Increasing G during the formation of helium.

[EL]

A hypothetical question:

Say that Newton's constant G is increased a bit during the period between weak interaction decoupling and the time when photodisintegration becomes ineffective, and the helium is formed. (I.e. during the period when neutrons just decay). Would that give a larger or smaller abundance of helium compared to "normal"?

Intuitively one might think that increased G leads to increased gravitational strength and therefore halts the expansion more, and thus it would take a longer time for the rate of photodisintegration to drop below the expansion rate (i.e. more time for neutrons to decay, and hence smaller helium abundance).

On the other hand the Friedman eq say that the expansion rate increases with G, and thus would lead to a shorter time for neutrons to decay (i.e. larger helium abundance).

So which is correct?

 

[SpaceTiger]

Are you assuming zero curvature in the Friedmann equation? If you take a flat universe and strengthen G, you're effectively giving the universe positive curvature. Then the simple:

$$H^2=\frac{8\pi G\rho}{3}$$

no longer applies.

 

[Garth]

EL The second option: the presence of matter in the universe, and therefore gravity, causes the universe to decelerate in its expansion. This means it must have expanded more quickly in the past than if there were no gravitation attraction between matter particles.
i. In an empty Friedmann universe (the Milne model)
R ~ t
ii. In a dust filled universe (no pressure)
R ~ t^2/3
ii. In a radiation filled universe (maximum pressure - the pressure as a form of 'energy density' causes even more gravitational attraction and threfore deceleration):
R ~ t^1/2.
If you draw these curves, you will notice the curve (expansion) as t -> 0 gets gradually steeper as you go from i to iii, and the time available before a certain size R' gets shorter and shorter.

Instead of increasing the density and pressure of the universe you could keep those values fixed and increase the force of gravity G to get the same effect.

Such a change would vastly affect nucleosynthesis in the BB as a longer time would allow more neutrons to decay thus reducing the amount of helium (and deuterium) for a certain mass density. Thus in a radiation filled Friedmann model (the standard hot big bang) the correct amount of helium is formed when the baryon density is only about 2 - 3 % closure density. This has now been 'stretched' to 4% to agree with the WMAP modern standard model.

As the matter density appears to be an order of magnitude greater than this at 27% by WMAP, an large amount of exotic non-baryonic Dark Matter is required to make the observations and theory agree.

This DM may not be required if the expansion rate is 'slower' - say in the Milne model which predicts over 20% baryonic density - this may be achieved in the Freely Coasting Model or by varying G as you suggest. Happy hunting!

Garth

 

[SpaceTiger]

The second option: the presence of matter in the universe, and therefore gravity, causes the universe to decelerate in its expansion. This means it must have expanded more quickly in the past than if there were no gravitation attraction between matter particles.

It depends on the interpretation of the question. If he/she's "suddenly" perturbing a universe that had already evolved, then the option is the first. If they're assuming flatness in both cases, then it requires different evolution histories and your conclusion is the right one.

 

[EL]

It depends on the interpretation of the question. If he/she's "suddenly" perturbing a universe that had already evolved, then the option is the first. If they're assuming flatness in both cases, then it requires different evolution histories and your conclusion is the right one.

(For the first I'm a "he" )

Yes I mean that I suddenly perturb the universe that has already evolved, and then suddenly perturb it back again after the helium is formed.
I do not assume flatness. In fact I don't assume flatness in the first case either, but this curvature should not be important at such early times anyway? So then you're sure the first option is the correct? Is it because the Friedman eq only holds for constant G?

 

[EL]

EL The second option...

I suppose you are talking about different universes with different values of G in each, or? What I really ment was a universe where G is not a constant.

To put the question another way:
If we suddenly increase G during a period, and then suddenly decrease it back again, will the expansion rate decrease more rappidly or slower during this perturbed period, compared to how it should have evolved if G wasn't changed?

 

[Garth]

That depends on what else changes with G, certainly it may affect flatness for example. A sudden increase in G followed by a decrease would put a break on the expansion, but that would also increase the present age of the universe. So how do you measure time, and are clock rates affected by the change in G? If the rate of atomic processes are unaffected then yes there would be less helium for a certain baryonic density.

Of course to be consistent we also have to acknowledge that if G is allowed to vary then the GR field equation, and its conservation properties, are thrown out of the window. So it is a little premature to discuss the effect of such variation without first having a consistent theory that embodies that varying G in which nucleosynthesis can be recalculated from scratch.

Garth