83. Quintessence on the string theory landscape?

Nemanja Kaloper and Lorenzo Sorbo have recently released a paper explaining how the quintessence can be realized on string theory landscape. What is quintessence and why the question is important?

As we know, currently the energy density in the Universe is dominated (in proportion about 70/30) by dark energy. The latter behaves almost like a cosmological constant. We are not sure yet whether the corresponding effective equation of state changes with time, but if it does, there is some large probability that the dark energy is actually a very light scalar or axion field with mass at the level

eV (1)

(the latter can be easily calculated from the present value of the energy density in the Universe corresponding to the critical value ). This field is what we call quintessence.

As we have heard many times, since the number of vacua on string theory landscape is extremely large, there may exist de Sitter vacua with extremely low energy scale (small or equal than (1)). Why Nature wants to choose such a vacuum, is not quite clear. One can usually follow anthropic argumenation or try to figure out how low energy vacua may be dynamically preferrable.  Although we know from vacuum counting that vacua with small cosmological constant are supposed to be present, no explicit examples of such vacua were present in literature so far. That is what Kaloper-Sorbo paper is about.

The authors basically show the sector where such vacua can appear from. Components of high rank forms that correspond to internal space (10-dim string theory has to be compactified to 4 dimensions, and we call 6 remaining dimensions internal) look like axions from the point of view of a 4-dimensional observer. These components may mix with 4-forms after compactification of Chern-Simons terms due to fluxes in internal space, and this mixing gives rise to the mass term which preserves the axion shift symmetry.This is exactly what we need – unbroken shift symmetry would correspond to a massless axion. The shift symmetry gets however broken by the background, and this induces very small mass term. The resulting field behaves quite like a quintessence.

Therefore, a prototype example of quintessence field is presented. I think, what remains to be understood is  1) how all moduli actually get stabilized in such a scenario (could it be that some of them actually have a run away behavior and we end up with decompactification?) and 2) why such vacua are preferable on the landscape (and if they are not, what is the probability for us to be in such a vacuum).