An Introduction to Loop Quantum Gravity Through Cosmology

Abhay Ashtekar

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An Introduction to Loop Quantum Gravity Through Cosmology

Abhay Ashtekar

General Relativity and Quantum Cosmology · Submitted 5 Feb 2007

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The authors' main claim In particular, these examples illustrate: i) how `emergent time' can arise; ii) how the technical issue of solving the Hamiltonian constraint and constructing the \emph{physical} sector of the theory can be handled; iii) how questions central to the Planck scale physics can be answered using such a framework; and, iv) how quantum geometry effects can dramatically change physics near singularities and yet naturally turn themselves off and reproduce classical general relativity when space-time curvature is significantly weaker than the Planck scale.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.08 · mentions code or data availability 0.02.

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This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how `emergent time' can arise; ii) how the technical issue of solving the Hamiltonian constraint and constructing the \emph{physical} sector of the theory can be handled; iii) how questions central to the Planck scale physics can be answered using such a framework; and, iv) how quantum geometry effects can dramatically change physics near singularities and yet naturally turn themselves off and reproduce classical general relativity when space-time curvature is significantly weaker than the Planck scale.

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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	This introductory review is addressed to beginning researchers.	background 0.76	0.26	0.02	asserted 0.99
s1	Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models.	method 0.61	0.40	0.07	asserted 0.91
s2	In particular, these examples illustrate: i) how `emergent time' can arise; ii) how the technical issue of solving the Hamiltonian constraint and constructing the \emph{physical} sector of the theory can be handled; iii) how questions central to the Planck scale physics can be answered using such a framework; and, iv) how quantum geometry effects can dramatically change physics near singularities and yet naturally turn themselves off and reproduce classical general relativity when space-time curvature is significantly weaker than the Planck scale.	contribution 0.63	0.35	0.51	asserted 0.99

What kind of paper the classifier reports this is: review 1.00 · evidence from argument 0.41.

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arXiv listing abstract v2

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full text
figures and tables
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T body sentences
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The paper

Original abstract

This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how `emergent time' can arise; ii) how the technical issue of solving the Hamiltonian constraint and constructing the \emph{physical} sector of the theory can be handled; iii) how questions central to the Planck scale physics can be answered using such a framework; and, iv) how quantum geometry effects can dramatically change physics near singularities and yet naturally turn themselves off and reproduce classical general relativity when space-time curvature is significantly weaker than the Planck scale.

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References

Forward citations

Cited by 12 Pith papers

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

Flipped spinfoam vertex and loop gravity
gr-qc 2007-08 conditional novelty 8.0 of 10

A new spinfoam vertex derived from quantized Regge calculus reproduces the SO(3) loop quantum gravity boundary states, linking the covariant and canonical formulations.
Loop quantum cosmology of Bianchi I models
gr-qc 2009-03 conditional novelty 7.0 of 10

The Bianchi I loop-quantum-cosmology Hamiltonian constraint, built with a new state-dependent loop size, is a volume-driven difference equation that maps exactly onto the isotropic Friedmann constraint under a sum ove...
LQG vertex with finite Immirzi parameter
gr-qc 2007-11 conditional novelty 7.0 of 10

Imposing the simplicity constraints on a finite-Immirzi-parameter spinfoam vertex yields a boundary Hilbert space and area spectrum identical to loop quantum gravity, in both Euclidean and Lorentzian signatures.
Robustness of key features of loop quantum cosmology
gr-qc 2007-10 conditional novelty 7.0 of 10

Using a harmonic-time reformulation, the k=0 loop quantum cosmology model becomes exactly soluble, and the resulting closed-form volume evolution proves the bounce is generic and bounds matter density at about 0.41 Pl...
The Polymer representation for the scalar field: A Wigner functional approach
gr-qc 2019-08 conditional novelty 6.0 of 10

The polymer Wigner functional for a real scalar field is derived as a weak covariance limit of the Gaussian-measure Wigner functional, reproducing earlier GNS and Fock results.

Show 7 more citing papers

On the semiclassical limit of 4d spin foam models
gr-qc 2008-09 conditional novelty 6.0 of 10

In the large-spin limit the FK-gamma spin foam amplitude on an arbitrary triangulation is exponentially suppressed unless the face spins come from a discrete geometry, in which case it reduces to exp(i times the Regge...
The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
gr-qc 2007-08 conditional novelty 6.0 of 10

The Barrett-Crane spinfoam vertex does not reproduce the correct long-distance graviton propagator in loop quantum gravity, and the failure traces to its independence from intertwiners.
Matter Bounce Loop Quantum Cosmology from $F(R)$ Gravity
gr-qc 2014-10 conditional novelty 4.0 of 10

A reconstruction method yields F(R) gravities that reproduce the loop-quantum-cosmology matter bounce, but the resulting inflationary spectral index (about 0.33) does not match Planck data.
Fundamental Structure of Loop Quantum Gravity
gr-qc 2005-09 conditional novelty 3.0 of 10

The review assembles the standard construction of loop quantum gravity, from the real SU(2) connection variables through the kinematical Hilbert space and spin-network basis to the Hamiltonian and master constraint op...
Introduction to Loop Quantum Cosmology
gr-qc 2011-09 accept novelty 2.0 of 10

A structured survey of loop quantum cosmology reporting that minisuperspace models replace the big bang with a bounce, while midisuperspace and effective-dynamics work remains incomplete.
Inflationary cosmology in modified gravity theories
hep-th 2015-03 conditional novelty 1.5 of 10

With hand-picked parameters, three modified-gravity inflation models can reproduce Planck-compatible values of the scalar spectral index and tensor-to-scalar ratio.
Loop Quantum Cosmology: A Status Report
gr-qc 2011-08 unverdicted novelty 1.0 of 10

Loop quantum cosmology, built from loop quantum gravity, replaces the big-bang singularity with a quantum bounce in homogeneous models and predicts a universal Planck-scale density cap.

How the literature uses it

40 arXiv papers cite this in 50 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 · 14 sentences without a confident label

Uses its method or tool 1 paper

We will use a method essentially coming from that described in [ref] , and briefly mentioned in [ref] ; the method is the following.

Flipped spinfoam vertex and loop gravity · Symplectic structure · 1.00

Compares with it 3 papers

For this case the Friedmann equation is it is interesting to note that, this kind of modified Friedmann equation can be derived also from effective loop quantum cosmology [ref] [equation] where we have now the constraint $0<x<1$.

Bare and effective fluid description in brane world cosmology · SCENARIOS FOR A NEGATIVE BRANE TENSION · 0.80
The state-dependence of our bounce is in contrast to some other approaches such as that of loop quantum cosmology [ref] .

Nonlinear Quantum Cosmology · Conclusion · 0.98
We want to finish this section with a comparison of our formalism with the structure that was obtained in the context of loop quantum cosmology with $k=0$ [ref] the modified Friedmann equation can be written as, 3H^2 =ρ( 1-ρ/ρ_c) , where $ρ_c$ is the critical energy density set by quantum gravity.

Randall-Sundrum model with $\lambda<0$ and bulk brane viscosity · Bulk viscosity and the Eckart's theory in Randall-Sundrum Cosmological Scenario · 1.00

Cites it as support 1 paper

Our analysis is motivated by the fact that quantum geometry leads to resolution of space-like singularities in a number of simple models (see, e.g., [ref] ).

Information is Not Lost in the Evaporation of 2-dimensional Black Holes · Introduction · 0.96

Cites it as background 28 papers

Curvature singularities have been recently studied in the framework of Loop Quantum Cosmology (LQC) [ref] , which is a canonical quantization of homogeneous cosmological spacetimes based on Loop Quantum Gravity (LQG).

Graceful exit via polymerization of pre-big bang cosmology · Introduction · 0.99
The restriction of LQG to symmetric states gives rise to Loop Quantum Cosmology (LQC) [ref] .

Super-inflation in Loop Quantum Cosmology · Introduction · 0.95
Recently, however, methods from loop quantum gravity have been applied to this setting (see, for example [ref] ).

Higher curvature counter terms cause the bounce in loop cosmology · Introduction · 0.98

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