On dark radiation from string moduli decay to ALPs
  We examine the issue of dark radiation (DR) from string moduli decay into
axion-like particles (ALPs). In KKLT-type models of moduli stabilization, the
axionlike phases of moduli fields are expected to decouple whilst in LVS-type
moduli stabilization some can remain light and may constitute dark radiation.
We evaluate modulus decay to Minimal Supersymmetric Standard Model (MSSM)
particles and dark radiation for more general compactifications. In spite of
tightening error bars on \Delta N_{eff}, we find only mild constraints on
modulus-ALP couplings due to the somewhat suppressed modulus branching fraction
to DR owing to the large number of MSSM decay modes. We anticipate that future
CMB experiments with greater precision on \Delta N_{eff} may still turn up
evidence for DR if the ALP associated with the lightest modulus field is indeed
light.
