arXiv subjects

Steffen Gielen

Publications and source records attributed to Steffen Gielen.

At least 37 records · Page 2Linked to original sources

arXiv2023

Towards anisotropic cosmology in group field theory

In cosmological group field theory (GFT) models for quantum gravity coupled to a massless scalar field the total volume, seen as a function of the scalar field, follows the classical Friedmann dynamics of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) Universe at low energies while resolving the Big Bang singularity at high energies. An open question is how to generalise these results to other homogeneous cosmologies. Here we take the first steps towards studying anisotropic Bianchi models in GFT, based on the introduction of a new anisotropy observable analogous to the $β$ variables in Misner's parametrisation. In a classical Bianchi I spacetime, $β$ behaves as a massless scalar field and can be used as a (gravitational) relational clock. We construct a GFT model for which in an expanding Universe $β$ initially behaves like its classical analogue before "decaying" showing a previously studied isotropisation. We support numerical results in GFT by analytical approximations in a toy model. One possible outcome of our work is a definition of relational dynamics in GFT that does not require matter.

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arXiv2023

Stationary cosmology in group field theory

Group field theory (GFT) models for quantum gravity coupled to a massless scalar field give rise to cosmological models that reproduce the (expanding or contracting) dynamics of homogeneous and isotropic spacetimes in general relativity at low energies, while including high-energy corrections that lead to singularity resolution by a "bounce." Here we investigate two possibilities for obtaining stationary solutions in GFT cosmology, which could be useful as an analogue of Minkowski spacetime. We first focus on a limit in which interactions are neglected and the effective Newton's constant in GFT cosmology is taken to zero. In this limit, we derive an effective Friedmann equation that shows no stationary solutions, but departures from the trivial classical dynamics falling off rapidly, similar to the usual correction terms responsible for the bounce. Since the effective Newton's constant needs to be exactly zero, the scenario is fine-tuned. A more satisfactory approach is obtained in a weakly interacting model: we find bound states with sharply peaked volume, representing a stationary semiclassical cosmology, and show that coherent states peaked around the minimum of the potential remain stable with small quantum fluctuations, and only small oscillations around a nearly constant volume. These coherent states realise the idea of a "quantum gravity condensate."

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arXiv2023

Quantum resolution of the cosmological singularity without new physics

We study a quantum Hot Big Bang in the connection representation, with a matter constant of motion m whose conjugate defines time. Superpositions in m induce a unitary inner product. The wavefunction reveals a resolution of the singularity problem without new physics or supplementary boundary conditions. Backtracking in time, the probability peak eventually halts at a maximum curvature, its height dropping thereafter while a symmetric contracting peak rises. The Big Bang is replaced by a superposition of contracting and expanding regular Universes. We contrast these findings with the situation in the metric representation, where boundary conditions at the singularity are needed for unitary evolution.

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arXiv2023

Gauge-invariant perturbations at a quantum gravity bounce

We study the dynamics of gauge-invariant scalar perturbations in cosmological scenarios with a modified Friedmann equation, such as quantum gravity bouncing cosmologies. We work within a separate universe approximation which captures wavelengths larger than the cosmological horizon; this approximation has been successfully applied to loop quantum cosmology and group field theory. We consider two variables commonly used to characterise scalar perturbations: the curvature perturbation on uniform-density hypersurfaces $ζ$ and the comoving curvature perturbation $\mathcal{R}$. For standard cosmological models in general relativity as well as in loop quantum cosmology, these quantities are conserved and equal on super-horizon scales for adiabatic perturbations. Here we show that while these statements can be extended to a more general form of modified Friedmann equations similar to that of loop quantum cosmology, in other cases, such as the simplest group field theory bounce scenario, $ζ$ is conserved across the bounce whereas $\mathcal{R}$ is not. We relate our results to approaches based on a second order equation for a single perturbation variable, such as the Mukhanov-Sasaki equation.

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arXiv2023

Quantum analysis of the recent cosmological bounce in the comoving Hubble length

We formulate the transition from decelerated to accelerated expansion as a bounce in connection space and study its quantum cosmology, knowing that reflections are notorious for bringing quantum effects to the fore. We use a formalism for obtaining a time variable via the demotion of the constants of Nature to integration constants, and focus on a toy Universe containing only radiation and a cosmological constant $Λ$ for its simplicity. We find that, beside the usual factor ordering ambiguities, there is an ambiguity in the order of the quantum equation, leading to two distinct theories: one second, the other first order. In both cases two time variables may be defined, conjugate to $Λ$ and to the radiation constant of motion. We make little headway with the second-order theory, but are able to produce solutions to the first-order theory. They exhibit the well-known "ringing" whereby incident and reflected waves interfere, leading to oscillations in the probability distribution even for well-peaked wave packets. We also examine in detail the probability measure within the semiclassical approximation. Close to the bounce, the probability distribution becomes double-peaked, with one peak following a trajectory close to the classical limit but with a Hubble parameter slightly shifted downwards, and the other with a value of $b$ stuck at its minimum. An examination of the effects still closer to the bounce, and within a more realistic model involving matter and $Λ$, is left to future work.

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arXiv2022

Frontiers of Quantum Gravity: shared challenges, converging directions

Understanding the quantum nature of spacetime and gravity remains one of the most ambitious goals of theoretical physics. It promises to provide key new insights into fundamental particle theory, astrophysics, cosmology and the foundations of physics. Despite this common goal, the community of quantum gravity researchers is sometimes seen as divided into sub-communities working on different, mutually exclusive approaches. In practice however, recent years have shown the emergence of common techniques, results and physical ideas arising from different sub-communities, suggesting exciting new prospects for collaboration and interaction between traditionally distinct approaches. In this White Paper we discuss some of the common themes which have seen a growing interest from various directions, and argue that focusing on them will help the quantum gravity community as a whole towards shared objectives.

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arXiv2022

Unitarity and quantum resolution of gravitational singularities

We explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at finite time implies quantum singularity resolution, but for a clock that encounters future infinity at finite time leads to a quantum recollapse. We then find that our starting point - assuming the general covariance of general relativity - is actually incompatible with general quantum unitarity: singularity resolution in quantum gravity can always be engineered by choosing the right clock, or avoided by using a different one.

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arXiv2022

Unitarity, clock dependence and quantum recollapse in quantum cosmology

We continue our analysis of a quantum cosmology model describing a flat Friedmann--Lemaître--Robertson--Walker universe filled with a (free) massless scalar field and an arbitrary perfect fluid. For positive energy density in the scalar and fluid, each classical solution has a singularity and expands to infinite volume. When quantising we view the cosmological dynamics in relational terms, using one degree of freedom as a clock for the others. Three natural candidates for this clock are the volume, a time variable conjugate to the perfect fluid, and the scalar field. We have previously shown that requiring unitary evolution in the "fluid" time leads to a boundary condition at the singularity and generic singularity resolution, while in the volume time semiclassical states follow the classical singular trajectories. Here we analyse the third option of using the scalar field as a clock, finding further dramatic differences to the previous cases: the boundary condition arising from unitarity is now at infinity. Rather than singularity resolution, this theory features a quantum recollapse of the universe at large volume, as was shown in a similar context by Pawłowski and Ashtekar. We illustrate the properties of the theory analytically and numerically, showing that the ways in which the different quantum theories do or do not depart from classical behaviour directly arise from demanding unitarity with respect to different clocks. We argue that using a Dirac quantisation would not resolve the issue. Our results further illustrate the problem of time in quantum gravity.

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arXiv2022

Effective cosmology from one-body operators in group field theory

We propose a new method for obtaining an effective Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology from the quantum gravity dynamics of group field theory (GFT), based on the idea that an FLRW universe is characterised by a few macroscopic observables. Rather than relying on assuming a particular type of quantum state and computing expectation values in such a state, here we directly start from relations between macroscopic observables (defined as one-body operators) and formulate dynamics only for those observables. We apply the effective approach to constrained quantum systems (as developed by Bojowald and collaborators) to GFT, providing a systematic expansion in powers of $\hbar$. We obtain a kinematical phase space of expectation values and moments, which does not require an a priori choice of clock variable. We identify a gauge fixing of the system which corresponds to choosing one of the cosmological variables (with the role of extrinsic curvature) as a clock and which allows us to rewrite the effective dynamics in relational form. We show necessary and sufficient conditions for the resulting dynamics of expectation values to be compatible with those of classical FLRW cosmology and discuss the impact of quantum fluctuations.

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arXiv2022

Lorentzian quantum cosmology goes simplicial

We employ the methods of discrete (Lorentzian) Regge calculus for analysing Lorentzian quantum cosmology models with a special focus on discrete analogues of the no-boundary proposal for the early universe. We use a simple 4-polytope, a subdivided 4-polytope and shells of discrete 3-spheres as triangulations to model a closed universe with cosmological constant, and examine the semiclassical path integral for these different choices. We find that the shells give good agreement with continuum results for small values of the scale factor and in particular for finer discretisations of the boundary 3-sphere, while the simple and subdivided 4-polytopes can only be compared with the continuum in certain regimes, and in particular are not able to capture a transition from Euclidean geometry with small scale factor to a large Lorentzian one. Finally, we consider a closed universe filled with dust particles and discretised by shells of 3-spheres. This model can approximate the continuum case quite well. Our results embed the no-boundary proposal in a discrete setting where it is possibly more naturally defined, and prepare for its discussion within the realm of spin foams.

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arXiv2021

Frozen formalism and canonical quantization in group field theory

Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears "frozen." Two strategies towards the quantization of such systems are the identification of a clock degree of freedom before quantization (deparametrization), and quantization on a kinematical Hilbert space which is subject to constraints (Dirac quantization). The usual canonical quantization in quantum field theory is analogous to deparametrization. Here we introduce a frozen formalism and Dirac quantization for a complex Klein-Gordon scalar field, and show that the resulting theory is equivalent to usual canonical quantization. We then apply the formalism to the group field theory formalism for quantum gravity, for which both deparametrization and a "timeless" quantization have been proposed in past work. We show how a frozen formalism for group field theory links between these two existing approaches, and illustrate in particular the construction of physical observables. We derive effective cosmological dynamics for group field theory in the new formalism and compare these to previous work. The frozen formalism could be extended to other approaches to quantum gravity that do not use a preferred time parameter.

hep-th↗

arXiv2021

Hamiltonian group field theory with multiple scalar matter fields

One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field theory leading to a Hamiltonian formulation in which states or operators evolve with respect to the clock given by a free massless scalar field, similar to what happens in deparametrised models in quantum cosmology. Here we extend the construction of Hamiltonian group field theory to models with multiple scalar matter fields, encountering new features and technical subtleties compared with the previously studied case. We show that the effective cosmological dynamics for these more general models reduce to the Friedmann dynamics of general relativity with multiple scalar fields in the limit of large volume, if suitable (non-generic) initial conditions are chosen. At high energy, we find corrections to the classical Friedmann equations whose form is similar to what is found in loop quantum cosmology. These corrections lead to generic singularity resolution by a bounce. For generic initial conditions, the effective cosmological dynamics treat the 'clock' field and other matter fields differently, in disagreement with the Friedmann dynamics of general relativity. We speculate on a possible interpretation in terms of inhomogeneities.

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arXiv2020

Singularity resolution depends on the clock

We study the quantum cosmology of a flat Friedmann-Lemaître-Robertson-Walker universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the action, as in unimodular gravity. We study two versions of the quantum theory: the first is based on a time coordinate conjugate to the radiation/dark energy matter component, i.e., conformal time (for radiation) or unimodular time. As shown by Gryb and Thébault, this quantum theory achieves a type of singularity resolution; we illustrate this and other properties of this theory. The theory is then contrasted with a second type of quantisation in which the logarithm of the scale factor serves as time, which has been studied in the context of the "perfect bounce" for quantum cosmology. Unlike the first quantum theory, the second one contains semiclassical states that follow classical trajectories and evolve into the singularity without obstruction, thus showing no singularity resolution. We discuss how a complex scale factor best describes the semiclassical dynamics. This cosmological model serves as an illustration of the problem of time in quantum cosmology.

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arXiv2020

Generalised effective cosmology from group field theory

We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter-Weyl representation labels), we first consider dynamics given by a quadratic Hamiltonian, which takes the form of a squeezing operator, and then add a quartic interaction that can be seen as a toy model for interactions in full GFT. Our derivation of effective Friedmann equations does not require a mean-field approximation; we mostly follow a general approach in which these equations in fact hold for any state. The resulting cosmological equations exhibit corrections to classical Friedmann dynamics similar to those of loop quantum cosmology, leading to generic singularity resolution, but also involve further state-dependent terms. We then specify these equations to various types of coherent states, such as Fock coherent states or Perelomov-Gilmore states based on the su(1,1) structure of harmonic quantum cosmology. We compute relative uncertainties of volume and energy in these states, clarifying whether they can be interpreted as semiclassical. In the interacting case, both analytical and numerical approximations are used to obtain modified cosmological dynamics. Our results clarify how effective cosmological equations derived from GFT can provide reliable approximations to the full dynamics.

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arXiv2020

Editorial for the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms"

This Editorial introduces the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" which includes a number of research and review articles covering results in the group field theory (GFT) formalism for quantum gravity and in various neighbouring areas of quantum gravity research. We give a brief overview of the basic ideas of the GFT formalism, list some of its connections to other fields, and then summarise all contributions to the Special Issue.

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arXiv2019

Addendum to "Relational Hamiltonian for group field theory"

In this addendum to [Phys. Rev. D 99 (2019) 086017], we extend the construction of a Hamiltonian formalism to a new class of group field theory actions with a kinetic term that is local in the group variables and depends only on their derivatives; such a kinetic term will couple magnetic indices of opposite sign in the Peter-Weyl decomposition. The main results of [Phys. Rev. D 99 (2019) 086017] for the resulting cosmology extend to this case.

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arXiv2019

Inhomogeneous universe from group field theory condensate

One of the fundamental challenges for quantum cosmology is to explain the emergence of our macroscopic Universe from physics at the Planck scale. In the group field theory (GFT) approach to quantum gravity, such a macroscopic universe results from the formation of a "condensate" of fundamentally discrete degrees of freedom. It has been shown that the effective dynamics of such GFT condensates follows the classical Friedmann dynamics at late times, while avoiding the classical singularity by a bounce akin to the one of loop quantum cosmology (LQC). It was also shown how quantum fluctuations in a GFT condensate provide an initial power spectrum of volume fluctuations around exact homogeneity. Here we connect the results for quantum fluctuations in GFT to the usual formalism for cosmological perturbations within quantum field theory in curved spacetime. We consider a bouncing universe filled with a massless scalar field, in which perturbations are generated by vacuum fluctuations in the contracting phase. Matching conditions at the bounce are provided by working within LQC. We then compare the results to the GFT condensate scenario for quantum gravity with massless scalar matter. Here, instead, an initial quantum phase described by a GFT condensate generates initial scalar perturbations through quantum fluctuations. We show general agreement in the predictions of both approaches, suggesting that GFT condensates can provide a physical mechanism for the emergence of a slightly inhomogeneous universe from full quantum gravity.

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arXiv2018

Cosmological perturbations from full quantum gravity

The early universe provides an opportunity for quantum gravity to connect to observation by explaining the large-scale structure of the Universe. In the group field theory (GFT) approach, a macroscopic universe is described as a GFT condensate; this idea has already been shown to reproduce a semiclassical large universe under generic conditions, and to replace the cosmological singularity by a quantum bounce. Here we extend the GFT formalism by introducing additional scalar degrees of freedom that can be used as a physical reference frame for space and time. This allows, for the first time, the extraction of correlation functions of inhomogeneities in GFT condensates: in a way conceptually similar to inflation, but within a quantum field theory of both geometry and matter, quantum fluctuations of a homogeneous background geometry become the seeds of cosmological inhomogeneities. We find approximately scale-invariant initial quantum fluctuations in the local volume, with naturally small amplitude; this behaviour extends to other quantities such as the matter density. These results confirm the potential of GFT condensate cosmology to provide a purely quantum gravitational foundation for the understanding of the early universe.

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