Built on

J. Engle, R. Pereira, C. Rovelli, “The loop-quantum-gravity vertex amplitude”, Phys. Rev. Lett. 99 (2007) 161301. J. Engle, R. Pereira, C. Rovelli, “Flipped spinfoam vertex and loop gravity”, arXiv:0708.1236. E. Livine, S. Speziale, “A New spinfoam vertex for quantum gravity”, arXiv:0705.0674. E. Livine, S. Speziale, “Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity”, arXiv:0708.1915. L. Freidel, K. Krasnov, “A New Spin Foam Model for 4d Gravity”, arXiv:0708.1595. S. Alexandrov, “Spin foam model from canonical quantization,” arXiv:0705.3892. R. Pereira, “Lorentzian LQG vertex amplitude”, to appear. J. Engle, E. Livine, R. Pereira, C. Rovelli, “LQG vertex for general values of the Immirzi parameter”, to appear
Original
1915
Earlier work this paper cites.
A. Einstein, “Kosmologische Betrachtungen zur allgemeinen Relativittstheorie”, Koniglich Preussische Akademie der Wissenschaften, Sitzungsberichte 1 (1917) 421
1917
Earlier work this paper cites.
M. Born, R. Oppenheimer, “Zur Quantentheorie der Molekeln”, Annalen der Physik, 17 (1927) 457
1927
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C. Rovelli, L. Smolin, “The physical Hamiltonian in nonperturbative quantum gravity”, Phys. Rev. Lett. 72 (1994) 446
1994
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A Barbieri, “Quantum tetrahedra and simplicial spin networks”, Nucl. Phys. B518 (1998) 714-728. J. C. Baez, J. W. Barrett, “The quantum tetrahedron in 3 and 4 dimensions,” Adv. Theor. Math. Phys. 3 (1999) 815–850. A. Ashtekar, A. Corichi, J. A. Zapata, “Quantum theory of geometry. III: Non-commutativity of Riemannian structures,” Class. Quant. Grav. 15 (1998) 2955–2972
1998
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A. Ashtekar, M. Bojowald, J. Lewandowski “Mathematical structure of loop quantum cosmology”, Adv. Theor. Math. Phys. 7 (2003) 233-268. A. Ashtekar, T. Pawlowski, P. Singh, “Quantum Nature of the Big Bang”, arXiv:gr-qc/0602086v2. A. Ashtekar, A. Corichi, P. Singh, “Robustness of key features of loop quantum cosmology”, arXiv: 0710.3565. A. Ashtekar, “An Introduction to Loop Quantum Gravity Through Cosmology”, arXiv:gr-qc 0702030
2003
Earlier work this paper cites.
C. Rovelli, L. Smolin, “Knot theory and quantum gravity” Phys. Rev. Lett 61 (1988) 1155-1158. C. Rovelli, L. Smolin, “Loop space representation for quantum general relativity”, Nucl. Phys. B331 (1990) 80-152.A. Ashtekar, C. Rovelli, L. Smolin, “Weaving a classical geometry with quantum threads”, Phys. Rev. Lett 69, 237 (1992). C. Rovelli, L. Smolin, “Discreteness of Area and Volume in Quantum Gravity”, Nucl. Phys. B442 (1995) 593-619; Nucl. Phys. B456, 734 (1995).C. Rovelli, “Loop quantum gravity and black hole physics,” Helv. Phys. Acta 69, 582 (1996). A. Perez, “Spin foam models for quantum gravity,” Class. Quant. Grav. 20 (2003) R43
2003
Earlier work this paper cites.

Similar

M. Bojowald, D. Cartin, G. Khanna, “Lattice refining loop quantum cosmology, anisotropic models and stability”, Phys. Rev. D 76 (2007) 064018, arXiv:0704.1137. M. Bojowald, H. Hernandez, M. Kagan, P. Singh, A. Skirzewski, “Formation and Evolution of Structure in Loop Cosmology”, Phys. Rev. Lett. 98 (2007) 031301, arXiv:astro-ph/0611685. M. Bojowald, R. Swiderski, “Spherically Symmetric Quantum Geometry: Hamiltonian Constraint”, Class. Quant. Grav. 23 (2006) 2129-2154, arXiv:gr-qc/0511108. M. Bojowald, H. H. Hernandez, H. A. Morales-Tecotl, “Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies”, Class. Quant. Grav. 23 (2006) 3491-3516, arXiv:gr-qc/0511058. M. Bojowald, “Spherically Symmetric Quantum Geometry: States and Basic Operators”, Class. Quant. Grav. 21 (2004) 3733-3753, arXiv:gr-qc/0407017
Original
2004
Cited alongside, same era.
T. Buchert, “Dark Energy from Structure - A Status Report,” Gen. Rel. Grav. 40 (2008) 467. T. Buchert and M. Carfora, “On the curvature of the present-day Universe,” arXiv:0803.1401. F. Debbasch. “What is a mean gravitational field?” Eur. Phys. J. B, 37 (2004) 257Ð270
Original
2004
Cited alongside, same era.
M. Bojowald, “Isotropic loop quantum cosmology”, Class. Quant. Grav. 19 (2002) 2717-2742. M. Bojowald, “Loop Quantum Cosmology”, Liv. Rev. Rel. 8 (2005) 11
2005
Cited alongside, same era.

Then

T. Thiemann, “The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity”, Class. Quant. Grav. 23 (2006) 2211-2248
2006
Later among the works it cites.
C. Rovelli S. Speziale, “A Semiclassical tetrahedron”, Class. Quant. Grav. 23 (2006) 5861-5870
2006
Later among the works it cites.
C. Rovelli, Quantum Gravity, (Cambridge University Press, Cambridge, 2004). A. Ashtekar, J. Lewandowski, “Background independent quantum gravity: a status report”, Class. Quantum Grav. 21 (2004) R53. T. Thiemann, “Modern canonical quantum general relativity,” (Cambridge University Press, Cambridge, UK, 2007)
2007
Later among the works it cites.
B. Dittrich and J. Tambornino, “Gauge invariant perturbations around symmetry reduced sectors of general relativity: Applications to cosmology,” Class. Quant. Grav. 24 (2007) 4543 arXiv:gr-qc/0702093
2007
Later among the works it cites.

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2008

Stepping out of Homogeneity in Loop Quantum Cosmology

Rovelli, Carlo, Vidotto, Francesca

Understand

We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity.

We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity.
We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation.
This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation.

Built on

J. Engle, R. Pereira, C. Rovelli, “The loop-quantum-gravity vertex amplitude”, Phys. Rev. Lett. 99 (2007) 161301. J. Engle, R. Pereira, C. Rovelli, “Flipped spinfoam vertex and loop gravity”, arXiv:0708.1236. E. Livine, S. Speziale, “A New spinfoam vertex for quantum gravity”, arXiv:0705.0674. E. Livine, S. Speziale, “Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity”, arXiv:0708.1915. L. Freidel, K. Krasnov, “A New Spin Foam Model for 4d Gravity”, arXiv:0708.1595. S. Alexandrov, “Spin foam model from canonical quantization,” arXiv:0705.3892. R. Pereira, “Lorentzian LQG vertex amplitude”, to appear. J. Engle, E. Livine, R. Pereira, C. Rovelli, “LQG vertex for general values of the Immirzi parameter”, to appear
Original
1915
Earlier work this paper cites.
A. Einstein, “Kosmologische Betrachtungen zur allgemeinen Relativittstheorie”, Koniglich Preussische Akademie der Wissenschaften, Sitzungsberichte 1 (1917) 421
1917
Earlier work this paper cites.
M. Born, R. Oppenheimer, “Zur Quantentheorie der Molekeln”, Annalen der Physik, 17 (1927) 457
1927
Earlier work this paper cites.
C. Rovelli, L. Smolin, “The physical Hamiltonian in nonperturbative quantum gravity”, Phys. Rev. Lett. 72 (1994) 446
1994
Earlier work this paper cites.
A Barbieri, “Quantum tetrahedra and simplicial spin networks”, Nucl. Phys. B518 (1998) 714-728. J. C. Baez, J. W. Barrett, “The quantum tetrahedron in 3 and 4 dimensions,” Adv. Theor. Math. Phys. 3 (1999) 815–850. A. Ashtekar, A. Corichi, J. A. Zapata, “Quantum theory of geometry. III: Non-commutativity of Riemannian structures,” Class. Quant. Grav. 15 (1998) 2955–2972
1998
Earlier work this paper cites.
A. Ashtekar, M. Bojowald, J. Lewandowski “Mathematical structure of loop quantum cosmology”, Adv. Theor. Math. Phys. 7 (2003) 233-268. A. Ashtekar, T. Pawlowski, P. Singh, “Quantum Nature of the Big Bang”, arXiv:gr-qc/0602086v2. A. Ashtekar, A. Corichi, P. Singh, “Robustness of key features of loop quantum cosmology”, arXiv: 0710.3565. A. Ashtekar, “An Introduction to Loop Quantum Gravity Through Cosmology”, arXiv:gr-qc 0702030
2003
Earlier work this paper cites.
C. Rovelli, L. Smolin, “Knot theory and quantum gravity” Phys. Rev. Lett 61 (1988) 1155-1158. C. Rovelli, L. Smolin, “Loop space representation for quantum general relativity”, Nucl. Phys. B331 (1990) 80-152.A. Ashtekar, C. Rovelli, L. Smolin, “Weaving a classical geometry with quantum threads”, Phys. Rev. Lett 69, 237 (1992). C. Rovelli, L. Smolin, “Discreteness of Area and Volume in Quantum Gravity”, Nucl. Phys. B442 (1995) 593-619; Nucl. Phys. B456, 734 (1995).C. Rovelli, “Loop quantum gravity and black hole physics,” Helv. Phys. Acta 69, 582 (1996). A. Perez, “Spin foam models for quantum gravity,” Class. Quant. Grav. 20 (2003) R43
2003
Earlier work this paper cites.

Similar

M. Bojowald, D. Cartin, G. Khanna, “Lattice refining loop quantum cosmology, anisotropic models and stability”, Phys. Rev. D 76 (2007) 064018, arXiv:0704.1137. M. Bojowald, H. Hernandez, M. Kagan, P. Singh, A. Skirzewski, “Formation and Evolution of Structure in Loop Cosmology”, Phys. Rev. Lett. 98 (2007) 031301, arXiv:astro-ph/0611685. M. Bojowald, R. Swiderski, “Spherically Symmetric Quantum Geometry: Hamiltonian Constraint”, Class. Quant. Grav. 23 (2006) 2129-2154, arXiv:gr-qc/0511108. M. Bojowald, H. H. Hernandez, H. A. Morales-Tecotl, “Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies”, Class. Quant. Grav. 23 (2006) 3491-3516, arXiv:gr-qc/0511058. M. Bojowald, “Spherically Symmetric Quantum Geometry: States and Basic Operators”, Class. Quant. Grav. 21 (2004) 3733-3753, arXiv:gr-qc/0407017
Original
2004
Cited alongside, same era.
T. Buchert, “Dark Energy from Structure - A Status Report,” Gen. Rel. Grav. 40 (2008) 467. T. Buchert and M. Carfora, “On the curvature of the present-day Universe,” arXiv:0803.1401. F. Debbasch. “What is a mean gravitational field?” Eur. Phys. J. B, 37 (2004) 257Ð270
Original
2004
Cited alongside, same era.
M. Bojowald, “Isotropic loop quantum cosmology”, Class. Quant. Grav. 19 (2002) 2717-2742. M. Bojowald, “Loop Quantum Cosmology”, Liv. Rev. Rel. 8 (2005) 11
2005
Cited alongside, same era.

Then

T. Thiemann, “The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity”, Class. Quant. Grav. 23 (2006) 2211-2248
2006
Later among the works it cites.
C. Rovelli S. Speziale, “A Semiclassical tetrahedron”, Class. Quant. Grav. 23 (2006) 5861-5870
2006
Later among the works it cites.
C. Rovelli, Quantum Gravity, (Cambridge University Press, Cambridge, 2004). A. Ashtekar, J. Lewandowski, “Background independent quantum gravity: a status report”, Class. Quantum Grav. 21 (2004) R53. T. Thiemann, “Modern canonical quantum general relativity,” (Cambridge University Press, Cambridge, UK, 2007)
2007
Later among the works it cites.
B. Dittrich and J. Tambornino, “Gauge invariant perturbations around symmetry reduced sectors of general relativity: Applications to cosmology,” Class. Quant. Grav. 24 (2007) 4543 arXiv:gr-qc/0702093
2007
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

G. F. R. Ellis, “Relativistic Cosmology” , http://www.pv.infn.it/ spacetimeinaction/ speakers/transparencies/Ellis/pdf/Ellis1.pdf, slide 58, Conference “Spacetime in Action”, Pavia 2005

2005

Cited alongside, same era.

M Bojowald, H. A. Kastrup, “Quantum symmetry reduction for diffeomorphism invariant theories of connections ”, Class. Quantum Grav. 17 (2000) 3009-3043. M Bojowald, H. A. Kastrup, “Symmetric states in quantum geometry”, gr-qc/0101061. T. Koslowski, “Reduction of a quantum theory”, gr-qc/0612138. J. Engle, “Black Hole Entropy, Constraints, and Symmetry in Quantum Gravity”, Ph.D. Thesis, Penn State University, http://igpg.gravity.psu.edu/archives/thesis/2006/englethesis.pdf. J. Engle, “On the physical interpretation of states in loop quantum cosmology”, gr-qc/0701132. J. Engle, “Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings”, gr-qc/0701132

2006

Cited alongside, same era.

M. Bojowald, “Loop quantum cosmology and inhomogeneities”, Gen. Rel. Grav. 38 (2006) 1771-1795. arXiv:gr-qc/0609034

2006

Cited alongside, same era.

C. Kiefer and B. Sandhoefer, “Quantum Cosmology”, arXiv:0804.0672

Original

Cited in the paper.

T. Konopka, F. Markopoulou, L. Smolin, “Quantum graphity”, hep-th/0611197. T. Konopka, F. Markopoulou, S. Severini, “Quantum Graphity: a model of emergent locality”, arXiv:0801.0861

Original

Cited in the paper.

J. Brunnemann, C. Fleischhack, “On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity”, arXiv:0709.1621v1

Original

Cited in the paper.

M. Martin-Benito, L. J. Garay and G. A. Mena Marugan, “Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations”, arXiv:0804.1098 [gr-qc]

Original

Cited in the paper.

K. Giesel, T. Thiemann, “Algebraic Quantum Gravity (AQG) I. Conceptual Setup”, arXiv:gr-qc/ 0607099. K. Giesel, T. Thiemann, “Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity”, arXiv:0711.0119v1 [gr-qc]

Original

Cited in the paper.

J.W. Barrett, M. Galassi, W.A. Miller, R.D. Sorkin, P.A. Tuckey, R.M. Williams, “A Parallelizable Implicit Evolution Scheme for Regge Calculus”, arXiv:gr-qc/9411008v1

Cited in the paper.

J. Halliwell, S. Hawking, “Origin of structure in the universe”, Phys Rev D 31 (1985) 1777-91. A. Vilenkin, “Interpretation of the wave-function of the universe”, Phys Rev D39 (1989) 1116-1122. C. Kiefer, “The semiclassical approximation to QG”, in Canonical Quantum Gravity: from classical to quantum

2007

Later among the works it cites.

L. Modesto, C. Rovelli, “Particle scattering in loop quantum gravity,” Phys. Rev. Lett. 95 (2005), 191301. C. Rovelli, “Graviton propagator from background–independent quantum gravity”, Phys. Rev. Lett. 97 (2006), 151301. E. Bianchi, L. Modesto, C. Rovelli, S. Speziale, “Graviton propagator in loop quantum gravity,” Class. Quant. Grav. 23 (2006), 6989-7028. E. R. Livine, S. Speziale, “Group integral techniques for the spinfoam graviton propagator,” JHEP 11 (2006) 092. S. Speziale, “Towards the graviton from spinfoams: The 3d toy model,” JHEP 05 (2006) 039. E. R. Livine, S. Speziale, J. L. Willis, “Towards the graviton from spinfoams: Higher order corrections in the 3d toy model,” Phys. Rev. D75 (2007) 024038. E. Bianchi, L. Modesto, “The perturbative Regge-calculus regime of Loop Quantum Gravity”, arXiv: 0709.2051. E. Alesci, C. Rovelli, “The complete LQG graviton propagator: I. Difficulties with the Barrett-Crane vertex”, Phys. Rev. D, to appear (2007), arXiv:07080883

2007

Later among the works it cites.