# Co-moving density should be constant?

1. Oct 14, 2012

### johne1618

If one considers a proper region of space then the (proper) density of mass/energy will change for two reasons.

1/ Matter is carried out of the region by the expansion of space.
2/ Energy changes as work is done on that matter by pressure.

But if one considers a co-moving region of space then there is no expansion and therefore there should be no change in co-moving density.

Is this correct?

2. Oct 14, 2012

### marcus

Correct if there were just cold particles.

If you include light, then not correct because the wavelengths increase with expansion. So energy goes down.

Also "relativistic" particles can be taken to mean stuff where the kinetic energy is large enough compared with the restmass energy to be taken into account. Expansion bleeds out kinetic energy. In comoving frame things slow down. It is simply analogous to redshift of light. Expansion makes both light and relativistic matter lose energy in the CMB rest frame. (intuitively because where it was going to was backing off from it, if you like to think of it that way, expansion is a shock absorber, rolling with the punches)

But "cold" particles are taken to mean stuff where you can NEGLECT the kinetic energy. So you can essentially treat it as particles sitting still in an expanding volume. In that case the mass/energy contained in the volume does not change.

Last edited: Oct 14, 2012
3. Oct 14, 2012

### johne1618

If one defines density as total energy content in an expanding volume then one is talking about proper density which does change as the Universe expands.

But I am defining co-moving density as total energy content in a co-moving volume. In co-moving co-ordinates there is no Universal expansion so neither the wavelength of photons change nor the size of the co-moving volume.

4. Oct 14, 2012

### marcus

I see, so for you the CMB light is still 3000 kelvin because you measure the wavelength of the photons in comoving coordinate "length units"? So the wavelengths cannot have changed!

but to me the light feels strangely cool.

5. Oct 14, 2012

### johne1618

Good point!

I guess we actually experience proper co-ordinates in which the Universe evolves rather than timeless co-moving co-ordinates.

Last edited: Oct 14, 2012
6. Oct 14, 2012

### BillSaltLake

In co-moving length units, Planck's constant h would be decreasing, so the photon energy will be decreasing.

7. Oct 14, 2012

### Drakkith

Staff Emeritus
Marcus I never thought of it until you mentioned it, but will high velocity particles moving towards far away galaxies will arrive at some at significantly reduced speeds thanks to expansion? I think that's what you were saying but I want to make sure.

8. Oct 14, 2012

### marcus

Yes Drakkith, I believe so. To make the discussion more precise it seems to be about the comoving frames of reference or the idea of CMB rest. If it weren't for that the discussion might not be as interesting as it is, for us.

Because of the apparent uniformity of ancient matter before it began to fall together into clumps, and because of the near uniformity of the CMB light emitted by the ancient matter, we have in cosmology a nice concept of the stationary observer. And by extension, the idea of galaxies being nearly at rest (save for a bit of individual random motion).
And it is distances between stationary observers that the Hubble law of expansion is really about.

Well this expansion can be seen as responsible not only for the redshifting of light but also the SLOWING of moving objects if you measure their speed relative to CMB rest whereever they happen to be. Moving objects do lose momentum and kinetic energy in that sense.

And it is completely commonsensical because where they were going was backing away from them. It can all be analysed in Doppler or relative motion terms, if one wishes. The redshifting of light can be resolved into a huge number of little infinitesimal Doppler shifts along the way as the expansion rate changes while the light is in transit. It is completely unmysterious if you want to think of it that way. And objects of course slow down by the same mechanism, due to distance expansion.
======================

I like to think of Dark Matter particles starting out with a lot of random kinetic energy and being cooled by expansion so they are now moving slowly and can collect in clouds (which formed the basis for structure formation in ordinary matter). And when DM particles fall together and selfgravitate they interact gravitationally and some get slowed down and stay in the cloud while others get speeded up and thrown out of the cloud. THEY CARRY AWAY THE EXCESS KINETIC ENERGY and allow the remainder to condense.

DM has no other way to get rid of excess energy than by sacrificing some of itself, to carry the energy away.

Now because of EXPANSION the sacrificial DM can lose energy in the sense that when it arrives somewhere else it is going slower. So it can be RECYCLED and again participate in cloud condensation. So it is the expansion cooling of DM which provided the seeds of structure.

Expansion was the PARENT of all the structure which we see and which we are. Because stars and galaxies of ordinary matter condensed around an ARMATURE of DM cobwebs and filaments. And those DM filaments and clouds would not be there without the cooling effect expansion.

This is a familiar story, in a sense. We know the parallel story concerning light, expansion cooled the light and thus the ordinary matter in equilibrium with the light. But now I am saying the same thing but talking about DM particles that cannot emit and absorb light. So the only way they have to slow down is by way of expansion.

I wanted to add that, tangentially related to what you asked about particles slowing, even though you didnt ask directly about DM, because it just seems nice. Another role expansion has played in our lives.

Last edited: Oct 14, 2012
9. Oct 14, 2012

### Drakkith

Staff Emeritus
So an observer at a high velocity will lose velocity with respect to the CMB frame? It makes sense. I think lol.

10. Oct 14, 2012

### Chronos

It certainly raises questions about the origins of ultra high energy cosmic rays. Their origins must be relatively local, or, they would not be UHE.

11. Oct 15, 2012

### Lino

Marcus, Can two (separated) points / observers both be jointly at rest relative to CMB?

Regards,

Noel.

Last edited: Oct 15, 2012
12. Oct 15, 2012

### marcus

For sure!

The criterion for being at CMB rest is approximate---CMB temperature is uniform to within 1/1000 of a percent. As a practical observational matter we can only determine something is at rest to within, say, 0.001%. So you need a ENOUGH separation so that the uncertainty about what is at rest is negligible.

Think about points or observers initially placed one megaparsec apart. Each approximately at rest (as well as can be determined, within a tolerance of 0.001%).

I think this corresponds to the situation you are asking about. The two observers are at rest and they remain at rest, and the distance between them will of course be growing at 70-75 km/s.

13. Oct 15, 2012

### Lino

Thanks Marcus. That makes sense.

Regards,

Noel.

14. Oct 15, 2012

### Drakkith

Staff Emeritus
Say an observer moves away from our galaxy at 0.9c and he arrives later at a galaxy of redshift z=1, without accelerating during the trip. (Not sure if the measurement of z should be when he leaves or arrives) What velocity will the observer be at? Half of his original velocity?

15. Oct 16, 2012

### Staff: Mentor

I didn't do the maths, but I think it is more a reduced energy than a reduced velocity - if a proton of 10^19 eV loses 90% of its energy (relative to the CMB background), it is still a proton at 10^18 eV and moving close to the speed of light.

@marcus: You can determine "at rest" as "zero dipole moment", which can be determined better than the fluctuations of the CMB. For large distances, I would expect that the fluctuations vary. This will limit the precision, but the expected variation in the dipole moment is much smaller than the variation of the temperature in different directions.