19. Disorder on the landscape: non-technical intro
DmitryToday I will kindly allow myself a bit of selfpromotion :-) As I said yesterday, our paper “Disorder on the landscape” is finally out (by the way, Lubos Motl already has a very nice post about it on his blog).
So, what is the paper about?
1. Cosmological constant problem
There exists a serious problem in present cosmology: according to observations, Universe is currently expanding with acceleration. The effect of acceleration only becomes noticeable at redshifts 
, by itself it is not a problem, but the problem is that the value of this acceleration is extremely small in natural units (namely, energy density 
associated with this acceleration is approximately 120 orders of magnitude smaller than the Planckian energy density). I think I will not be far from truth saying that nobody currently has a convincing explanation why such a huge gap exists in the spectrum of the Theory of Everything.
The reason, in a few words, is that theory predicts that a) this acceleration should be zero if the SUSY is unbroken, b) it should correspond to Planckian energy density if the underlying theory is non-supersymmetric (due to radiative corrections) and c) should be related to the scale of SUSY breakdown if SUSY is spontaneously broken (that would give one an energy scale of order of 1 TeV). Instead, it looks like the vacuum energy (one possible source of this acceleration) is extremely small but non-zero. This problem is known as the cosmological constant problem in cosmology.
2. Anthopic principle
One solution for this problem (if one can call it so) can be found by using anthropic arguments. The logic of anthropic principle is the following. Universes (or Hubble patches) with negative cosmological constant very rapidly collapse into Big Crunch singularity. Universes with large positive cosmological constant, on the other hand, expand so rapidly that the large scale structure does not
have enough time to form. So, one says that observers, intelligent creatures, able to measure the value of cosmological constants do not appear in universes with large positive and negative cosmological constants, and the bare fact of our existence automatically implies that the value of the cosmological
constant is small in our Universe. As Leonard Susskind says, cosmological constant is small since if it were wrong there would be no observer to measure the cosmological constant.
But why the cosmological constant is not zero then? Zero would be also perfectly compatible with anthropic arguments. To answer this question, we have to introduce a Multiverse - extremely large set
of Hubble patches with different values of cosmological constants. Than, the issue of the smallness of the cosmological constant is simple resolved by statistics - among these Hubble patches, surely exists one such that the cosmological constant determining the rate of its expansion is positive and small.
A sounding argument in favor of the anthropic reasoning is that Multiverse can be realized on the string theory landscape of metastable vacua populated by eternal inflation: string theory has an immense number of vacua (estimations give number of the order of 
), and each vacuum has its own value of the cosmological constant.
Even thinking about string theory landscape, one can be unhappy with anthropic reasoning, since many questions remain unresolved within anthropic framework. For example, it is yet unknown how to define a gauge invariant probability for a given observer to measure a given value of the cosmological constant or how to determine the distribution function of vacua within the string theory landscape (in the end, it turns out that problems related to statistics on the string theory landscape are NP-hard).
3. Anderson localization: dynamical selection principle on the landscape
Instead of following the anthropic arguments, one could try to establish a dynamical vacuum selection principle on the string theory landscape. Dynamical selection here means that the theory itself automatically guarantees that some vacua are preferable over others. It would be especially nice if vacua with low positive values of the cosmological constant are particularly preferable.
One such dynamical selection principle on the landscape is based on the analogue of the Anderson localization. In condensed matter theory, Anderson localization was first discovered as a phenomenon
of electron wave function localization inside a semiconductor, provided that the disorder (for example, impurities or defects) of the effective potential that electrons are experiencing is sufficiently strong.
Likewise, strong “disorder” on the string theory landscape may give rise to the localization of the wave function of the Universe in some preferable vacua.
Our goal in the paper was to systematically study effects of such disorder, but let me leave the discussion of our results for the next time.
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18. Eye on ArXiv: 15 Apr 2008 - Transplanckian physics, brane cosmology and holographic mesons
DmitrySorry for being quiet for so long. The reason is we were finising a paper, asked for comments and got a lot of them. The paper is finally submitted to appear on ArXiv in tomorrow’s listings. The title is “Disorder on the landscape”, and the abstract will be available tonight Helsinki time (and tomorrow for you, my humble US readers :-)) Also, I hope to discuss the paper tomorrow on this blog.
In the mean time kindly allow me go through interesting papers which recently appeared in ArXiv’s listings.
1. Jean Macher, Renaud Parentani, “Signatures of transplankian dispersion in inflationary era”
Renaud (together with his student) continue his study of transplanckian effects. As you probably well know, the idea of relation between transplanckian physics and inflation is very simple: if one considers scales with are today deeply inside the cosmological horizon, they turn out to correspond to subplanckian scales in the beginnning of inflation. In other words, the fluctuations we observe today were generated from vacuum fluctuations with wavelengths much shorter than the Planck length at the onset of inflation. This problem is known as transplanckian problem of cosmic inflation, and its essence is in the fact that we have no idea about underlying physics at transplanckian scales.
The authors argue that dispersion relation of the QFT itself should be modified at transplanckian scales, simply parametrize this modification as
where 
is cutoff of the order of 
. Background dynamics of the scalar field is not modified at all (corresponds to 
), while the initial state and quantum dynamics of 
are strongly modified. Authors calculate corrections to the power spectrum of tensor and scalar perturbations - they are of the form 
. In order for these corrections to be small I would expect that 
should be larger than 1.
2. Robert C. Myers, Aninda Sinha, “The fast life of holographic mesons”
The authors study non-equilibrium properties of 
super Yang-Mills in the approximation of large number of colors 
(or, more accurately, quenched approximation) by applying AdS/CFT. Gravity dual for this QFT is described as 
probe D7-branes in the black hole background created by 
D3-branes.
At some temperatre there exists a first order phase transition in the theory. The low-temperature phase corresponds to the D7 branes sitting outside the black hole. On the QFT side the meson spectrum is discrete (and mass gap is present). At high temperature phase, D7 branes extend through the event horizon of the black hole; on the QFT side, the meson spectrum is continuous and there is no mass gap, so that the phse transition corresponds to the dissociation of mesons.
From the point of view of non-equilibrium physics the situation is the following. At low temperatures mesons are stable (their width is suppressed as 
). At high temperatures they are unstable; in the gravity dual meson excitations are absorbed by the black hole horizon, and their quasinormal frequences are such that 
. Also, meson exictations can be rendered unstable if nonzero quark density 
is introduced, and the width can be controlled by changing .
In the paper, authors study dispersion relations of these meson excitations.
3. Christos Charmousis, Antonios Papazoglou, “Self-properties of codimension-2 braneworlds”
The authors consider 4-dim branes embedded in a 6-dim spacetime with geometry determined by Einstein-Hilbert + Gauss-Bonnet eff. action. It is shown that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of EH + Gauss-Bonnet gravity. 4-dim physics on the brane is similar to the one of DGP model (gravity is 4-dim up to some scale).
And one more braneworld paper…
4. D.S. Gorbunov, S.M. Sibiryakov, “Self-accelerated brane Universe with warped extra dimension”
Instead of considering induced gravity term on the brane, authors introduce energy exchange mechanism between the brane and the bulk carried by bulk vector fields. Self-acceleration in his setup works as follows. When brane expands, energy flow from the brane into the bulk increases, and a bulk black hole appears with growing mass. This black hole reacts back on the brane and this gives rise to the Hubble parameter being constant at late times.
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