Cosmological implications of interacting group field theory models: Cyclic universe and accelerated expansion

Abstract

We study the cosmological implications of interactions between spacetime quanta in the Group Field Theory (GFT) approach to Quantum Gravity from a phenomenological perspective. Our work represents a first step towards understanding Early Universe Cosmology by studying the dynamics of the emergent continuum spacetime, as obtained from a fundamentally discrete microscopic theory. In particular, we show how GFT interactions lead to a recollapse of the Universe while preserving the bounce replacing the initial singularity, which has already been shown to occur in the free case. It is remarkable that cyclic cosmologies are thus obtained in this framework without any a priori assumption on the geometry of spatial sections of the emergent spacetime. Furthermore, we show how interactions make it possible to have an early epoch of accelerated expansion, which can be made to last for an arbitrarily large number of e-folds, without the need to introduce an ad hoc potential for the scalar field.

Quantum gravity and gravitational-wave astronomy

“…Quantum-gravity theories have mainly implications in the UV regime, hence often recovering an early era of accelerated expansion while avoiding the introduction of an inflaton field with a fined-tuned potential (e.g., [144,145] in the context of group field cosmology). Here we addressed the question of whether such theories can leave an imprint in late-time GW astronomy through dimensional-flow effects.…”

Minisuperspace models of discrete systems

“…Good knowledge of the fundamental theory is required in order to select a reliable minisuperspace model. Alternatively, non-trivial dynamics can be obtained by using condensate states, as employed also in cosmological models of group-field theories [19,20,21,22,23,24,25,26].…”

“…This procedure is well known from the description of Bose-Einstein condensates, where it results in the non-linear Gross-Pitaevsky equation for the analog of χ. In quantum gravity, the procedure has been used in particular in the context of group-field theory [19,20,21,22,23,24,25,26], and it can also be seen in certain approximations that go beyond minisuperspace models by including perturbative inhomogeneity at an effective quantum level [27]. A non-linear equation for the single-spin wave function χ can be derived by first computing an effective Hamiltonian Ψ|Ĥ|Ψ for (5) in a state of the form (10):…”

Quantum Gravity and Cosmology: an intimate interplay

“…A detailed study has shown [13] that the occurrence of a bounce and an early epoch of accelerated expansion found in the free theory, both hold in the interacting case. In the latter case, the solutions are cyclic motions describing oscillations around a stable minimum, hence interactions induce recollapse leading to cyclic cosmologies.…”

“…In the following we will turn on the interactions, which is indeed the more natural and consistent scenario, as the quanta of geometry must be somehow glued with each other. Depending on our results we may also be able to give a prescription for the way one must build the GFT model and assign specific type of interactions in order to get at the semi-classical limit the desired properties for the space-time that must be then seen as the emergent 3-geometry of our homogeneous and isotropic universe [13]. Let us consider the effective action (46) for an isotropic GFT condensate, and take [13] V(σ) = B|σ(φ)| 2 + 2 n w|σ| n + 2 n w |σ| n , with n > n .…”