Bounds on Scalar Masses in Theories of Moduli Stabilization

TL;DR

In string/$M$ theory with stabilized moduli, at least one modulus-like field generically has mass $\lesssim m_{3/2}$, driving a non-thermal cosmology that dominates before BBN. To avoid spoiling BBN, the gravitino mass must satisfy $m_{3/2}\gtrsim 30\,\mathrm{TeV}$, and dark matter can arise from modulus decays most naturally if the LSP is wino-like, yielding a non-thermal WIMP relic. These results imply significant constraints on gauge mediation in string vacua and predict a spectrum with heavy scalars and comparatively lighter gauginos, with distinctive LHC and direct-detection signatures. The conclusions are supported by analyses of multiple well-studied vacua (Appendix) and carry broad implications for cosmology and beyond-Standard-Model phenomenology.

Abstract

In recent years it has been realised that pre-BBN decays of moduli can be a significant source of dark matter production, giving a `non-thermal WIMP miracle' and substantially reduced fine-tuning in cosmological axion physics. We study moduli masses and sharpen the claim that moduli dominated the pre-BBN Universe. We conjecture that in any string theory with stabilized moduli there will be at least one modulus field whose mass is of order (or less than) the gravitino mass. Cosmology then generically requires the gravitino mass not be less than about 30 TeV and the cosmological history of the Universe is non-thermal prior to BBN. Stable LSP's produced in these decays can account for the observed dark matter if they are `wino-like.' We briefly consider implications for the LHC, rare decays, and dark matter direct detection and point out that these results could prove challenging for models attempting to realize gauge mediation in string theory.