Classification of primary constraints of quadratic non-metricity theories of gravity

A bstract We perform the ADM decomposition of a five-parameter family quadratic non-metricity theories and study their conjugate momenta. After systematically identifying all possible conditions which can be imposed on parameters such that different sets primary constraints arise, we find five-parametric theory space compartmentalized into nine sectors, based presence or absence constraints. This classification allows to dismiss certain classes as unphysical invites further investigations remaining may contain phenomenologically interesting modifications General Relativity.