The Axiverse induced Dark Radiation Problem
  The string/$M$ theory Axiverse -- a plethora of very light Axion Like
Particles (ALPs) with a vast range of masses -- is arguably a generic
prediction of string/$M$ theory. String/$M$ theory also tends to predict that
the early Universe is dominated by moduli fields. When the heavy moduli decay,
before nucleosynthesis, they produce dark radiation in the form of relativistic
ALPs. Generically one estimates that the number of relativistic species grows
with the number of axions in the Axiverse, in contradiction to the observations
that $N_{eff} \leq 4$. We explain this problem in detail and suggest some
possible solutions to it. The simplest solution requires that the lightest
modulus decays only into its own axion superpartner plus Standard Model
particles and this severely constrains the moduli Kahler potential and mass
matrix.
