Unimodular Loop Quantum Cosmology

Abstract

Unimodular gravity is based on a modification of the usual Einstein-Hilbert action that allows one to recover general relativity with a dynamical cosmological constant. It also has the interesting property of providing, as the momentum conjugate to the cosmological constant, an emergent clock variable. In this paper we investigate the cosmological reduction of unimodular gravity, and its quantization within the framework of flat homogeneous and isotropic loop quantum cosmology. It is shown that the unimodular clock can be used to construct the physical state space, and that the fundamental features of the previous models featuring scalar field clocks are reproduced. In particular, the classical singularity is replaced by a quantum bounce, which takes place in the same condition as obtained previously. We also find that requirement of semi-classicality demands the expectation value of the cosmological constant to be small (in Planck units). The relation to spin foam models is also studied, and we show that the use of the unimodular time variable leads to a unique vertex expansion.

26 pages. Revised version taking into account referee's comments

References in corpus (12)

• Quantum Nature of the Big Bang: Improved dynamics
• Loop quantum cosmology of k=1 FRW models
• Loop Quantum Dynamics of the Schwarzschild Interior
• Loop Quantum Cosmology: An Overview
• Loop quantum cosmology of Bianchi type IX models
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Singularity Resolution in Loop Quantum Cosmology: A Brief Overview
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Loop quantum cosmology with higher order holonomy corrections

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• Hawking's information puzzle: a solution realized in loop quantum cosmology
• Hamiltonian analysis of unimodular gravity and its quantization in the connection representation
• Unimodular conformal and projective relativity
• The landscape of polymer quantum cosmology
• A dialog on the fate of information in black hole evaporation
• Low-curvature quantum corrections from unitary evolution of de Sitter space
• Canonical analysis of covariant unimodular gravity and an extension of the Kodama state
• Spacetime Quanta? : The Discrete Spectrum of a Quantum Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology
• Wavepacket evolution in unimodular quantum cosmology