Thermal quantum gravity condensates in group field theory cosmology

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.

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Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity

Universe ◽

10.3390/universe5050107 ◽

2019 ◽

Vol 5 (5) ◽

pp. 107 ◽

Cited By ~ 7

Author(s):

Marco de Cesare

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Effective Field ◽

Time Varying ◽

Reconstruction Procedure ◽

Cosmological Background ◽

Bouncing Universe ◽

Physical Information ◽

Group Field Theory ◽

Mimetic Gravity

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f(□ϕ) implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power-law expansions of f in different regimes, corresponding e.g., to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we provide two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational “constants” in the cosmological equations.

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Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

Universe ◽

10.3390/universe5020041 ◽

2019 ◽

Vol 5 (2) ◽

pp. 41 ◽

Cited By ~ 3

Author(s):

Bekir Baytaş ◽

Martin Bojowald ◽

Sean Crowe

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Quantum Cosmology ◽

Loop Quantum Gravity ◽

Loop Quantum Cosmology ◽

Canonical Realization ◽

Group Field Theory

The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.

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Impact of nonlinear effective interactions on group field theory quantum gravity condensates

Physical Review D ◽

10.1103/physrevd.94.064056 ◽

2016 ◽

Vol 94 (6) ◽

Cited By ~ 15

Author(s):

Andreas G. A. Pithis ◽

Mairi Sakellariadou ◽

Petar Tomov

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Effective Interactions ◽

Group Field Theory

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Spin Foam Models with Finite Groups

Journal of Gravity ◽

10.1155/2013/549824 ◽

2013 ◽

Vol 2013 ◽

pp. 1-28 ◽

Cited By ~ 7

Author(s):

Benjamin Bahr ◽

Bianca Dittrich ◽

James P. Ryan

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Finite Groups ◽

Loop Quantum Gravity ◽

Theory Approach ◽

Test Bed ◽

Spin Foam Models ◽

Spin Foam ◽

Group Field Theory ◽

The Many

Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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

Universe ◽

10.3390/universe6010019 ◽

2020 ◽

Vol 6 (1) ◽

pp. 19

Author(s):

Sylvain Carrozza ◽

Steffen Gielen ◽

Daniele Oriti

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Special Issue ◽

Review Articles ◽

Group Field Theory ◽

Basic Ideas

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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