Group field cosmology: a cosmological field theory of quantum geometry

Abstract

Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.

14 pages, 2 figures. v2: minor typos corrected, references added

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Cited by in corpus (30)

• Cosmology from Group Field Theory Formalism for Quantum Gravity
• Quantum cosmology: a review
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• Quantum Cosmology from Group Field Theory Condensates: a Review
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• Critical evaluation of common claims in loop quantum cosmology
• Group field theory condensate cosmology: An appetizer
• Observational effects from quantum cosmology
• Super-Group Field Cosmology
• Minisuperspace models as infrared contributions
• Non-linear (loop) quantum cosmology
• Noether's Charge in the Super-Group Field Cosmology
• The interacting multiverse and its effect on the cosmic microwave background
• Third quantization of $f(R)$-type gravity
• Nilpotent Symmetries in Super-Group Field Cosmology
• Equivalence of models in loop quantum cosmology and group field theory
• Third quantization of $f(R)$-type gravity II - General $f(R)$ case -
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Constraints on Operator Ordering from Third Quantization
• Fourth Quantization
• Semiclassical solutions of generalized Wheeler-DeWitt cosmology
• Minisuperspace models of discrete systems
• Super-group field cosmology in Batalin-Vilkovisky formulation
• Renormalizability of Supersymmetric Group Field Cosmology
• Rainbow Spacetime from a Nonlocal Gravitational Uncertainty Principle
• Operator Ordering Ambiguity and Third Quantization
• Closer look at cosmological consequences of interacting group field theory
• A stochastic quasi-classical wavefunction of the Universe from the third quantization procedure
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Effective cosmology from one-body operators in group field theory