How does the expansion of the universe work?

[PeterDonis]

how massive are the two objects, how far apart they are

Since it is specified that there is no other matter between them, just empty space, this doesn't make any difference qualitiatively; all it affects is how fast the objects will fall together. Of course that specification might not be realistic for large enough separations.

If there is dark energy present then that is an additional interaction.

I thought we had ruled out dark energy for this particular scenario. You said there is "nothing inside the boundary except those two objects". That means no dark energy. Obviously the presence of dark energy will change things--but the separation would have to be very, very large (tens to hundreds of millions of light years) for it to change things significantly.

Also, if you are trying to understand what effect "expansion" has in itself, it would seem that you would want to rule out dark energy.

Space (which includes dark energy)

"Space" in itself does not have to include dark energy. It happens to in our actual universe, but we are considering thought experiments in order to understand the underlying physical principles involved. In such thought experiments it's perfectly reasonable to say there is no dark energy. "Space" without dark energy is perfectly consistent physically.

I agree that there will always be an attraction between the two objects in proportion to the inverse square law. But that attractive force does not tell me anything about the relative motion between the two bodies.

It does if it's the only force acting, which is what I thought the specification of the scenario was.

I am now thinking that we shouldn't talk about expansion without dark energy, as it is a real part of 'space'.

No, it isn't. Dark energy is something separate from "space". It happens to be present everywhere in our universe, but that is not required by the laws of physics. It's just a contingent fact about our universe. If you are trying to understand expansion in and of itself, it is perfectly reasonable to assume, for purposes of a thought experiment, that there is no dark energy; the physical model you get is perfectly consistent. See my comments above.

One of the other big confusion factors is when people talk about recession as distant bodies being at rest wrt each other and the space growing between them.

Yes, and I am saying that a good way to avoid this confusion is to understand that there is no force associated with expansion. There is a force associated with dark energy, but that is a force associated with accelerating expansion. You can have expansion without having accelerated expansion.

To put this another way, there is no force associated with "space" in and of itself. "Space" cannot expand in the sense of pushing or pulling things apart. Dark energy can push things apart, but that's because dark energy is not "space"; it's something separate from space. It can be thought of as a kind of "exotic" substance that causes repulsive instead of attractive gravity. It's not the same as empty space.

 

[rede96]

if you are trying to understand what effect "expansion" has in itself, it would seem that you would want to rule out dark energy.

Yes, you're right of course. I started to jump around a bit sorry.

It does if it's the only force acting, which is what I thought the specification of the scenario was.

Ok got it. However looking at this another way. If I take the FRW equations, assuming flat space and no dark energy, and as the radiation energy density today is negligible, then all I am left with is the matter energy density, this would give me a 'rate' of movement. But as I understand it, that in itself doesn't tell me if the universe is expanding or contracting, is that correct?

Today we model this movement on 'expansion' as that matches the observations, so the FRW equations tell us that expansion rate. But in the scenario we mentioned (ie two bodies at rest) then what does the FRW equations tell us about that situation? The rate of attraction? (I am also assuming I can't get a negative rate of expansion from the FRW equations.)

Dark energy can push things apart, but that's because dark energy is not "space"; it's something separate from space. It can be thought of as a kind of "exotic" substance that causes repulsive instead of attractive gravity. It's not the same as empty space.

Quite often I hear / read of vacuum energy being a property of empty space and we can't have totally 'empty' space. I also read a lot that vacuum energy is the same as dark energy, hence why I assumed dark energy it is a property of empty space as you can't have empty space that consists of 'nothing'

Just to clarify is vacuum energy of empty space different from dark energy? If so why isn't there a term for both energy densities in the FRW equations?

 

[PeterDonis]

If I take the FRW equations, assuming flat space and no dark energy, and as the radiation energy density today is negligible, then all I am left with is the matter energy density, this would give me a 'rate' of movement. But as I understand it, that in itself doesn't tell me if the universe is expanding or contracting, is that correct?

The first Friedmann equation has the square of the Hubble constant on the LHS, so for a given density there are two possible solutions, expanding and contracting, yes. (Note that there is also a curvature term on the LHS, but you can always just try each of the three possibilities, k = +1, 0, -1, to see which of them give possible solutions.) To distinguish between them, you need some kind of initial condition--for example, the observation that the universe right now is expanding.

in the scenario we mentioned (ie two bodies at rest) then what does the FRW equations tell us about that situation?

Nothing, because it isn't applicable. The Friedmann equations assume that the matter in the universe is a continuous fluid; it can't be applied to the case of two isolated bodies in empty space.

If we assumed we had a matter-only universe where all the matter (the continuous fluid) was at rest at some instant of time, the Friedmann equations--more precisely, the second Friedmann equation--would tell us that it would start contracting. "At rest at some instant of time" is an initial condition, and is enough to allow the equations to give a unique solution.

Quite often I hear / read of vacuum energy being a property of empty space and we can't have totally 'empty' space.

Now you're talking quantum field theory, not classical GR. It is true that in quantum field theory, what we normally think of as "empty space" should have a nonzero vacuum energy. However, when we try to calculate this energy, we come up with an enormous answer: something like 123 orders of magnitude larger than the largest value which is compatible with our observations. So something is clearly wrong with our current understanding of how this works in quantum field theory.

is vacuum energy of empty space different from dark energy?

In terms of what the physical origin of dark energy (meaning, "whatever it is that is causing the accelerated expansion of the universe") is, we don't know; it could be vacuum energy or it could be something else like a scalar field, or it could be a combination of several such things. In terms of how vacuum energy would behave in the equations, it would behave the same as dark energy--like a cosmological constant. (At least, assuming that dark energy works the way we assume it does in our best current model--see below.) So the cosmological constant term in the equations covers both possibilities.

There are other speculations about types of "dark energy" that work differently from a cosmological constant--such as "quintessence", which causes accelerated expansion but not quite as strongly as a cosmological constant; or "phantom energy", which causes even more acceleration than a cosmological constant and leads to a "Big Rip" scenario. None of these speculations have any evidence to back them up; our best current evidence is that the accelerated expansion we observe is exactly what it should be if it were due to a very, very tiny cosmological constant.

 

[rede96]

The first Friedmann equation has the square of the Hubble constant on the LHS, so for a given density there are two possible solutions, expanding and contracting, yes. (Note that there is also a curvature term on the LHS, but you can always just try each of the three possibilities, k = +1, 0, -1, to see which of them give possible solutions.) To distinguish between them, you need some kind of initial condition--for example, the observation that the universe right now is expanding.

Thanks Peter. Again just to check my understanding, wouldn't both solutions need to be positive, so we don't have to take the square root of a negative number. And if they are both positive, then I assume these two answers would just be different rates and we'd still need observation to tell us if the universe is contracting or expanding. Is that correct?

Now you're talking quantum field theory, not classical GR. It is true that in quantum field theory, what we normally think of as "empty space" should have a nonzero vacuum energy. However, when we try to calculate this energy, we come up with an enormous answer: something like 123 orders of magnitude larger than the largest value which is compatible with our observations. So something is clearly wrong with our current understanding of how this works in quantum field theory.

Just out of interest, is the 123 orders of magnitude larger calculated for the present vacuum energy anywhere near the estimate for the energy in the initial inflaton field prior to inflation? I was just curious to see if there was any link between them.

 

[PeterDonis]

is the 123 orders of magnitude larger calculated for the present vacuum energy anywhere near the estimate for the energy in the initial inflaton field prior to inflation?

Good question. I don't think it's close, but I don't know for sure.

 

[PeterDonis]

wouldn't both solutions need to be positive, so we don't have to take the square root of a negative number. And if they are both positive, then I assume these two answers would just be different rates and we'd still need observation to tell us if the universe is contracting or expanding. Is that correct?

The first Friedmann equation reads

$$
H^2 + \frac{k}{a^2} = \frac{8}{3} \pi \rho + \frac{1}{3} \Lambda
$$

Since $H^2$ appears on the LHS, there will be two values of $H$ corresponding to any solution of this equation--the positive square root of $H^2$, and the negative square root of $H^2$. These two values correspond to an expanding and a contracting universe, with the same rate numerically in both cases, just opposite signs; so we need observation to tell us the sign. Of course $H^2$ itself must be positive, but that doesn't make both of its square roots positive.

 

[Jorrie]

These two values correspond to an expanding and a contracting universe, with the same rate numerically in both cases, just opposite signs; so we need observation to tell us the sign.

Hypothetically, if we have observed blueshifts instead of redshifts, with the same values for Lambda and matter density, would we have observed a present decelerating contraction? With no observable CMB?

 

[PeterDonis]

Hypothetically, if we have observed blueshifts instead of redshifts, with the same values for Lambda and matter density, would we have observed a present decelerating contraction?

Hypothetically, yes.

With no observable CMB?

Whether or not we would observe a CMB in this hypothetical universe would depend on what it was like in the past.