Axions in String Theory and the Hydra of Dark Radiation
  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.
