The dark universe: the interplay of cosmological moduli, axions, and the MSSM

Abstract

In this work, we introduce two effective field theories which parameterize a light modulus field interacting both with the MSSM ($\phi$MSSM) and with the MSSM combined with an additional supersymmetric DFSZ axion ($\phi$PQMSSM). All two-body decays of the modulus are cataloged and connected to explicit string scenarios, with all model-independent decay widths calculated incorporating mixing and phase-space effects for the first time. Dark matter and dark radiation production are studied in both models for a subset of string scenarios, with comments provided on expectations for the remaining scenarios. Quite generally, we find that many string scenarios with a modulus-driven early matter dominated period overproduce dark matter and/or dark radiation. The overproduction of dark matter may be remedied with a sufficiently large modulus mass, however various consistency conditions show that most scenarios are incompatible with weak-scale supersymmetry and with a DFSZ-type axion, at least without additional model-building. We also study statistical properties of the Peccei-Quinn scale $f_a$ and the derived value of the SUSY $\mu$-term in the string landscape. Here, we find the predicted value of $f_a$ is in the cosmological sweet-spot for axion dark matter, while the predicted higgsino masses are slightly above current LHC bounds. Additionally, we study the predicted nature of viable dark matter candidates in explicit inflationary scenarios in string theory, finding a WIMP in K\"{a}hler inflation and open string axions in fibre inflation to be natural dark matter candidates.