  Light scalar fields called moduli arise from a variety of different models
involving supersymmetry and/or string theory; thus their existence is a generic
prediction of leading theories for physics beyond the standard model. They also
present a formidable, long-standing problem for cosmology. We argue that an
anthropic solution to the moduli problem exists in the case of small moduli
masses, and that it automatically leads to dark matter in the form of moduli.
The recent discovery of the 125 GeV Higgs boson implies a lower bound on the
moduli mass of about a keV. This form of dark matter is consistent with the
observed properties of structure formation, and it is amenable to detection
with the help of X-ray telescopes. We present the results of a search for such
dark matter particles using spectra extracted from the first deep X-ray
observations of the Draco and Ursa Minor dwarf spheroidal galaxies, which are
dark matter dominated systems with extreme mass-to-light ratios and low
intrinsic backgrounds. No emission line is positively detected, and we set new
constraints on the relevant new physics.
