A Cosmological Sector in Loop Quantum Gravity

Tim A. Koslowski

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A Cosmological Sector in Loop Quantum Gravity

Tim A. Koslowski

General Relativity and Quantum Cosmology · Submitted 7 Nov 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The full operator algebra however turns out to be different from standard Loop Quantum Cosmology.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.91 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.92 · mentions code or data availability 0.02.

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We use the method of embedding a subsystem (i.e. its observable algebra) into a larger quantum system to extract a cosmological sector from full Loop Quantum Gravity. The application of this method provides a setting for a systematic study of the interplay between diffeomorphism invariance and symmetry reduction. The non-triviality of this relation is shown by extracting a cosmological system that has configurations variables that are very similar to the ones of a super-selection sector of standard Loop Quantum Cosmology. The full operator algebra however turns out to be different from standard Loop Quantum Cosmology. The homogeneous isotropic sector of pure gravity turns out to be quantum mechanics on a circle. The dynamics of our system seems pathological at first sight, and we give both mathematical and physical reasons for this behavior and we explain a strategy to cure these pathologies.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We use the method of embedding a subsystem (i.e. its observable algebra) into a larger quantum system to extract a cosmological sector from full Loop Quantum Gravity.	method 0.96	0.95	0.09	asserted 1.00
s1	The application of this method provides a setting for a systematic study of the interplay between diffeomorphism invariance and symmetry reduction.	contribution 0.62	0.71	0.08	asserted 0.94
s2	The non-triviality of this relation is shown by extracting a cosmological system that has configurations variables that are very similar to the ones of a super-selection sector of standard Loop Quantum Cosmology.	result 0.95	0.93	0.24	asserted 1.00
s3	The full operator algebra however turns out to be different from standard Loop Quantum Cosmology.	result 1.00	0.93	0.22	asserted 1.00
s4	The homogeneous isotropic sector of pure gravity turns out to be quantum mechanics on a circle.	result 1.00	0.93	0.19	asserted 0.99
s5	The dynamics of our system seems pathological at first sight, and we give both mathematical and physical reasons for this behavior and we explain a strategy to cure these pathologies.	result 0.50	0.93	0.14	hedged possibility 0.78

What kind of paper the classifier reports this is: method or tool 0.69 · evidence from proof or derivation 0.98.

What was examined, and what was not

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We use the method of embedding a subsystem (i.e. its observable algebra) into a larger quantum system to extract a cosmological sector from full Loop Quantum Gravity. The application of this method provides a setting for a systematic study of the interplay between diffeomorphism invariance and symmetry reduction. The non-triviality of this relation is shown by extracting a cosmological system that has configurations variables that are very similar to the ones of a super-selection sector of standard Loop Quantum Cosmology. The full operator algebra however turns out to be different from standard Loop Quantum Cosmology. The homogeneous isotropic sector of pure gravity turns out to be quantum mechanics on a circle. The dynamics of our system seems pathological at first sight, and we give both mathematical and physical reasons for this behavior and we explain a strategy to cure these pathologies.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Anomaly freedom in perturbative loop quantum gravity
gr-qc 2008-06 conditional novelty 6.0 of 10

Non-trivial inverse-triad corrections can be implemented in anomaly-free effective constraints for cosmological perturbations, at the cost of adding counterterms whose coefficients are fixed by the requirement that th...
Loop Quantum Cosmology: A brief review
gr-qc 2016-12 conditional novelty 1.0 of 10

Loop quantum cosmology replaces the big bang singularity with a bounce near the Planck density and provides a framework for computing early-universe perturbations, though the observational bridge still rests on test-f...

How the literature uses it

8 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 7 sentences without a confident label

Cites it as background 1 paper

However, the relation between LQC and full LQG is still an open question, given that to date, there is no precise way of deriving the homogeneous theory from the full theory (however, see [ref] for recent attempts).

Is loop quantization in cosmology unique? · Introduction · 0.82

What it cites · 23 sentences without a confident label

Uses the method or tool of 2 papers

Given a particular gauge fixing for the diffeomorphisms, we can apply the techniques of [ref] to construct a cosmological sector of Loop Quantum Gravity.

Reduction of a Quantum Theory · Strategy · 0.99
We will work with an adaption of the Weyl-algebra setting for LQG [ref] in this paper, which allows us to work in the the $C^*$-algebraic framework.

Energy conditions outside a dielectric ball · Introduction · 0.98

Compares with 2 papers

We have already mentioned differences between our approach outlined in this paper and Loop Quantum Cosmology as it is presented by [ref] .

Mathematical structure of loop quantum cosmology · Comparison with Standard Loop Quantum Cosmology · 0.99
The resulting isotropic model would be similar to [ref] , which has the Bohr compactification of $ℝ$ as its quantum configuration space.

Comments on the kinematical structure of loop quantum cosmology · Comments about the Embedding Maps · 0.91

Cites as background 2 papers

A successful theory of quantum gravity is provided by Loop Quantum Gravity (LQG) [ref] which has sparked investigations into Loop Quantum Cosmology (LQC) premiered by Bojowald [ref] .

Oscillatory approach to the singularity in vacuum $T^2$ symmetric spacetimes · Introduction · 1.00
The states of LQC need a physical interpretation and is not induced by the relation of Loop Quantum Cosmology and Loop Quantum Gravity itself; see [ref] for a discussion of the physical interpretation of the states of Loop Quantum Cosmology.

Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings · Treatment of Observables and States · 0.87

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