Correlation between dark matter and dark radiation in string compactifications

Reheating in string compactifications is generically driven by the decay of the lightest modulus which produces Standard Model particles, dark matter and light hidden sector degrees of freedom that behave as dark radiation. This common origin allows us to find an interesting correlation between dark matter and dark radiation. By combining present upper bounds on the effective number of neutrino species N_eff with lower bounds on the reheating temperature as a function of the dark matter mass m_DM from Fermi data, we obtain strong constraints on the (N_eff, m_DM)-plane. Most of the allowed region in this plane corresponds to non-thermal scenarios with Higgsino-like dark matter. Thermal dark matter can be allowed only if N_eff tends to its Standard Model value. We show that the above situation is realised in models with perturbative moduli stabilisation where the production of dark radiation is unavoidable since bulk closed string axions remain light and do not get eaten up by anomalous U(1)s.