Re-thinking geometrogenesis: Instantaneity in quantum gravity scenarios

Abstract

Abstract Recent Quantum Gravity approaches revealed that spacetime emergence opens conceptual difficulties when the theory allows for cosmological scenarios compatible with geometrogenesis. In particular, it appears extremely difficult to think of an a-temporal transition from a non-geometric to a geometric phase and vice versa. In this paper we advance the proposal of a concept of atemporality, i.e., instantaneity that is suitable for the description of the transition occurring among fundamental phases from which spacetime emerges in some Quantum Gravity approaches, including Group Field Theory and its cosmological implications. After discussing the ontology at different levels of spacetime emergence in a theory of Quantum Gravity in Section 2, we shall focus on the definition of the notion of instantaneity to interpret the atemporal transition of geometrogenesis (Section 3.1), thereby arguing that atemporality dominates at Renormalization Group flow fixed points (Section 3.2). In Section 4, we apply for the first time our notion of instantaneity to the study of geometrogenesis in the context of tensorial Group Field Theory and we conclude by suggesting that atemporality plays a significant role for the understanding of our world at different scales.