Group Field Theory Condensate Cosmology: An Appetizer

Abstract

This contribution is an appetizer to the relatively young and fast evolving approach to quantum cosmology based on group field theory condensate states. We summarize the main assumptions and pillars of this approach which has revealed new perspectives on the long-standing question of how to recover the continuum from discrete geometric building blocks. Among others, we give a snapshot of recent work on isotropic cosmological solutions exhibiting an accelerated expansion, a bounce where anisotropies are shown to be under control and inhomogeneities with an approximately scaleinvariant power spectrum. Finally, we point to open issues in the condensate cosmology approach.Most important part of doing physics is the knowledge of approximation.Lev Davidovich Landau * andreas.pithis@kcl.ac.uk † mairi.sakellariadou@kcl.ac.uk 1 The introduction of discrete structures can be motivated to bypass the issue of perturbative non-renormalizability of GR within the continuum path integral formulation. Alternative points of view of dealing with this issue would be to assume the existence of a nonperturbative (i.e. interacting) fixed point for gravity in the UV as done by the asymptotic safety program [7] or to increase the amount of symmetries as compared to GR and QFT with the aim to regain perturbative renormalizability as proposed by string theory [8].Yet another view, as presented by non-commutative geometry, is that above the Planck scale the concept of geometry collapses and spacetime is replaced by a non-commutative manifold [9].arXiv:1904.00598v2 [gr-qc] 13 Jun 2019 4 Notice that by attributing an additional combinatorial degree of freedom named color to the fields, one can guarantee that the terms of the perturbative expansion are free of topological pathologies [38]. 5 A detailed discussion on the subtle differences in between the Fock space of GFT and the kinematical Hilbert space of LQG, which are mostly related to the absence of the so-called cylindrical consistency and equivalence in the former, is found in Ref. [42]. 6 The assumption of bosonic statistics is crucial for the condensate cosmology program where spacetime is thought to arise from a GFT condensate. To justify this choice of statistics from a fundamental point of view is an open problem, see Ref.[42] for a discussion and Refs. [38,43] for explorations into other statistics. 7 We refer e.g. to Appendix C of Ref.[32] for an extensive discussion of this matter for the case of the volume operator.

Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models

“…transition with respect to this symmetry. But from a quantum-gravity perspective, a transition from the discrete geometries in the perturbative regime of TGFT to a phase of continuum geometries is of high interest and of particular relevance to the GFT condensate cosmology approach [32][33][34][35][36][37][38][39]. It still has to be checked explicitly if our result of a universal symmetry restoration also applies to TGFT with other groups such as SU (2) or with additional structure such as a closure constraint [6][7][8]; but the zero-mode should have the same effect for such models, too.…”

“…In particular, understanding whether and under which conditions phase transitions and different phases can truly exist for such models has remained an open issue. Settling this point is also highly relevant for the group field theory condensate cosmology program [32][33][34][35][36][37][38][39] which assumes the existence of condensate phases with a tentative continuum geometric interpretation as a working hypothesis.…”

The phase diagram of the multi-matrix model with ABAB interaction from functional renormalization

“…In spite of the physical discreteness that some of these settings exhibit, such as, e.g., Loop Quantum Gravity [62][63][64], taking a universal continuum limit is a central goal also in this setting. For instance, in group field JHEP12(2020)131 theory [65][66][67][68], promising results regarding asymptotic freedom [69,70] and asymptotic safety [22,71] have been obtained, see [67] for a review. Similarly, RG techniques are being developed and applied in the search for a critical point in spin foams, see [72,73].…”

Hamiltonian group field theory with multiple scalar matter fields

“…First of all, one might argue that matter is essential for the physical interpretation of any theory of quantum gravity; whether there is a realistic coupling of matter and gravity is one of the most basic consistency questions for any approach. The main motivation for including scalar matter fields has come from the cosmological application of GFT [19,25,26]. Just as in traditional quantum cosmology [27] and in loop quantum cosmology (LQC) [28][29][30], in GFT a free scalar field can serve as a relational 'clock' which parametrises the evolution of the spacetime geometry.…”