Axions in string theory and the hydra of dark radiation - Hebecker, Arthur; Jaeckel, Joerg; Wittner, Manuel (Arxiv, 2022)
It is widely believed that string theory easily allows for a QCD axion in the cosmologically favored mass range. The required small decay constant, $f_a\ll M_P$, can be implemented by using a large compactification volume. This points to the Large Volume Scenario (LVS), which in turn makes certain cosmological predictions: First, the axion behaves similarly to a field-theoretic axion in the pre-inflationary scenario, i.e. the initial value can be tuned but one is constrained by isocurvature fluctuations. In addition, the volume naively represents a long-lived modulus, that may lead to an early matter-dominated phase. Finally, the volume modulus' decay to its own axion tends to produce excessive dark radiation. In this paper we aim to carefully analyze the cosmology by studying models that not only allow for a QCD axion but also include inflation. Quite generally, limits on isocurvature fluctuations restrict us to relatively low-scale inflation, which in the present stringy context points to Kahler or blowup inflation models. Moreover, we find as a novel and at first sight encouraging feature that the lightest (volume) modulus is likely to couple strongly to the Higgs. It hence quickly decays to the Standard Model, thus seemingly resolving the dark radiation problem. This decay is much faster than that of the inflaton such that the latter comes to dominate the Universe. Since the inflaton distributes its energy equally between the QCD axion and the Standard Model, this turns out to be a curse rather than a blessing: Generically, the dark radiation abundance remains too high. We briefly discuss possibilities to circumvent this issue. In particular, the rapid decay of the volume modulus into Higgses demotes dark radiation from a generic LVS problem to an issue resolvable by inflationary model building.