$\mathrm{FIMP}$ dark matter in heterotic $\mathrm{M}$-theory
Within the context of N = 1 supersymmetric heterotic M-theory, we present a “freeze-in” mechanism for producing dark matter via a “moduli portal” between the observable and hidden sectors. It is assumed that the observable sector consists of the MSSM or some physically acceptable extension of it, while the hidden sector is chosen to satisfy all physical and mathematical constraints. Dark matter production processes are examined for two fundamental types of hidden sectors; those whose gauge bundle structure group contains an anomalous U(1) and those whose structure group is non-Abelian and anomaly free. The couplings of the dilaton and the “universal” modulus to all fields of the observable and hidden sectors are presented and analyzed. These interactions are then combined to produce a moduli portal from a thermal bath of observable sector particles to the hidden sector. These processes are then analyzed for both anomalous and non-anomalous cases. It is shown that only the uncharged hidden sector matter scalars can play the role of dark matter and that these are predominantly produced during the “reheating” epoch on the observable sector. Within the context of both an anomalous and non-anomalous hidden sector, we calculated the dark matter “relic density”. We show that in both cases, for a wide choice of moduli vacua, one can correctly predict the observed relic density. For the anomalous U(1) case, we choose a specific physically acceptable vacuum within the context of the B - L MSSM and show that one precisely obtains the measured dark matter relic abundance.