Quantum fluctuations in the effective relational GFT cosmology

Effective dynamics of scalar cosmological perturbations from quantum gravity

“…However, one cannot just take → 0, because as a consequence of the Heisenberg uncertainty principle, the fluctuations of the operator Π0 defined in equation (2.14d) would become arbitrarily large, which is certainly not ideal if one wants to interpret the scalar field as a classical clock, at least in some appropriate limit. In order to guarantee the existence of such classical clock regime, in [18,65] the condensate wavefunction (2.22) was also assumed to be dependent on the parameter π 0 , satisfying π 2 0 1. As a concrete example of the above peaking function, one can consider a Gaussian [18,65]:…”

“…In order to guarantee the existence of such classical clock regime, in [18,65] the condensate wavefunction (2.22) was also assumed to be dependent on the parameter π 0 , satisfying π 2 0 1. As a concrete example of the above peaking function, one can consider a Gaussian [18,65]:…”

“…In this sense, the CPSs realize a notion of effective relational evolution of averaged geometric quantities with respect to the physical clock (x 0 ), with the effective approach becoming increasingly accurate the smaller one takes and the larger N σ grows. Indeed, it has been shown in [65] that this latter condition, typically associated to an emergent regime and dynamically related to a very large value of the relational clock |x 0 |, is what ultimately allows for a suppression of fluctuations of both geometric and clock variables. In this large N σ regime, the evolution of expectation values of geometric quantities with respect to x 0 can thus be interpreted as classical relational dynamics 6 .…”

“…Analogously to what has been done in [53,65], here we will only extract an effective mean field dynamics from the full quantum equations of motion. In other words, we will only consider the imposition of the quantum equations of motion averaged on the states that we consider to be relevant for an effective relational description of the cosmological system, which, in our case, would be coherent states |σ µ ; x µ , π µ as in equation (2.15a) whose condensate wavefunction is assumed to take the form (2.25):…”

“…Many intriguing results have been obtained from the effective relational GFT condensate cosmology framework, by making use of an EPRLlike GFT model (see [53] and Section 2.1 for more details). In particular, two regimes of the resulting emergent relational dynamics are worth mentioning [18,53,65]. First, a continuum classical regime, characterized by a large number of GFT quanta, which matches the flat Friedmann cosmological dynamics.…”