**Steffen Gielen, Imperial College**

**Title: Cosmology with group field theory condensates**

PDF of the talk (136K)

Audio [.wav 39MB]

by Mercedes Martín-Benito, Rabdoud University

One of the most important open questions in physics is how gravity (or in other words, the geometry of spacetime) behaves when the energy densities are huge, of the order of the Planck density. Our most reliable theory of gravity, general relativity, fails to describe the gravitational phenomena in high energy density regimes, as it generically leads to singularities. These regimes are achieved for example at the origin of the universe or in the interior of black holes, and therefore we do not have yet a consistent explanation for these phenomena. We expect quantum gravity effects to be important in such situations, but general relativity, being a theory that treats the geometry of the spacetime as classical, do not take those quantum gravity effects into account. Thus, in order to describe black holes or the very early universe in a physically meaningful way it seems unavoidable to quantize gravity.

The quantization of gravity not only requires attaining a mathematically well-described theory with predictive power, but also the comparison of the predictions with observations to check that they agree. The regimes where quantum gravity plays a fundamental role, such as black holes or the early universe, might seem very far from our observational or experimental reach. Nevertheless, thanks to the big progress that precision cosmology has undergone in the last decades, in the near future we may be able to get observational data about the very initial instants of the universe that could be sensitive to quantum gravity effects. We need to get prepared for that, putting our quantum gravity theories at work in order to extract cosmological predictions from them.

This is the main goal of Steffen's analysis. He bases his research in the approach to quantum gravity known as Group Field Theory (GFT). GFT defines a path integral for gravity, namely, it replaces the classical notion of unique solution for the geometry of the spacetime with a sum over an infinity of possibilities to compute a quantum amplitude. The formalism that it uses is pretty much like the usual quantum field theory formalism employed in particle physics. There, given a process involving particles, the different possible interactions contributing to that process are described by so-called Feynman diagrams, that are later summed up in a consistent way to finally lead to the transition amplitude of the process that we are trying to describe. GFT follows that strategy. The corresponding Feynman diagrams are spinfoams, and represent the different dynamical processes that contribute to a particular spacetime configuration. GFT is thus linked to Loop Quantum Gravity (GFT), since spinfoams are one main proposal for defining the dynamics of LQG. The GFT Feynman expansion extends and completes this definition of the LQG dynamics by trying to determine how these diagrams must be summed up in a controlled way to obtain the corresponding quantum amplitude.

GFT is a fundamentally discrete theory, with a large number of microscopical degrees of freedom. These degrees of freedom might organize themselves, following somehow a collective behavior, to lead to different phases of the theory. The hope is to find a phase that in the continuum limit agrees with having a smooth spacetime as described by the classical theory of general relativity. In this way, we would make the link between the underlying quantum theory and the classical one that explains very well the gravitational phenomena in regimes where quantum gravity effects are negligible. To understand this, let us make the analogy with a more familiar theory: Hydrodynamics.

We know that the fundamental microscopical constituents of a fluid are molecules. The dynamics of this micro-constituents is intrinsically quantum, however these degrees of freedom display a collective behavior that leads to macroscopic properties of the fluid, such as its density, its velocity, etc. In order to study these properties it is enough to apply the classical theory of hydrodynamics. However we know that it is not the fundamental theory describing the fluid, but an effective description coming from an underlying quantum theory (condense matter theory) that explains how the atoms form the molecules, and how these interact among themselves giving rise to the fluid.

The continuum spacetime that we are used to might emerge, in a similar way to the example of the fluid, from the collective behavior of many many quantum building blocks, or atoms of spacetime. This is, in plane words, the point of view employed in the GFT approach to quantum gravity.

While GFT is still under construction, it is mature enough to try to extract physics from it. With this aim, Steffen and his collaborators, are working in obtaining effective dynamics for cosmology starting from the general framework of GFT. The simplest solutions of Einstein equations are those with spatial homogeneity. These turn out to describe cosmological solutions, which approximate rather well at large scales the dynamics of our universe. Then, in order to get effective cosmological equations from their GFT, they postulate very particular quantum states that, involving all the degrees of freedom of the GFT, are states with collective properties that can give rise to a homogeneous and continuum effective description. The similarities between GFT and condense matter physics allows Steffen and collaborators to exploit the techniques developed in condense matter. In particular, based on the experience on Bose-Einstein condensates, the states that they postulate can be seen as condensates.

The collective behavior that the degrees of freedom display leads, in fact, to a homogeneous description in the macroscopic limit. The effective equations that they obtain agree in the classical limit with cosmological equations, but remarkably retaining the main effects coming from the underlying quantum theory. More specifically, these effective equations know about the fundamental discreteness, as they explicitly get corrections (non-present in the standard classical equations) that depend on the number of quanta (spacetime “atoms”) in the condensate. These results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

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