Where in the string landscape is quintessence?

Abstract

We argue that quintessence may reside in certain corners of the string landscape. It arises as a linear combination of internal space components of higher-rank forms, which are axionlike at low energies, and may mix with 4-forms after compactification of the Chern-Simons terms to 4D due to internal space fluxes. The mixing induces an effective mass term, with an action which preserves the axion shift symmetry, breaking it spontaneously after the background selection. With several axions, several 4-forms, and a low string scale, as in one of the setups already invoked for dynamically explaining a tiny residual vacuum energy in string theory, the 4D mass matrix generated by random fluxes may have ultralight eigenmodes over the landscape, which are quintessence. We illustrate how this works in the simplest cases, and outline how to get the lightest mass to be comparable to the Hubble scale now, ${H}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}33}\text{ }\text{ }\mathrm{eV}$. The shift symmetry protects the smallest mass from perturbative corrections in field theory. Further, if the ultralight eigenmode does not couple directly to any sector strongly coupled at a high scale, the nonperturbative field theory corrections to its potential will also be suppressed. Finally, if the compactification length is larger than the string length by more than an order of magnitude, the gravitational corrections may remain small too, even when the field value approaches ${M}_{\mathrm{Pl}}$.