Critical Insight into the Cosmological Sector of Loop Quantum Gravity

Abstract

This article sheds new light on the problem of cosmological reduction in Loop Quantum Gravity. We critically analyze Quantum Reduced Loop Gravity -- an attempt to extract the cosmological sector of the full theory. We reconsider the reduction procedure applied to the states of the kinematical Hilbert space, developing a comparative analysis with previous efforts in the literature. We show that the constraints of the model were formerly instantiated in an inconsistent fashion, leading to an overconstrained dynamics and an ill-defined Hilbert space. We then scrutinize alternative implementations of symmetry-reduction. While remaining unaffected by the shortcomings encountered in Quantum Reduced Loop Gravity, these latter procedures bridge the gap between the full theory and former endeavors in Loop Quantum Cosmology.

arXiv comment25 pages, significantly improved version of the manuscript, accepted for publication in Physical Review D. arXiv admin note: text overlap with arXiv:1707.00065

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Cited by in corpus (3)

• Genericness of pre-inflationary dynamics and probability of the desired slow-roll inflation in modified loop quantum cosmologies
• Effective $f(R)$ actions for modified Loop Quantum Cosmologies via order reduction
• Regularization of the cosmological sector of loop quantum gravity with bosonic matter and the related problems with general covariance of quantum corrections