How does the creation of virtual particles allow the universe to accelerate?

[PikminExpert]

Based on theories of an accelerating universe, how can the creation and annihilation of pairs of particles/anti-particles (virtual particles) generate energy in a vacuum (space) thus contribute to Eintstein's theory of a cosmological constant (positive pressure).

And if the quantum fluctuations (creation of virtual particles) produces energy to promote the accelerated expansion of the universe, how would the universe suddenly start accelerating if the fluctuations are supposed to be constant? (because it has no variables to rely on in space)

 

[robousy]

Well, solving Einsteins for the FRW metric one obtains something like:

$$H=\frac{\dot{a}}{a}=\frac{8 \pi G \rho}{3}+\Lambda$$

Where $$\rho$$ is the energy density if the universe and H is Hubble's constant which characterizes the expansions of the universe.

You spoke of the vacuum. In QFT the basic 'object' is a quantum harmonic oscillator with ground state energy $$E_n=\frac{\hbar c}{2} k_n$$

And so the total energy is given by summing over all the modes of the vacuum.

This gives as a non-zero $$\rho$$ . The trouble is that the predicted vacuum energy is vast, on the order of $$10^8 GeV^4$$ (at least). To obtain the observed value of Hubble's constant $$\Lambda$$ must cancel this vacuum energy density to an extremely high precision.

How can a car accelerate if the flow of fuel is constant? Easy. Same sort of idea with the vacuum energy. Think of it as a sort of a fuel that accelerates the universe.

 

[marcus]

Well, solving Einsteins for the FRW metric one obtains something like:

$$H=\frac{\dot{a}}{a}=\frac{8 \pi G \rho}{3}+\Lambda$$

Where $$\rho$$ is the energy density if the universe and H is Hubble's constant which characterizes the expansions of the universe.

Equation looks like one of the two Friedmann eqns except needs a square on the H. H².

But there is another Friedmann eqn which treats acceleration explicitly. It too is derived from Einsteins. It has a double-dot----the second time derivative of the scalefactor a(t).

Any energy density tends to slow down expansion, so gasoline "fuel" can be a misleading analogy. The key thing is the pressure term, which you get in the other Friedmann, the Friedmann acceleration eqn.

Wikipedia "Friedmann equations" article is fairly adequate, if you want to fix stuff up and need a source for the acceleration eqn.

 

[robousy]

Thanks Marcus, yes I forgot that it should have been squared. Thanks for correcting the analogy too.

Rich

 

[PikminExpert]

I found out that the negative pressure that dark energy is supposed to have, would help an "already" expanding universe accelerate. A closed universe is supposed to eventually slow down and the velocity of the expansion drops below the escape velocity needed to escape the gravitational effects. This would cause the critical density to drop to a low, and the matter in the universe would exceed this point and thus the universe would collapse.

I think that's how it goes, but I'm not too sure about all the mathematical calculations on this.

 

[marcus]

... A closed universe is supposed to eventually slow down and the velocity of the expansion drops below the escape velocity needed to escape the gravitational effects. ... and thus the universe would collapse.

I think that's how it goes, but I'm not too sure...

It is good you asked. That is not how it goes.

Closed, in modern cosmology, means spatially closed. That is Omega > 1 which is the condition for spatial closure. It is not a condition that ensures eventual collapse. Thinking a spatially closed universe must eventually collapse is a misconception caused by holdover of pre-1998 ideas.

A closed universe can expand forever, assuming it has enough Lambda, the dark energy term.

In particular OUR universe could well be closed, and yet it is expected to expand forever.
The 95 percent confidence interval for Omega, as currently measured, includes 1.01. That would make us closed----finite volume space, finite but very large. and of course growing. And accelerating, not slowing down!

 

[PikminExpert]

But wouldn't a closed universe mean that it's closed both in space and time? If it's closed in time, that means it would EVENTUALLY stop expanding, right? Plus, I read up how gravity can become a repulsive force when the universe is at high energy densities, according to Martin Bojowald (leading person in loop quantum gravity theories).

 

[Chronos]

It would only be necessarily closed in the absence of dark energy - i.e. the universe only received an initial 'kick' from the big bang / expansion and has since been freely coasting. The force of gravity would then inexorably pull it all back together, unless the intial 'kick' was enough to achieve 'escape' velocity. This is why scientists are so interested in obtaining a precise value for lambda. There is no guarantee lambda is constant over time. It does, however, seem long odds that we happened to be looking when lambda was so close to exactly 1.000 [if it varies with age]. This is sometimes referred to as the 'coincidence problem'.