Could Changing Gravitational Constant Explain Hubble's Law Alternatives?

[Garth]

There is no such confusion

BTW A Very Happy Birthday!

If there is no confusion and we agree that in cosmological red shift objects are treated as if they had no proper motion through space, only that of the expanding space in which they are embedded. Then the observed red shift can only come from the evolution of the scale factor with time.

That scale factor, R(t), and the curvature factor, (1 - kr^2)^{-1/2}, determined by the average density, are the only descriptions of the "cosmological gravitational field" in the cosmological R-W metric.

Therefore in the Milne universe (where k = -1), the observed red shift is due to the scale factor, R(t) ~ t, i.e. the null gravitational field. (See d'Inverno "Introducing Einstein's Relativity" pages 324-5 for a derivation of the cosmological red shift)

I think it is confusing that this cosmological red shift is also called doppler shift when the objects are not moving through space.

Garth

 

[gptejms]

Thanks, Garth!

 

[ratfink]

Isn't this a bit strong

If there is no confusion and we agree that in cosmological red shift objects are treated as if they had no proper motion through space, only that of the expanding space in which they are embedded. Then the observed red shift can only come from the evolution of the scale factor with time.

(bolding etc is from me)
Just a thought, my understanding is that the Doppler interpretation is abandoned because if the redshift was due to proper motion then galaxies would distort as they approach the speed of light.
They don't ergo we say that it is space expanding carrying the galaxies along with it.
1) is this true?
2) Is there any test that we can carry out to differentiate between the two scenarios?
Ratfink typing with slapped wrists

 

[Garth]

Hi ratfink.
If you think "Then the observed red shift can only come from the evolution of the scale factor with time." is a bit 'strong', then where else might it come from?

Note: we are in the field of GR, which is a theory that may not be the last word on the subject and might in future be adapted or modified, however, while we are understanding cosmology under the standard GR paradigm then we are accepting that cosmological red shift is due to the expansion of space itself rather than the motions of galaxies etc. through space.

As in GR we understand the universe to be expanding and the proper distance to these distant objects increasing with time then it is understandable that the observed red shift is described as Doppler shift. All I am saying in my posts above is that this is the same phenomenon as that described by the expression "evolution of the gravitational field".

Garth

 

[gptejms]

I have a question on CMB.Due to the expansion of the universe there should be two sources of cooling of background radiation--1.)adiabatic expansion like that of any gas,2.)stretching of wavelengths due to cosmological expansion of space.Is the latter effect taken into account in calculations?

 

[gptejms]

Okay,I see from Ned Wright's cosmology tutorial that the latter effect is indeed taken care of.Now my question is about the first effect--is that taken care of?

 

[Garth]

Okay,I see from Ned Wright's cosmology tutorial that the latter effect is indeed taken care of.Now my question is about the first effect--is that taken care of?

There are two temperatures referred to in cosmology, the black body temperature of the CMB, which is at the present time equal to 2.76⁰K, and the temperature of matter, whcih can be anything today above 2.76⁰K. (There may be super-cooled gas around below this temperature in which case please let me have any links to published papers)

The temperature of the CMB is slowly decreasing because of the "stretching of wavelengths due to cosmological expansion of space". T \propto R(t)^{-1}.

When the universe was ionised the plasma within it was heated to the temperature of the then temperature of the CMB by photon-particle interactions.

Once the universe became transparent the radiation cooled adiabatically until other processes, such as it forming dense halos, changed the physical conditions, the matter temperature evolution then became a bit messy!

I think SpaceTiger is the expert in this regime!

Garth

 

[hellfire]

I have a question on CMB.Due to the expansion of the universe there should be two sources of cooling of background radiation--1.)adiabatic expansion like that of any gas,2.)stretching of wavelengths due to cosmological expansion of space.Is the latter effect taken into account in calculations?

When a (relativistic) photon gas cools adiabatically, the dependence of its energy with volume is E \propto V^{-1/3}. This is equivalent to E \propto 1/a with a scale factor. Since E = h \nu and \nu \propto 1/a in an expanding space, this energy loss in an comoving (expanding) volume is due to the decrease of the frequency. As far as I know this accounts for all the energy loss and one has not to consider anything additionally.

 

[gptejms]

I think both the effects mentioned in post #65 can be taken into account.Consider an ideal bose gas(background radiation) undergoing cosmological expansion.Internal energy of a bose gas per unit volume, U/V \sim T^4,where T is the temperature.Now consider V increasing due to (cosmological) expansion.V\sim R^3,so it would seem that T goes as R^\frac{-3}{4}.

But since every photon in the background radiation is red shifted by an equal factor,the (total) internal energy U also goes down by the same factor i.e. U goes as 1/R.So one can see that the temperature T goes as 1/R rather than R^\frac{-3}{4}.

There could be loopholes in the argument(!) but because it's appealing I am reporting it as soon as I've thought of it.

 

[gptejms]

The above argument is obviously wrong.Temperature can not depend on volume,so all the relation means is that for a gas at temperature T,larger volume means larger internal energy.In fact it sheds no light on how the temperature varies with increasing size of the universe.

Now assuming that temperature T~1/R (due to cosmological expansion),how does internal energy scale as a function of R?This is the only valid question to ask.Does the above relation answer this question?What is the answer?

Well, the answer is U ~ 1/R(!).See,there is a difference in what 'exactly' was said in the last post and this one.If in post #69 we were to 'if U goes as 1/R due to cosmological expansion then T goes as 1/R too' then it would be a correct statement.The present post says the reverse('if T goes as 1/R then U goes as 1/R).

So we have said nothing so far about cooling of the bose gas due to the effect of adiabatic expansion.Hope the cosmo tigers here have at least something to say on this.

 

[hellfire]

If you apply the assumption of adiabatic expansion to a photon gas with P \propto u/3 = E/3V...

dE + PdV = 0

dE = - \frac{EdV}{3V}

E \propto V^{-1/3}

With V \propto R^3, this is:

E \propto R^{-1}

For the internal energy per unit volume:

u \propto R^{-4}

But I am confused. This follows merely from the assumption of adiabatic expansion, without taking into consideration the expansion of space. If a photon gas expands adiabatically in a piston of some characteristic lengt L (in static space), it will also increase its wavelengh, because E \propto L^{-1} and E \propto \lambda^{-1}. However, in an expanding space the same relation applies. Why?

 

[Garth]

If the photon number remains constant there is no problem. Adiabatic expansion yields E \propto R^{-1}, which means the energy of each photon E_\nu \propto R^{-1} that reveals itself as cosmological red shift.

The expansion of space dilution of each photon's energy is consistent with the time dilation cosmological red shift.

1 + z = R_0/R(t)

Garth

 

[hellfire]

OK, the evolution of the internal energy of a photon gas that is expanding adiabatically in static space is the same as the evolution of the internal energy of the photon gas that is comoving (constant comoving volume) in an expanding space.

But consider a photon gas in a cylinder with a piston. The piston moves due to the gas pressure that expands adiabatically. Additionally, consider that during the adiabatic expansion the space within the cylinder expands. Would this scenario imply a E \propto R^{-2} dependence (due to gas expansion and space expansion)? (Such a scenario is not relevant for cosmology because the photon gas would increase its comoving volume which is against the cosmological principle, at least for the CMB).

 

[Garth]

I do not understand what you mean by: "Additionally, consider that during the adiabatic expansion the space within the cylinder expands."

Is everything expanding? The whole cylinder and the piston? Rulers as well? How are you measuring this expansion?

In cosmology, the work done by the pressure in the expanding co-moving volume of the universe is equal to the change in total energy. If that pressure is mediated by a photon gas then that photon gas loses energy, even though the total photon number remains constant. Thus each photon loses energy and is red shifted as a result.

Garth

 

[hellfire]

The piston would be moving, as in a usual thermodynamical experiment in laboratory. Additionally there would be a nonnegligible expansion of space within the cylinder.

In cosmological terms you could imagine that the CMB would increase its comoving volume (it would be flowing radially "outwards" of the observable universe) instead of mantaining it constant.

 

[gptejms]

But I am confused. This follows merely from the assumption of adiabatic expansion, without taking into consideration the expansion of space. If a photon gas expands adiabatically in a piston of some characteristic lengt L (in static space), it will also increase its wavelengh, because E \propto L^{-1} and E \propto \lambda^{-1}. However, in an expanding space the same relation applies. Why?

I haven't carefully gone thru your derivation,but P seems to be constant.Why?What makes the calculation adiabatic?

If the universe were to expand like an ordinary gas,its temperature wouldn't change at all---because unlike an ordinary gas which does work against external pressure and loses internal energy,there is nothing for the universe's 'background photon gas' to work against.Its internal energy would remain constant in this scenario.So the only thing that causes temperature loss for the background radiation is the cosmological expansion.

 

[hellfire]

I haven't carefully gone thru your derivation,but P seems to be constant.

The pressure is P = u/3 and therefore has the same dependence with R as u.

 

[gptejms]

Ok---you are using the first law(with dQ=0 for adiabaticity).But the gas is working against the external constant pressure P (distinguish this from internal pressure of the gas which is not constant and as you say given as u/3).

Anyway,as I have said there is no similarity here with the expansion of the universe's photon gas--the only effect that causes its cooling is the cosmological red shift due to expanding space.