Effective relational cosmological dynamics from Quantum Gravity

Quantum fluctuations in the effective relational GFT cosmology

“…The second is a classical limit/approximation of the sector of the theory corresponding to (would-be) spacetime and geometry, to show that indeed an effective classical dynamics compatible with General Relativity and observations emerges, once in the continuum description [1]. The third is a definition of suitable observables that can, on the one hand, give a physical meaning to both continuum and classical approximations in terms of spacetime geometry and gravity, and, on the other hand, allow to make contact with phenomenology [2]. In particular, suitable observables are needed to recast the dynamics of the quantum gravity system, in the same continuum and classical approximations, at least, in more customary local evolutionary terms, i.e.…”

“…In "emergent quantum gravity" theories, in which the fundamental degrees of freedom are pre-geometric and non-spatiotemporal, and not identified with (quantized) continuum fields, the situation has an additional layer of complications [2]. Any kind of continuum notion in such theories is expected to emerge in a proto-geometric phase of the theory from the collective behavior of the fundamental entities, i.e.…”

“…Specifically, the hydrodynamic regime of models of 4d quantum geometry admits a cosmological interpretation and has been analysed in some detail for simple condensate states [17,27,28]. The corresponding effective dynamics has been recast in terms of cosmological observables both via the relational strategy and by a deparametrization with respect to the added matter degrees of freedom [2,17,[28][29][30][31]. Among many results [32][33][34][35][36][37], the correct classical limit in terms of a flat FRW universe has been obtained rather generically for large expectation values of the volume operator at late relational (clock) times [2,28,34], and the big bang singularity is resolved, with a similar degree of generality [28,34], and replaced with a quantum bounce.…”

Hamiltonian group field theory with multiple scalar matter fields

“…The usual objection that Newton-Wigner operators do not transform well under boosts would not necessarily be an issue in our setting which is anyway only covariant with respect to rotations of the d 'spatial' fields. We would then have to deal with other issues such as the rather unclear physical meaning of the 'total scalar field value' given by the sum of all values for a scalar field in a many-particle configuration (see [41,58] for related discussions). We will not study these operators further in this paper, but they may be of interest in future work.…”

“…The method of deparametrisation using scalar fields had previously appeared in canonical LQG [38][39][40], where it also leads to a different Hilbert space which is not subject to (Hamiltonian or diffeomorphism) constraints. An extended discussion of these two avenues to defining a canonical quantisation and relational time evolution in GFT was recently given in [41].…”