String moduli inflation: an overview
Michele Cicoli, Fernando Quevedo
TL;DR
This overview surveys how string theory can realise inflation with closed-string moduli as inflatons, detailing the eta-problem, de Sitter moduli stabilisation (KKLT and LVS), and a spectrum of closed-moduli inflation scenarios (blow-up, fibre, axion-based approaches, racetrack, N-flation, and axion monodromy). It highlights how protective features like no-scale structure and shift symmetries help tame dangerous corrections, and discusses observational implications—predominantly small tensor modes in many models, with some large-field possibilities such as axion monodromy predicting observable gravity waves. The work emphasizes two-step model-building: stabilise all moduli in a controlled vacuum, then identify inflationary directions within that setup, and it outlines remaining challenges in reheating, finite-temperature effects, and achieving fully explicit compactifications. Overall, the paper maps the landscape of string-inspired inflation, clarifying both the promise and the hurdles of embedding early-universe cosmology in a UV-complete framework.
Abstract
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.