19. Disorder on the landscape: non-technical intro

Today 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.