String moduli inflation: an overview
  We present an overview of inflationary models derived from string theory
focusing mostly on closed string moduli as inflatons. After a detailed
discussion of the eta-problem and different approaches to address it, we
describe possible ways to obtain a de Sitter vacuum with all closed string
moduli stabilised. We then look for inflationary directions and present some of
the most promising scenarios where the inflatons are either the real or the
imaginary part of Kaehler moduli. We pay particular attention on extracting
potential observable implications, showing how most of the scenarios predict
negligible gravitational waves and could therefore be ruled out by the Planck
satellite. We conclude by briefly mentioning some open challenges in string
cosmology beyond deriving just inflation.
