Current observational evidence strongly suggests that our universe is accurately described by the standard model of cosmology [1]. This model relies on Einstein’s theory of general relativity (GR) and assumes its validity on all scales. However, this picture proves fully inadequate to describe the earliest stages of our universe, as our concepts of spacetime and its geometry as given by GR are then expected to break down due to the extreme physical conditions encountered in the vicinity of and shortly after the Big Bang. More explicitly, it appears that our universe emerged from a singularity, as implied by the famous theorems of Penrose and Hawking [2]. From a fundamental point of view, such a singularity is unphysical, and it is expected that quantum effects lead to its resolution [3]. This motivates the development of a quantum theory of gravity in which the quintessential features of GR and quantum field theory (QFT) are consistently unified. Such a theory will revolutionize our understanding of spacetime and gravity at a microscopic level and should be able to give a complete and consistent picture of cosmic evolution.

The difficulty in making progress in this field is ultimately rooted in the lack of experiments which have access to the physics at the smallest length scales and highest energies and so would provide a clear empirical guideline for the construction of such a theory. In turn, this severe underdetermination of theory by experiment is a reason for the current presence of a plethora of contesting approaches to quantum gravity [4]. Against this backdrop, the cosmology of the very early universe represents a unique window of opportunity out of this impasse [5]. For instance, it is naturally expected that traces of quantum gravity have left a fingerprint on the spectrum of the cosmic microwave background radiation, see e.g., Refs. [6,7,8,9,10,11]. Hence, cosmology provides an ideal testbed where the predictions of such competing theories can be compared and tested against forthcoming cosmological data.

A central conviction of some approaches to quantum gravity is that it should be a non-perturbative, background-independent, and diffeomorphism-invariant theory of quantum geometry. In this sense, the spacetime continuum is renunciated and is instead replaced by degrees of freedom of a discrete and combinatorial nature.1Particular representatives of this class of theories are the closely related canonical and covariant loop quantum gravity (LQG) [20,21,22,23], group field theory (GFT) [24,25], tensor models (TM) [26,27,28,29,30,31,32], and simplicial quantum gravity approaches such as quantum Regge calculus (QRC) [33] and Euclidean and causal dynamical triangulations (EDT, CDT) [34,35,36]. The perturbative expansion of their path integrals each yields a sum over discrete geometries and the most difficult problem for all of them then lies in the recovery of continuous spacetime geometry and GR describing its dynamics in an appropriate limit. This is challenging because it ideally requires formulating statements about the continuum by only calling upon notions rooted in the discontinuum. Taking the continuum limit in these approaches crucially depends on whether the discreteness of geometry is considered physical or unphysical therein, the proper weighting of configurations in the partition function, and the precise specification of the continuum limit itself. Consequently, strategies to reach this goal differ among them strongly, see e.g., Ref. [37] for an overview.

In the light of the above, it is vitally important to consider these approaches in a cosmological context, which has been accomplished to a varying degree of success by them. In this contribution, we give a brief and rather non-technical panorama of the GFT condensate cosmology program [38,39] which has been developed over the last few years and has so far borne promising fruits.2 This program is motivated by the idea that the mechanism for regaining a continuum geometry from a physically discrete quantum gravity substratum in GFT is provided by a phase transition to a condensate phase [40,42]. Research on the phase structure of different GFT models in terms of functional renormalization group analyses finds support for such a conjecture in terms of IR fixed points [43,44,45,46,47,48,49,50]. Further backing is provided by saddle point studies [51] and Landau–Ginzburg mean field analyses [52] which probe non-perturbative aspects of GFT models, see also Ref. [37]. In this picture, a condensate would correspond to a non-perturbative vacuum which comprises of many bosonic GFT quanta and in the context of GFT models of four-dimensional quantum gravity is tentatively interpreted as a continuum geometry. Given this basic premise, the most striking successes and milestone results of the condensate cosmology approach are the recovery of Friedmann-like dynamics of an emergent homogeneous and isotropic geometry [53], an extended accelerated phase of expansion [54,55] right after a cosmological bounce [56], a simple yet effective mechanism for dynamical isotropization of microscopic anisotropies [57,58] and the finding of an approximately scale-invariant and small-amplitude power spectrum of quantum fluctuations of the local volume over a homogeneous background geometry perturbed by small inhomogeneities [59]. In the following, we will quickly review the GFT formalism, give the basic structures behind its condensate cosmology spin-off, highlight the main results, and give an outlook for future challenges of this program.3