Big bangs in the multiverse.

skydivephil

If I understand things correctly a multiverse is argued to be generated in slow roll inflation beucase whilst some of the false vacuum/inflaton field decays into a true vacuum state , the remaining section which has not decayed yet, is expanding exponentially, so the total volume of inflating space never declines and hence inflation is eternal. So in order to prevent a multiverse something presumbaly has to happen to get the whole inflaton field to decay everywhere at the same rate and at the same time. Is that the case in LQC or have I misunderstood?

marcus

I think you are imagining eternal inflation scenario rightly. I'm not expert but I'll suggest an alternative picture:

A universe with finite spatial volume collapses and rebounds. There is no "horizon problem" since as it collapses it is all in causal contact.
The entire universe enters superinflation together at a single moment. The scalar field (Higgs or whatever is serving as inflaton) is everywhere primed to the same energy. "Pushed up to the same place on the potential hill" by superinflation.

The entire (still quite small) universe stops superinflation at the same moment when the Hubble rate reaches Planck max, and enters inflation mode. The scalar field rolls down uniformly and the entire universe exits from inflation at the same moment.

I found Tom Pawlowski's article quite interesting at first glance yesterday. I'll take another look now. You might wish to also, as a way of getting a more definite idea of inflation in Loop cosmology.

marcus

I'll quote some sample excerpts from Pawlowski http://arxiv.org/abs/1207.4353
==quote 1207.4353 page 1==
The inflation paradigm is one of the most successful ideas allowing to explain recent precise cosmological observations. However one of its main problems is the construction of the physically viable scenario featuring sufficiently long inflation epoch (> 60 e-foldings) with sufficiently large probability. In this context a lot of hope is attached to the models featuring a non-minimal coupling of gravity and a scalar field (e.g. the Higgs field [1–3]), ... Such mechanism of driving the inflation is also efficient in generating the correct primordial curvature perturbations.
...
At this point it is worth noting that the type of the potential considered, while usually associated with the models of Higgs inflation, is not restricted just to this particular field...
...Thus, recent results from CMS [8] and ATLAS [8] (m_H ≃ 125 GeV) are both consistent with SM Higgs inflation.

While the considered model is very successful on the classical level it still suffers the standard problems related with the presence of initial singularity, which are expected to be solved by quantum gravity. One of the leading approaches to provide quantum description of spacetime itself is Loop Quantum Gravity (LQG) [9–11]. The cosmological application of its symmetry reduced version, known as Loop Quantum Cosmology (LQC) [12], has indeed provided a qualitatively new picture of early Universe dynamics. The prediction of the so-called big bounce phenomenon [13] offered a new mechanism of resolving long standing cosmological problems. For example, the existence of a pre-bounce epoch of the Universe evolution provides an easy solution to the horizon problem, while preliminary studies indicate that the dynamics in the near-bounce superinflation epoch prevents the catastrophic entropy increase [14, 15] usually considered a danger to bouncing cosmological models (following the consideration of [16]). What’s even more important, the spacetime discreteness effects amount to a dramatic increase of the probability of inflation in the models with standard m²φ² potential scalar fields [17] (see also [18]). Indeed for such models the probability of inflation with enough e-foldings to ensure consistence with 7 years WMAP data happens with probability greater than 0.999997. These results make the loop approach very attractive in inflationary cosmology.
==endquote==
In looking over 1207.4353, I followed reference [15] and found another interesting Pawlowski one:
http://arxiv.org/abs/1106.3793
"Effective dynamics of the hybrid quantization of the Gowdy T³ universe"
Basically they study a compact highly inhomogeneous bounce. The challenge was to incorporate a lot of inhomogeneity (gravity waves) in the geometry. Parts of the conclusions section on page 18 were thought-provoking. But this doesn't directly relate to the topic of inflation, which our discussion was about.

Naty1

Marcus:

yes.....
Can someone comment on the end of inflation....are there compelling reasons for us to believe that once started, it naturally stops??....

I recall reading somewhere the decay of inflationary energy into radiation after inflation is governed by quantum mechanics...very similar to radioactive decay....but that seems a bit handwavy....like a 'patch' on the 'patch' of inflation itself.....

marcus

In the past the subject of inflation has been pretty speculative and some people were talking about nonmin'ly coupled scalar fields (e.g. Higgs) where the slow roll decay was predetermined according to a couple of slow-roll parameters. Perhaps other people were speculating about other kinds of inflatons where decay was more spontaneous and unpredictable.

With the type of scalar field in Pawlowski et al model, you know it is going to decay on a definite schedule, your problem is TO START IT HIGH ENOUGH UP THE POTENTIAL SO YOU GET ADEQUATE 60 EFOLDS. The problem is do you get ENOUGH. And the whole universe is together in this, not patchy.

So if you read the article you see it depends on strong coupling to gravity and you see that the challenge for them is to prove that you get ENOUGH with high probability.
So Naty this is kind of orthogonal to what you are talking about. They are talking about a specific known field (Higgs) and what is considered reasonable to suppose about it.

To get the flavor of it, you might look on page 2 at section II. NON-MINIMALLY COUPLED SCALAR FIELD

and in particular on page 3 at the subsection "Inflation from strong value of non-minimal coupling" that has equations (2.9) and (2.10) involving the Hubble parameter H, its derivatives H', and the slow-roll parameters of the scalar field.

The situation they are analyzing may be rather different from the infinite-volume bounceless inflation scenarios you have been imagining. The manifold is COMPACT, finite spatial volume. It gets really messed up by gravity waves around the time of the bounce Check it out! Without specialized knowledge we (or I at least) can't explain or understand this type of inflation at level of detail, but we can get a sense of how it differs from what people like Guth and Linde like to imagine.

marcus

Naty,
Another thing to look at related to your question is this paper
http://arxiv.org/abs/0710.3755 (209 cites)
The Standard Model Higgs boson as the inflaton
Bezrukov and Shaposhnikov
==quote==
In this Letter we argued that inflation can be a natural consequence of the Standard Model, rather than an indication of its weakness. The price to pay is very modest—a non-minimal coupling of the Higgs field to gravity. An interesting consequence of this hypothesis is that the amplitude of scalar perturbations is proportional to the square of the Higgs mass (at fixed ξ), revealing a non-trivial connection between electroweak symmetry breaking and the structure of the universe. The specific prediction of the inflationary parameters (spectral index and tensor-to-scalar ratio) can distinguish it from other models (based, e.g. on inflaton with quadratic potential), provided these parameters are determined with better accuracy.
The inflation mechanism we discussed has in fact a general character and can be used in many exten- sions of the SM. Thus, the νMSM of [36, 37] (SM plus three light fermionic singlets) can explain simultaneously neutrino masses, dark matter, baryon asymmetry of the universe and inflation without introducing any additional particles (the νMSM with the inflaton was considered in [30]). This provides an extra argument in favour of absence of a new energy scale between the electroweak and Planck scales, advocated in [32].
==endquote==

The presentation is nice and clear. You may remember Shaposhnikov as the guy who back in 2009 predicted 126 GeV for the Higgs mass. He seems fairly on top of things.
The paper I referred you to earlier USES the Higgs field inflaton in LQG context and TAKES OVER a fair amount of the treatment of it found in this Shaposhnikov Bezrukov paper.
So it's worth taking a look at. I think its a very promising approach to inflation because it uses something REAL, rather than all "made-up" stuff.

As a reminder, in case anyone else is reading, the paper cited earlier was by ADP
Artymowski, Dapor, Pawlowski and just came out this month.
http://arxiv.org/abs/1207.4353
Inflation from non-minimally coupled scalar field in loop quantum cosmology
Michal Artymowski, Andrea Dapor, Tomasz Pawlowski
(Submitted on 18 Jul 2012)
The FRW model with non-minimally coupled massive scalar field has been investigated in LQC framework. Considered form of the potential and coupling allows applications to Higgs driven inflation. The resulting dynamics qualitatively modifies the standard bounce paradigm in LQC in two ways: (i) the bounce point is no longer marked by critical matter energy density, (ii) the Planck scale physics features the "mexican hat" trajectory with two consecutive bounces and rapid expansion and recollapse between them. Furthermore, for physically viable coupling strength and initial data the subsequent inflation exceeds 60 e-foldings.
14 pages, 5 figures

skydivephil

Hi Marcus , this seems to be a very interesting result.
So is the uniformity of the decay rate of the inflaton field in LQC an agreed upon result or is it something that is still being thrashed out? The reason i ask is that I spoke to Martin Bojowald about this topic last year and he said that LQC was not incompatible with eternal inflation. But as far as I can see if the inflaton field decays everywhere at the seems rate at once then eternal inflation seems ruled out assuming LQC is true. If this is right and a clear bounce signal can be found say in the B mode this could also mean eternal inflation is falsifiable, correct?