What would happen if dark energy density decreased?

[KurtLudwig]

Dark energy density at this time is a constant and our universe is expanding (accelerating). This is expected to continue indefinitely. What would happen, if for some unknown reason, dark energy density started to decrease? If over time, in billion of years or longer, dark energy density decreased greatly, would the universe start to contract? There are Friedmann equations relating the Hubble constant H, first and second derivatives of a scale factor a, dark energy density and pressure and G. The scale factor a is a function of time. At what point would the universe neither expand or contract? At that time, gravity and dark energy are balanced. By how much would the dark energy density have to decrease for the universe to contract?

 

[PeterDonis]

What would happen, if for some unknown reason, dark energy density started to decrease? If over time, in billion of years or longer, dark energy density decreased greatly, would the universe start to contract?

No. The expansion would accelerate more slowly. In the extreme case where dark energy density hypothetically went to zero, the total density would still be less than or equal to the critical density, so the universe would expand forever (though the expansion would be decelerating, not accelerating).

Note that we have no evidence that the dark energy density is changing or could change.

 

[kimbyd]

Dark energy density at this time is a constant and our universe is expanding (accelerating). This is expected to continue indefinitely. What would happen, if for some unknown reason, dark energy density started to decrease? If over time, in billion of years or longer, dark energy density decreased greatly, would the universe start to contract? There are Friedmann equations relating the Hubble constant H, first and second derivatives of a scale factor a, dark energy density and pressure and G. The scale factor a is a function of time. At what point would the universe neither expand or contract? At that time, gravity and dark energy are balanced. By how much would the dark energy density have to decrease for the universe to contract?

It all depends upon the details. If, at some point, dark energy starts decreasing in density faster than matter does, until dark energy density is negligible, then the nature of matter will determine the future fate of the universe, which in turn means that if the spatial curvature is open or flat it will continue to expand forever. If the spatial curvature is closed, then it will recollapse.

For this to occur, dark energy would have to be composed of some kind of dynamical quantum field (these are broadly known as quintessence models) which has some field configuration where its density can drop quickly after staying near-constant for so long. I'm not aware that anybody has ever come up with a physical model where this kind of thing can actually happy.

Note that a decrease in dark energy density might stem from the dark energy field turning into other particles. In practice, this would likely just mean photons. So if the decrease occurred by this kind of process, it could heat up the universe by a bit. But the dark energy density is so incredibly low, I doubt it would have any noticeable impact.

 

[PeterDonis]

If, at some point, dark energy starts decreasing in density faster than matter does, until dark energy density is negligible, then the nature of matter will determine the future fate of the universe

A transition like this would have to conserve overall energy density, so the total density would at most be equal to the critical density (since the total density now, matter + dark energy, is the critical density). That is why I said in post #2 that the universe would still end up expanding forever in this (highly speculative) scenario.

Note that a decrease in dark energy density might stem from the dark energy field turning into other particles. In practice, this would likely just mean photons. So if the decrease occurred by this kind of process, it could heat up the universe by a bit.

To conserve overall energy density, it would have to heat up the rest of the universe by just enough to increase its energy density to compensate for the decrease in dark energy density.

 

[kimbyd]

That said, there is an alternative, similar possibility that, while it is still very hypothetical, is on at least slightly stronger theoretical footing than the stuff I described above: quantum vacuum decay.

In this situation, the accelerated expansion isn't driven by dark energy, but by the cosmological constant. However, the cosmological constant is specific to the vacuum state of the universe.

This is the case in string theory, for example, where the cosmological constant becomes the expectation value of a particular parameter of the theory. In this type of model, the universe tends to settle into a metastable vacuum field configuration. One way of understanding it is that in string theory, there are 9 spatial dimensions and one time dimension. But since we only observe 3 spatial dimensions, those extra dimensions must be hidden in some way. The classical way of dealing with them is to wrap up those extra dimensions so that they're small: if you can only move by 0.0000000000000000000000000000001 meters in that dimension before coming back where you started from, you'll never notice that you moved at all.

In string theory, there are a huge number of different ways you can bundle these extra dimensions up. Something like $10^{400}$ or so. And each one ends up with a different value of the cosmological constant. Furthermore, each one has different low-energy laws of physics. That means you might get different masses of elementary particles, different strengths of forces, or even different kinds of forces altogether.

So, in this paradigm, if it turns out that there exists another way those higher dimensions can be bundled, and that different vacuum state also has a lower vacuum energy, then there is a possibility that there will be a quantum tunneling event in one location in the universe which will tunnel this tiny region somewhere in the universe into this lower vacuum-energy state. This new region will have different laws of physics. It'll generally respect the same kinds of math that our physics uses, but all the numbers will be different. And because it has lower energy, it will spread. In fact, the boundary between our universe and this new region will rapidly accelerate, so that it reaches a speed near that of light within a second or so. It will then spread outward, obliterating everything in its path as it spreads. All matter/energy in our universe that it encounters will be distributed into a cloud of particles which will then behave according to whatever new laws of physics exist in this new region.

This process is known as "quantum vacuum decay".

Note that the this reply was written in the context of string theory, but quantum vacuum decay is a feature in any physics model which includes:
1) Multiple possible vacuum states.
2) Our vacuum state is not the lowest-energy state.

It's one of those scary things about theoretical physics that nobody knows how to interpret because the only way to know whether or not it happened would be for it to happen and for our universe to be destroyed. The one ray of hope: because the cosmological constant has an event horizon, such an event can only travel so far. If an event like this were to happen, say, 20 billion light years away from us today (a location which is outside our cosmological horizon), then the results of that event will never reach us.

The possibility of quantum vacuum decay is definitely one of the more mind-bending aspects of theoretical physics today.

 

[kimbyd]

A transition like this would have to conserve overall energy density, so the total density would at most be equal to the critical density (since the total density now, matter + dark energy, is the critical density). That is why I said in post #2 that the universe would still end up expanding forever in this (highly speculative) scenario.

It really depends upon what the nature of the change is. If this is a quintessence field which has a dynamical equation of state parameter $w$, and there is some physical process which causes its equation of state to change from its current value near $-1$ to some greater number (i.e., closer to positive or actually positive), then it will start to dilute as the universe expands. If $w > -1/3$ at some later time, then the rate at which the dark energy dilutes will be great enough that the effect of spatial curvature will slowly grow over time. Eventually, whether or not the universe recollapses is then determined by the spatial geometry (open, flat, closed). The spatial geometry is fixed by the initial conditions of our universe, and none of these processes change it.

Further, if the equation of state parameter grows so much such that $w > 0$, then it will dilute faster than normal matter. The same eventual fate will occur, of course, but the dark energy will in this case dilute away to effectively nothing eventually.

That said, this is only one possible way that the dark energy could go away. Another possibility is that the quintessence field could decay into other particles. Because the quintessence field is such a low-energy field, it would likely decay into radiation. That radiation would then dilute rapidly, resulting in a matter-dominated universe following similar rules to the above.

 

[PeterDonis]

It really depends upon what the nature of the change is. If this is a quintessence field which has a dynamical equation of state parameter $w$, and there is some physical process which causes its equation of state to change from its current value near $-1$ to some greater number (i.e., closer to positive or actually positive), then it will start to dilute as the universe expands.

Yes, you're right, this kind of change doesn't change the energy density instantaneously, so it wouldn't need to transfer any energy density to something else.