This universe would expand right?

[aquabug918]

In Einstein's view of a static universe what would happen if some mass turned into radiation?

I am thinking that since the density would decrease then the universe would expand since the cosmological constant would stay the same. Would it change?

 

[Garth]

Einstein's static model was unstable, a small perturbation towards either collapse or expansion would be magnified into full collapse or expansion.

However the conversion of mass into energy would not in itself achieve this as both would have an equal effect on the cosmological gravitational field.

Garth

 

[aquabug918]

Thank you very much! I still have a lot to learn but this is very interesting! Thanks again.

 

[chronon]

I've a feeling that since radiation has a contribution to the pressure term in Einstein's equation, the radiation would have a greater effect than the corresponding amount of matter, and so the universe would contract.

 

[Garth]

I've a feeling that since radiation has a contribution to the pressure term in Einstein's equation, the radiation would have a greater effect than the corresponding amount of matter, and so the universe would contract.

Agreed:-

if all the matter turned into radiation, and if the universe were spatially flat without DE or a cosmological constant then the expansion scale factor

$R(t) \propto t^{2/3}$ becomes

$R(t) \propto t^{1/2}$

Garth

 

[SpaceTiger]

Agreed:-

if all the matter turned into radiation, and if the universe were spatially flat without DE or a cosmological constant then the expansion scale factor

$R(t) \propto t^{2/3}$ becomes

$R(t) \propto t^{1/2}$

Wouldn't that mean you disagree? Neither case corresponds to contraction...

 

[Garth]

Wouldn't that mean you disagree? Neither case corresponds to contraction...

For clarification:

I was originally talking about the unstable Einstein static model, which does have a cosmological constant and is spatially closed i.e. geometrically spherical, but then used a simple flat Friedmann expanding model to show that the addition of pressure - radiation pressure - causes that expansion to decelerate more quickly.

The inference being that the addition of pressure would cause the Einstein static model instability to tend towards collapse.

Garth

 

[Chronos]

1 don't see how it would make any difference in GR. Mass and energy are interchangeable. Perhaps density would be a factor, but I doubt it would change physics as we know it. The photon v baryon ratio would not be affected, IMO.

 

[Garth]

Chronos take the standard flat non-CC expanding Friedmann universe as an example, the Einstein-de Sitter universe, as I did above.

Imagine its density is made up of dust particles, zero pressure, composed of equal numbers and masses of individual matter and anti-matter particles.

The average cosmological density is the critical density
$$\rho = \frac{3H_0^2}{8\pi G}$$
and the expansion rate will be
$$R(t) \propto t^{2/3}.$$

Now let the particles collide (slowly) and annihilate each other producing a radiation bath of gamma rays.

The matter density will be converted into an equal energy density of radiation but now there will also be pressure of

p = 1/3 rho c² (note: for some reason my tex gets screwed up here)

and the universe will expand as
$$R(t) \propto t^{1/2}.$$

Garth

 

[chronon]

The reason I picked up on this was that I've just read The Expanding Universe by Sir Arthur Eddington. His idea was that the universe began as Einstein's static universe but was tipped into expansion. On p51 he mentions that the conversion of matter into radiation will induce contraction. His theory is based on a rather obscure argument by Lemaitre that the condensation of parts of the universe will not directly tip the scales one way or the other, but will result in an overall reduction in pressure. Eddington says (p53)

Its effect is therefore the opposite to that of conversion of material mass into radiation, and it tends to make the universe expand

 

[hellfire]

Another way to see this is the following. A static universe means $\dot a = \ddot a = 0$, a condition that is reached with the help of a cosmological constant term $\Lambda$. According to the second Friedmann equation this, in turn, means that:

$$\frac{\ddot a}{a} = - \frac{4 \pi G}{3} (\rho + 3p) + \frac{\Lambda}{3} = 0$$

If matter is converted to radiation, the $p$ term converts from zero (non-relativistic matter exerts no pressure) to some positive value, making $\ddot a$ negative, different from zero. Note that at this initial instant of time when the conversion takes place, t₀, it still holds $\dot a = 0$. The $\rho$ and $\Lambda$ terms remain unchanged at t₀.

 

[Garth]

The reason I picked up on this was that I've just read The Expanding Universe by Sir Arthur Eddington. His idea was that the universe began as Einstein's static universe but was tipped into expansion. On p51 he mentions that the conversion of matter into radiation will induce contraction. His theory is based on a rather obscure argument by Lemaitre that the condensation of parts of the universe will not directly tip the scales one way or the other, but will result in an overall reduction in pressure. Eddington says (p53)

Its effect is therefore the opposite to that of conversion of material mass into radiation, and it tends to make the universe expand

Consulting page 45 of my 1940 edition (Pelican Books) of the 1932 Eddington's "The Expanding Universe"...

The problem they had in the early days was an age problem: their evaluation of Hubble's constant was too high, which inferred the universe was younger (at 1.9 Gyr.) than the Earth within it (at 4.6 Gyr.)!

The Eddington-Lemaitre suggestion was one model that tried to resolve this problem, in which the universe had a cosmological constant and had been almost static, remaining as such while large scale structure formed, right down to the scale of Earth sized planets.

In order to produce the expanding universe we now observe this unstable equilibrium had to have been disturbed about 1.9 Gyrs. ago into a runaway expansion.

What might have caused this expansion rather than a contraction?

The problem was that as stars etc formed in this static phase it might be expected that the radiation content of the universe would increase, as a result of this extra radiation flux, and cause a contraction instead of an expansion. Hence their need for a rather complicated and unconvincing process utilising "an empty crack all round" condensations of matter to reduce the overall pressure.

As we now know Hubble's constant is actually an OOM smaller than their estimate and the present estimation of the age of the universe (13.9 Gyrs.) leaves plenty of time for the Earth to form. Whether the present standard model contains another Age Problem remains to be seen...

Garth