15. Anderson localization. Just crossed my mind…
DmitryI personally consider Anderson localization as one of the most prominent dynamic vacuum selection principles on the string theory landscape. Let me remind you the main idea behind it.
In condensed matter theory, Anderson localization was first discovered as a phenomenon of electron wave function localization inside a semiconductor when disorder (for example, impurities or defects) of the effective potential electrons are moving in is sufficiently strong. Physics of Anderson localization in a semiconductor is related to existence of impurities with potential so strong that they bind the Bloch wave function of the electron propagating in a disordered medium. Mechanism responsible for the localization of the single electron wave function near such impurities is interference between Bloch waves scattered by impurities (defects).
In a few words, in a semiconductor the probability to find an electron near the localization center (impurity with strong attracting potential) is much higher than to find it somewhere in the bulk far away from impurities.
Likewise, the wave function of the Universe on the string theory landscape can be localized near some vacua if disorder on the landscape is sufficiently strong. In particular, there is a chance that it will be localized in vacua with very small positive cosmological constant , so that smallness of the value of CC is dynamically preferable, and one does not need to follow the logic of anthropic principle.
Now, this idea was discussed in details by Henry Tye and Laura Mersini in the context of WdW equation with random potential (the latter defines behavior of the wave function of the Universe); also, I have discussed it with Kari Enqvist in the context of eternal inflation.
Henry’s idea is the following. Suppose we have an inflaton in some very complicated potential with several minima (and stochastic force is weak, so that inflation is not in the eternal selfreproducing regime). If barriers are high between the minima are high, inflaton can quantum-mechanically tunnel between the minima (the rates of tunneling are given by Coleman-de Luccia instantons). If the potential is significantly disordered, there could be effect analogous to Anderson localization, and the inflaton will be localized near the deepest minimum of its potential (localization center).
Now, in Henry’s picture everything happens in the slow roll deterministic regime, since Henry does not like eternal inflation. However, the question is whether it is necessary to have it to reproduce our reality with small cosmological constant and flat power spectrum of inflationary perturbations.
I have just realized it is actually necessary to have eternal inflation. In slow roll deterministic regime inflaton of course can tunnel between the minima of its potential, but if a tunneling happens within last 60 efoldings of inflaton, it gives rise to features in the power spectrum. Indeed,
and 
suddenly changes during the tunneling. As a result, one gets a jump in power spectrum 
at 
, where 
is the value of scale factor coresponding to the moment of tunneling. Of course, we don’t see such features in the power spectrum.
The bottom line is that evolution of the inflaton should be smooth during last 60 efoldings, i.e., no tunnelings are allowed.
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14. Eye on ArXiv: 8 Apr 2008 - Unifying inflation, dark matter and dark energy?
DmitryThe title says for itself; the paper is a development of older Andrew’s idea, which is the following.
Suppose that inflation is driven by a scalar field with the potential 
. Inflaton slowly rolls down towards the minimum of its potential at 
and starts to oscillate near it after the end of inflation. If you calculate the effective equation of state of the inflaton condensate at this stage, you will see that it is the one of non-relativistic matter, i.e., 
; so, in principle, one may have a temptation to consider inflaton condensate as a candidate for cold dark matter.
But a bit deeper thinking leaves you with the feeling of disappointment. The reason is that the energy density stored in the condensate after the end of inflation is HUGE. Indeed, we have in the end of inflation
.
This amount of non-relativistic dark matter will clearly overclose the Universe, so we need this field to decay somehow. Decay is achieved by coupling the inflaton to some other field and is called reheating.
There are basically two possibilities.
a) If the inflaton is coupled to the field 
through quartic interaction 
, it does not decay completely, its fluctuations freeze out and still inevitably overclose the Universe (one can easily estimate inflaton abundance using standard formula from Kolb-Turner).
b) If the inflaton is coupled through trilinear interaction 
, it will decay completely, first by parametric resonance and than through perturbative decay channel.
Now, how can we build a model such that inflaton decays but in the end of decay there is still small amount of energy stored in the inflaton? (30% of the overall energy density)
Andrew et al. say: let us introduce the second (tiny in length, about 12 efolds) stage of inflation in order ro decrease the relic 
abundance. I think I am fine with this picture, the only problem is the amount of finetuning (not so clear from the paper) you need to apply to the theory in order to:
a) get correct energy density of dark matter
b) correct number of efoldings from inflation
c) correct reheating temperature.
Authors also claim that they can incorporate dark energy into the scenario by applying landscapism arguments.
More pressure on the Pierre Auger Collaboration :-) Let me remind you that PAC reported a strong correlation between the arrival directions of ultra-high-energy cosmic rays and positions of nearby Active Galactic Nuclei. If the correlation is indeed there, the famous problem of UHECRs is closed (UHECRs are NOT of the cosmological origin). There are however some tovarischs :-) who are in doubt that such interpretation of PAC observations is correct, and it seems even without their argumentation that one has rights to doubt: for example, similar correlation in the Northern hemisphere is absent, as AGASA data show.
Authors simulate expected flux of cosmic rays using AGN hypothesis and compare it with observed UHECR events. Expected fluxes from Virgo and Centaurus superclusters are the same , but, as it turns out, there is a deficite of observed events from Virgo supercluster allowing authors to rule out the AGN hypothesis.
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