Question About "The Big Rip" and Quark Confinement

Factual Questions
1

This just popped into my head. I have no idea if it makes any physical sense at all, but what the heck…

It has been hypothesized that whatever is apparently causing the expansion of the universe to accelerate will do so in the future to such a degree that literally everything, down to the sub-atomic particles that make up atoms and nuclei, will be pulled inexorably from every other particle at an exponentially-increasing rate. The result of this “Big Rip” will be a cold (converging on absolute zero), dark universe, with each quanta of matter and energy pulled so far and so fast from any other that they will be causally isolated, literally completely cut off from all else.

For some reason I got to thinking about this: For anything connected to anything else by any other force but the color force holding quarks together, the strength of the interaction decreases with distance. For gravity and electromagnetism, for instance, this relationship is defined by a simple inverse-square law.

Not so the color force: At extremely short distances, the force is weak, then increases to a maximum per unit distance very quickly (so-called “asymptotic freedom”) such that as two quarks are pulled further and further apart, the force needed increases linearly with distance until there is so much energy in this system that an entirely new pair of antiquarks (or quarks, if it’s two bound antiquarks) is created, thus creating a pair of mesons. Because of this, quarks are said to be “confined” such that they can never appear outside of multi-quark particles collectively referred to as hadrons. (of which there are quark-antiquark mesons, triple-quark or triple-antiquark baryons, and maybe some more exotic things).

So, it would seem that if, for instance the space between an electron and a proton increases, they move apart and that’s it. You’re left with nothing but the same proton and electron further away from one another. The forces between them decrease as the square of the distance, approaching zero at infinity. Quite mundane and a little depressing.

But if the space between two quarks increases, it seems the force in the system must, when something like the diameter of a hadron is breached, increase linearly, ultimately creating a meson. And as these two particles are pulled apart, you get another meson. It can’t be helped: No quark can be alone, per confinement.

So, as the big rip really rips into action, shouldn’t there be an exponentially growing number of mesons being created, apace with the expansion of space, such as the rate of expansion approaches infinite, the rate of meson creation would as well? Couldn’t this slow a big rip down? Or does the cosmological constant, quintessence, whatever, trump even the color force in the end?

Y’know…just curious.

2

First of all, the Big Rip cosmology ends with a singulularity. There is an abrupt, well-defined last moment of time, with no meaningful “after”. And quark separation, if it occured, would be at a time very, very close to the time of the singularity.

But what the heck, the very very short time near the beginning of the universe is of tremendous interest, so why not the time near the end? Naïvely, if the dark energy increased to a characteristic scale just shorter than the characteristic scale of quark confinement and then stopped, you’d get the hadron explosion you just described. Dark energy-type forces increase linearly with distance, the same scaling that the color force is believed to (approximately) have, so it would be able to keep up. This would presumably have the effect of converting a lot of energy from the dark energy field to a hadron field, which would presumably arrest the Rip.

However, this is predicated on the dark energy scale just passing the quark confinement scale and then stopping, and there’s no indication that would happen. One needs to perform a much more detailed calculation (which is not entirely reliable, absent a working theory of quantum gravity) to see what would happen then. I’m not conversant with all of the details, but my advisor and one of my colleagues have worked some on this, and the conclusion is that, in a semiclassical approach (the best we can do without full quantum gravity), it seems that such quantum effects would actually tend to strengthen the Rip.

3

You know, I sometimes simply cannot believe this place. It’s a wonder. I had no expectation this question I dreampt up even made sense to ask, much less I’d get such a concise and comprehensible answer so soon.

Thank you once again for indulging my curiosity, Chronos! I only wish I had the brains to return the favor. Muchos muchos!

4

Hey, I liked the question. It was a sensible extrapolation that I haven’t seen discussed and when I read it I realized I had no idea how to get past the seeming contradiction.

Good question!

(And man is it rare that I get to say that in GQ these days.)

5

Aaagh, I can’t help it; I gotta ask:

I wasn’t aware the Big Rip ends in a singularity. I logically grasp that a singularity of space-time must naturally involve quantum gravity. What I don’t get is what is catastrophic in terms of the maths about what I thought was perfectly flat space. Isn’t that what the Big Rip does, flatten everything out?

I basically comprehend (in my limited way, I think) what infinite curvature of space does to calculations like the strength of the gravitational field, for instance; and I get how quantum gravity might “rescue” us from true mathematical singularities by preventing infinite curvatures (perhaps by showing spacetime is quantized/discretized, and hence such infinities are physically meaningless).

But what’s going on at this Big Rip singularity? It seems to me that if the gravitational field in infinitely curved space has infinite strength, the field in perfectly flat space should be perfectly zero. Is this the source of the problem, that the value of the gravitation field can’t be zero, because it violates the uncertainty principle or something?

6

I thought the Big Rip means you eventually get infinite negative curvature, as opposed to the infinite positive curvature of the Big Crunch. I thought flat space is what you’d get if gravitational forces were just enough to asymptotically slow the expansion to a halt. But I’m not sure if that’s still a possibility in light of the discovery of dark energy.

7

You may be right. I thought I remember reading somewhere that the Big Rip just really flattens enverything, but I could be misremembering. Something about achieving perfect flatness in a finite vs. an infinite period of time, which an “asymptotically flat” universe would do.

But certainly, if the universe is “open” it’s supposed to have a negative curvature. Does the cosmological constant “open” the universe?

Locally, I know zero curvature means zero matter/energy, positive curvature means positive matter/energy, negative curvature means negative matter/energy. Thing is, I think the “scalar field” that caused inflation is supposed to be a form of “positive energy”, and so is the cosmological constant. Yet they’re repuslive. And they act a lot alike. Inflation flattened. I figured the cosmological constant would flatten more. Gah, it’s late, and my head hurts.

8

In attempting to answer some of my own questions, it becomes obvious that an accelerating universe is negatively curved, not flat. And, as you say, if this acceleration increases, the curvature will become more and more negative.

I suppose, then, if one were to take a 1D+1 “slice” of the universe, maybe it would look like some variant of a hyperbolic sine function, though between the deflections, the curve looks very flat for a while. I really don’t know.

9

It is a singularity, but it’s not the same sort of singularity as the Bang or Crunch, or the one at the center of a black hole (the Crunch is very much like a BH singularity, and the Bang is somewhat similar). But there are some similarities. For instance, at the Rip singularity, the energy density goes infinite, although in this case, it’s in vacuum energy. Another way to look at it is to look at the scale time of the Universe. A universe with a true cosmological constant would have a characteristic time, a time for the universe to increase in size by some constant factor (typically a factor of e). In a Big Rip universe, though, that characteristic time is not constant, but decreases with time. As you approach the singularity, that characteristic time approaches zero. So at the singularity, the universe would be e-folding in no time at all, and would expand by an infinite factor instantly. Clearly, this is not something the currently-known laws of physics are capable of discussing, so we can safely call it a singularity.

10

::ascertains that question is not about printing QuarkXPress documents to a Fiery RIP::

::stays behind and reads the astrophysics anyhow::

11

OK. Thanks!

So I guess the other part of my question would be: How does quantum gravity make this a tractable problem? By doing away with the notion of an infinitely small time increment (introducing a chronon or whatever the quantum of time is supposed to be)? Maybe then the Rip could keep going, but forever in increments of at least some multiple of infinity per smallest unit of time?

12

Quantum gravity does not necessarily make this a tractable problem. Or rather, it might be tractable, but the tract is just that “The world ends then”. In fact, based on our current (very incomplete) approaches to quantum gravity, that does in fact appear to be the answer.