improvement on Steven Weinberg's textbook method of proof. Zhang is a smart guy. I will get the link to Zhang's new paper.
It is free (whereas you have to buy Weinberg's textbook.)

http://arxiv.org/abs/0808.1552
Note on the thermal history of decoupled massive particles
Hongbao Zhang
(Submitted on 11 Aug 2008)

"This note provides an alternative approach to the momentum decay and thermal evolution of decoupled massive particles. Although the ingredients in our results have been addressed in [Weinberg's new Cosmology text], the strategies employed here are simpler, and the results obtained here are more general."

 

[Garth]

So at some time the neutrinos are 3000 kelvin (similar but not exactly same as CMB photons) and since that time the universe has expanded by a factor of 1000, so then the momentum of each individual is 1/1000 what it used to be. Expansion makes the neutrinos more sluggish/

(note, i am not talking about recession speeds away from some distant observer. I am talking about their speed compared with a nearby photon traveling in same direction).

Thank you marcus.

I think you mean " i am not talking about recession speeds away from some distant observer. I am talking about their speed relative to each other"

Their speed relative to a nearby photon is of course always c.

Given the 'cooling factor' of ~ 1000 it is interesting to note that the present epoch typical velocity of galaxies relative to each other and to the Surface of Last Scattering of the CMB is
OOM ~ 300 km/sec. i.e. ~0.001 c.

Garth

 

[marcus]

I am delighted that you are pleased with Hongbao Zhang's paper, Garth. I admire him. A cosmologist who, however, participated at the Loops 2005 conference in Potsdam----one of the senior people at Beijing Normal who early on saw the interest of Loop Quantum Cosmology. I suspect he will be one of the organizers of the next Loops conference.

There is possibly some misunderstanding about the following so I will clarify what I meant to say by it:

...
...So at some time the neutrinos are 3000 kelvin (similar but not exactly same as CMB photons) and since that time the universe has expanded by a factor of 1000, so then the momentum of each individual is 1/1000 what it used to be. Expansion makes the neutrinos more sluggish

(note, i am not talking about recession speeds away from some distant observer. I am talking about their speed compared with a nearby photon traveling in same direction).
...

I was imagining an observer who is at rest wrt CMB, perhaps he is in some galaxy approximately at rest. He observes a neutrino and a photon, and he measures the speed of the neutrino by comparing it with the photon as a kind of standard yardstick of speed. We always do this. The speed c is always the standard of comparison. So I hardly needed to mention the photon!

I was talking about the speed of the neutrino relative to CMB. And simply observing that it was now only 1/1000 of what it used to be.

I wasn't talking about the neutrino's motion relative to a photon , as if the photon were the landmark.

 

[Garth]

Okay, I understand, the speed of the neutrino relative to the CMB SLS frame measured as a proportion of c.

Garth

 

[marcus]

Right-o.

Garth you said something interesting I wanted to ask you about.

Present random velocities of galaxies are around 300 km/s, as you mentioned.

Now I think this does NOT imply that they were on the order of 1000 times faster if you go back to z = 1000------that is, the clumps of gas that eventually became them.

Although if you had a free massive particle that WAS moving at nearly c, back then, it WOULD have been slowed down 1000-fold according to what you and I and Hongbao Zhang were talking about.

what do you think? To me it seems obvious that you can't extrapolate back like that because the galaxy's current 300 km/s could be the result of many different things, not just of a straight line slowing down process.

Or to take a less extreme example, I think it does NOT imply that a typical speed back in z=10 days was 3000 km/s (that is, ten times a typical speed now). Even though a massive object with that speed WOULD have been slowed down tenfold (according to Zhang's analysis).

Any comment, Garth or anybody?

...
...Given the 'cooling factor' of ~ 1000 it is interesting to note that the present epoch typical velocity of galaxies relative to each other and to the Surface of Last Scattering of the CMB is
OOM ~ 300 km/sec. i.e. ~0.001 c.
...

 

[Garth]

You are correct, I was just throwing in some numbers to think about.

The cooling factor of ~1000 would apply to average kinetic energies, so the average velocities would drop by the square root or a velocity factor of around ~30.

Garth

 

[neutralseer]

The cooling factor of ~1000 would apply to average kinetic energies, so the average velocities would drop by the square root or a velocity factor of around ~30.

Doesn't this cooling factor applies to momentum not kinetic energies (eqn 2.7 in the arxiv article)?

It does seem like Marcus is correct that the average speed of galaxies w.r.t. the cmb is not related to the $p = \frac{const}{a}$ result at all. This result is for "freely traveling massive particles," not for galaxies (which are anything but freely traveling).

Now I wonder why is it that most galaxies have peculiar speeds of ~300 km/s w.r.t. the cmb? My guess is that it's simply a result of the gravitational interaction that galaxies have with other nearby galaxies. It could also be interactions between larger structures like groups and clusters and galaxies pulling on other groups and clusters of galaxies.

Still, why 300 km/s and not say 10 km/s? Is this a nonlinear structure formation question that only simulations like the Millenium simulation can answer? Or is there a way to get a handle on this question analytically?