Quantum Gravity and Cosmology: an intimate interplay

Abstract

Abstract. I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics. IntroductionMost of the fundamental questions in cosmology -which for a long time belonged to the realm of philosophy -can now be addressed within a physical theory and tested against increasingly accurate observational data. We live the golden age of cosmology. Still, fundamental puzzles remain. The most obvious is what, if anything, happened before the big bang? Another is what is the universe made of? Standard cosmology is formulated within the framework of Einstein's general theory of relativity. Notwithstanding, general relativity is not adequate to explain the earliest stages of cosmic existence, and cannot provide an explanation for the big bang itself. The reason is that quantum mechanics must have played a rôle at sufficiently early times. The majority of early universe cosmological models are studied at a semi-classical level, hence they leave basic questions such as the beginning of the universe, and the origin of inflation (or of alternative models) unanswered. Modern early universe cosmology is in the need of a rigorous underpinning in quantum gravity. More precisely, quantum gravity offers the appropriate framework to address fundamental questions such as the origin of the space-time continuum and its effective dynamics, and the pictures of the earliest moments of the universe which emerge. These pictures must include an approximately homogeneous background and superimposed perturbations. In return, cosmological data represent the best (if not the only) chance for testing quantum gravity, thus guiding the formulation of the complete fundamental theory.Quantum gravity proposals belong to two classes, they are either top-down or bottom-up. In the former class belong approaches like string/M-theory or a variant of non-perturbative approach to quantum gravity, like loop quantum gravity or group field theory. In the latter one belong the proposal of non-commutative (spectral) geometry, and that of asymptotic safety. String theory may provide the underlying theory required to resolve questions such as the initial

Group Field Theory Condensate Cosmology: An Appetizer

“…atoms of space, correspond to fundamental quanta which are created or annihilated by the field operators of GFT. 5 The GFT Fock space…”

“…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.…”

Cosmological implications of the hydrodynamical phase of group field theory

“…This is a period of accelerated expansion in absence of an inflaton field and its associated ad hoc potential. A detailed study of the condition for inflation can be found in [12]; however, in [83] it is argued that the number of e-folds computed for the free theory -V = 0 in the action ( 6)-suggests that such a geometric inflation cannot last sufficiently long to accommodate observational data. This implies that GFT cosmology in absence of interactions between building blocks cannot replace the standard inflationary scenario.…”

“…According to [56] a real-valued condensate field has solutions avoiding the singularity and also growing exponentially after a bounce, if and only if the GFT energy is negative. A discussion on the possible values of the parameter space of the interacting potential can be found in [83], together with the stability properties of the evolving isotropic system, giving rise to effective continuous and homogeneous 3-geometries built from many smallest and almost at building blocks of quantum geometry.…”

Gravitational Physics: the birth of a new era

“…Applied to cosmology, these ideas involve dramatic departures from the standard cosmological model [18], such as bouncing cosmological models, where the Universe undergoes a long, pre-big bang contracting phase which then bounces into the expanding Universe we observe today. Another possibility is an early era of accelerated expansion without the need for a special mechanism such as inflation.…”