Inflationary conditions via the Big Rip scenario

[J'Dona]

Hey, this is my first thread in a while, by which time I hope I'm now able to ask actually interesting questions, even if they are still pointless. (There's a summary at the end if you want to tear some speculations up as soon as possible.)

 

About a year ago when reading the Wikipedia article on the Big Rip scenario, I had a question as to what might happen at very late times. I wrote it up with, and I must stress this here, the explicit intention of proving it wrong and so learning from the endeavour; I expect it is entirely false and without merit, but I do not yet have sufficient knowledge, or have not yet considered it in the right way, to absolutely prove it wrong in an ironclad explanation.

 

So, I'm posting it here to see if anyone else can, or even better, can point me in the right direction so that I can disprove it. With any luck, I'll be doing a theoretical physics MSc next year so that by the end of that I would be able to tear it down in seconds, but if anyone wants to give a few hints on the way I thought it would be an interesting topic.

 

Here we go, I'll try to make it entertaining ...

 

Motivation:

 

Assume that the Universe ends in a Big Rip scenario, i.e. in the acceleration equation,

 

[math]

\frac{\ddot a}{a} = -\frac{\rho\left( 1 + 3\omega \right)}{6M^2_{Pl}}\text{,}

[/math]

 

we have [math]\omega < -1[/math]. The result is a Universe whose scale factor [math]a[/math] reaches infinity at a finite time. (This is estimated to be around some 50 billion years from now. A value of [math]\omega < -1[/math] is not inconsistent with current observations, but it's very unlikely.)

 

Hypotheses:

 

In this scenario, as [math]t \rightarrow t_{end} = t(a = \infty)[/math], stars will expand away from one another, then planets from their stars, the Earth will break up, etc. However, this would continue until the consituent quarks in hadrons are forced apart until they are free. (It may be more energetically favourable, while being pulled apart, to split into new quarks, but at the actual time [math]t_{end}[/math] these distances would still be infinite.) If we assume the conditions then are such that free quarks are forbidden (the entire observable Universe to each quark being that quark alone), then free quarks may still be forbidden.

 

In this case, we first hypothesise that the free quarks decay (1). But with an infinite scale factor, we cannot really talk about a multiple-body decay as there is no meaningful notion for the amount of separation between two bodies. In fact, even the definion of a point particle may be in confusion if "that which has no part" is scaled by an infinite amount, which I'm not even going to comment on.

 

The only meaningful form of decay I can imagine for something which either occupies one points or all points in space, is that the energy contributes to a scalar field (2) or similar, i.e., all points in space. This would occur at [math]t_{end}[/math] for every particle. However (and THIS is the point where we toss local causilty out the window), to maintain CPT conservation in the Universe (or just electric charge, colour, lepton number, etc.) we would need pretty much every other fundamental particle to decay as well, all contributing to a scalar field. (Photons, or any particles, really, we toss in regardless because quantum fluctuations or uncertainty in any direction might spread it over a distance which is scaled to infinity, and so on. It should be clear this is a particularly weak part of the description. This has the effect of ensuring that the total energy in the field at the end of the Universe is the same as that at the start, as all the random photons which had lead to an increase in entropy were still flying out in space)

 

Finally, just for the hell of it, we hypothesise that this scalar field has a potential sufficient for cosmological inflation (3), and invoke the Poincaré recurrence theorem or some deus ex machina to claim that the scale factor resets (whereupon we have finally transitioned to pure science fiction).

 

The end result is a Universe with the same energy as before the Big Bang, with the same conditions, and things happen all over again.

 

Criticisms:

 

If the parenthetical statements weren't indicative enough, I've thought about the problems with this already and produced a list. Specifically I am aware of the following assumptions/issues which I imagine are enough to break the hypothesis several times over (sorted only by how important they are to the basic hypotheses, not flagrant violation of physics). I imagine the most interesting, however, will be something not listed here:

 

1. Critical

• Free quarks decay (IFAIK this was not true at the GUT scale in the Big Bang, so maybe not here)
  
• Energy contributes to scalar field (given theories that the inflaton field for our Universe was generated by the convergence of two higher-dimension branes, I don't yet know enough to comment on this)
  
• Scalar field has form of inflation potential (unless a scalar field does by definition?)
  

2. Serious

• Reset of scale factor (not that a zero scale factor is any more meaningful than an infinite scale factor ...)
  
• Quarks "free" before [math]t_{end}[/math] (so scalar field sets up over a time, possibly longer than time needed for slow-roll or enough to affect number of e-foldings substantially and leave an effect on the CMB of the next Universe)
  
• Rest of Universe "knows" quarks decay (and subsequently decay themselves to conserve charges, which seems to VIOLATE CAUSALITY)
  
• Infinite stretching of a sacalr field (even if otherwise homogeneous, is a scalar field in this case still meaningful?)
  

3. Irritant

• Entropy (gets reset, and as philosophically pleasing as that sounds, the Universe is destroyed on the way so I have no personal investment in whether this is actually so)
  
• Loss of energy (if entropy is not reset because, e.g., radiated photons do not contribute to the field, there wold be a loss of energy in each "permutation")
  

I hope anyone bothering to read all this has had fun. I hope someone can disprove this theory because if someone who was, at the time, a 3rd-year undergraduate can come up with this and it isn't false entirely, modern physics is in a poor state. If someone replies on a point and I subsequently question their explanation, it's probably because I want to understand it better! But really, the best responses would be ones which allow me to find the answers for myself, so that I can best learn.

 

Summary (tl;dr):

 

Big Rip scenario [math]\implies[/math] Universe is stretched by infinity in a finite time. Even quarks in hadrons split apart. Hypotheses:

 

1. Free quarks decay
   
2. Energy contributes to a scalar field
   
3. Field has potential like in inflation
   

The Big Bang happens again and everyone does the macarena.

(Please disprove or help me disprove this so that I can learn.)

[Martin]

... A value of [math]\omega < -1[/math] is not inconsistent with current observations, but it's very unlikely.)

...

I can't give you much in the way of a satisfactory response. I think this is a recurrent rip scenario rather than a theory, because it doesn't seem to make any predictions. (Or did I miss something?)

 

Perhaps the best way to refute this scenario would be to measure the dark energy equation of state more and more accurately, so that it seems less and less likely that it is less than -1. In fact this has been happening. As you say it is very unlikely (already now using current data) to be less than -1.

 

It seems to me that since we don't yet have a clue as to what dark energy is, or even what the real cause of acceleration is (it might not be a dark energy field at all, it might be something we haven't thought of yet), we can't really follow through with your scenario and check consistency with known particle physics.

 

You would probably like someone to help by considering whether this recurrent rip re-birth scenario is consistent with the standard model of particle physics, but my thought is that we are still most likely 10 or more years away from understanding DE and putting it together with an expanded particle physics.

 

BTW Roger Penrose has a recurrent re-birth universe scenario where something like this happens (but without ripping). I just posted some links to it here

http://www.scienceforums.net/forum/showthread.php?p=484140#post484140

You may know Penrose's talk already. Like with yours, his scenario has complete particledecay and complete black hole evaporation and huge expansion eventually leading to conditions favorable to a big bang. He rationalizes this. To me it still is not clear how he gets there. Entertaining and informative talk though. Provocative. You might enjoy it especially because of the points of similarity.

Edited April 10, 2009 by Martin

[J'Dona]

Thanks, Martin. It's very fair to point out that the questions raised cannot really be answered without a complete theoretical description of the system ... that, coupled with the perhaps non-meaningful description that an infinite scale factor introduces, is something that I should have made clear, so I couldn't possibly expect an answer on every point.

 

However, hopefully I'll still be in the field in ten years' time (even if possibly moving away from my present emphasis on particle cosmology and toward quantum computing) and will be able to necro this post and fully disprove it (if [math]\omega[/math] is somehow still within range!).

 

I haven't seen Penrose's talk so I shall watch that now, thanks for the link!

 

If there are any aspects of this which aren't affected by the unknown dark energy equations or similar, anyone please feel free to comment if there's something to learn there.