Classification of Primary Constraints of Quadratic Non-Metricity Theories of Gravity

Understand

We perform the ADM decomposition of a five-parameter family of quadratic non-metricity theories and study their conjugate momenta.

• After systematically identifying all possible conditions which can be imposed on the parameters such that different sets of primary constraints arise, we find that the five-parametric theory space can be compartmentalized into nine different sectors, based on the presence or absence of primary constraints.
• This classification allows to dismiss certain classes of theories as unphysical and invites further investigations into the remaining sectors, which may contain phenomenologically interesting modifications of General Relativity.