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

TL;DR

This paper classifies primary constraints in a five-parameter family of quadratic non-metricity gravity theories using ADM decomposition, identifying sectors with potential physical relevance and dismissing unphysical classes.

Contribution

It systematically categorizes the parameter space of these theories into nine sectors based on primary constraints, guiding future research on viable modifications of General Relativity.

Findings

Nine distinct sectors identified based on primary constraints.

Certain parameter classes dismissed as unphysical.

Remaining sectors may offer phenomenologically interesting models.

Abstract

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.