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Reconstructing the Universe
Open accessAbstract
We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.
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Cites
Monte Carlo Methods in Statistical Physics
Newman, M. E. J., & Barkema, G. T. (1999) · doi:10.1093/oso/9780198517962.001.0001 · Cited by 3,165
Hartle, J. B., & Hawking, S. W. (1983) · Physical Review D · doi:10.1103/physrevd.28.2960 · Cited by 3,027
Kiefer, C. (2004) · Cited by 2,923
General Relativity – An Einstein Centenary Survey
Irvine, J. M. (1980) · Physics Bulletin · doi:10.1088/0031-9112/31/4/029 · Cited by 2,620
Rovelli, C. (2004) · doi:10.1017/cbo9780511755804 · Cited by 2,240
Nonperturbative evolution equation for quantum gravity
Reuter, M. (1998) · Physical Review D · doi:10.1103/physrevd.57.971 · Cited by 1,160
Creation of universes from nothing
Vilenkin, A. (1982) · Physics Letters B · doi:10.1016/0370-2693(82)90866-8 · Cited by 841
Diseases of triangulated random surface models, and possible cures
Ambjørn, J., Durhuus, B., & Fröhlich, J. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90356-6 · Cited by 645
Vilenkin, A. (1984) · Physical Review D · doi:10.1103/physrevd.30.509 · Cited by 592
Spin foam models for quantum gravity
Perez, A. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/6/202 · Cited by 532
The Spectral Dimension of the Universe is Scale Dependent
Ambjørn, J., Jurkiewicz, J., & Loll, R. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.171301 · Cited by 518
Self-citationFixed Points of Quantum Gravity
Litim, D. F. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.201301 · Cited by 506
Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation
Reuter, M., & Saueressig, F. (2002) · Physical Review D · doi:10.1103/physrevd.65.065016 · Cited by 496
Ultraviolet divergences in quantum theories of gravitation.
Weinberg, S. (1979) · Cited by 474
Emergence of a 4D World from Causal Quantum Gravity
Ambjørn, J., Jurkiewicz, J., & Loll, R. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.131301 · Cited by 447
Self-citationUltraviolet fixed point and generalized flow equation of quantum gravity
Lauscher, O., & Reuter, M. (2001) · Physical Review D · doi:10.1103/physrevd.65.025013 · Cited by 438
Non-perturbative Lorentzian quantum gravity, causality and topology change
Ambjørn, J., & Loll, R. (1998) · Nuclear Physics B · doi:10.1016/s0550-3213(98)00692-0 · Cited by 388
Self-citationNon-Trivial Ultraviolet Fixed Point in Quantum Gravity
Souma, W. (1999) · Progress of Theoretical Physics · doi:10.1143/ptp.102.181 · Cited by 322
Quantum creation of the inflationary universe
Linde, A. D. (1984) · Lettere al Nuovo Cimento · doi:10.1007/bf02790571 · Cited by 314
Dynamically triangulating Lorentzian quantum gravity
Ambjørn, J., Jurkiewicz, J., & Loll, R. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00297-8 · Cited by 312
Self-citationLectures on Loop Quantum Gravity
Thiemann, T. (2003) · Max Planck Institute for Plasma Physics · Cited by 283
Renormalization group and quantum gravity
Kawai, H., & Ninomiya, M. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90345-e · Cited by 277
Gibbons, G. W., & Hawking, S. W. (1993) · WORLD SCIENTIFIC eBooks · doi:10.1142/1301 · Cited by 277
Lectures on Loop Quantum Gravity
Thiemann, T. (2003) · Lecture Notes in Physics · doi:10.1007/978-3-540-45230-0_3 · Cited by 267
The Combinatorial Theory of Complexes
Alexander, J. W. (1930) · The Annals of Mathematics · doi:10.2307/1968099 · Cited by 255
The appearance of critical dimensions in regulated string theories
Ambjørn, J., Durhuus, B., Fröhlich, J., & Orland, P. (1986) · Nuclear Physics B · doi:10.1016/0550-3213(86)90563-8 · Cited by 241
Self-citationApproaches to quantum cosmology
Vilenkin, A. (1994) · Physical Review D · doi:10.1103/physrevd.50.2581 · Cited by 238
Quantum Geometry: A Statistical Field Theory Approach
Ambjørn, J., Durhuus, B., & Jonsson, T. (1997) · Cambridge University Press eBooks · doi:10.1017/cbo9780511524417 · Cited by 238
Self-citationLoop quantum gravity: An outside view
Nicolai, H., Peeters, K., & Zamaklar, M. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 229
Integration contours for the no-boundary wave function of the universe
Halliwell, J. J., & Hartle, J. B. (1990) · Physical Review D · doi:10.1103/physrevd.41.1815 · Cited by 218
Four-dimensional simplicial quantum gravity
Ambjørn, J., & Jurkiewicz, J. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)90709-d · Cited by 205
Self-citationNon-Trivial Ultraviolet Fixed Point in Quantum Gravity
Souma, W. (1999) · CERN Document Server (European Organization for Nuclear Research) · Cited by 197
Nonperturbative Lorentzian Path Integral for Gravity
Ambjørn, J., Jurkiewicz, J., & Loll, R. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.924 · Cited by 194
Self-citationQuantum gravity at astrophysical distances?
Reuter, M., & Weyer, H. (2004) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2004/12/001 · Cited by 191
Transfer matrix formalism for two-dimensional quantum gravity and fractal structures of space-time
Kawai, H., Kawamoto, N., Mogami, T., & Watabiki, Y. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91131-6 · Cited by 171
Quantum mechanics in the tunneling universe
Rubakov, V. A. (1984) · Physics Letters B · doi:10.1016/0370-2693(84)90088-1 · Cited by 170
Jan Ambjørn, A., & Watabiki, Y. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00154-k · Cited by 164
Halliwell, J. J., & Louko, J. (1989) · Physical Review D · doi:10.1103/physrevd.39.2206 · Cited by 160
Scaling exponents in quantum gravity near two dimensions
Kawai, H., Kitazawa, Y., & Ninomiya, M. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90246-l · Cited by 159
On the fractal structure of two-dimensional quantum gravity
Jan Ambjørn, A., Jurkiewicz, J., & Watabiki, Y. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00468-8 · Cited by 155
Self-citationProper Time Flow Equation for Gravity
Bonanno, A. M., & Reuter, M. (2005) · Journal of High Energy Physics · doi:10.1088/1126-6708/2005/02/035 · Cited by 154
Ultraviolet stable fixed point and scaling relations in (2 + ϵ)-dimensional quantum gravity
Kawai, H., Kitazawa, Y., & Masao Ninomiya, C. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90594-f · Cited by 151
A class of nonlocal truncations in quantum Einstein gravity and its renormalization group behavior
Reuter, M., & Frank Saueressig, B. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.125001 · Cited by 135
The Future of Theoretical Physics and Cosmology
Gibbons, G. W., Shellard, E. P. S., & Rankin, S. J. (2003) · Cited by 132
Focusing on the fixed point of 4D simplicial gravity
Białas, P., Burda, Z., Krzywicki, A., & Petersson, B. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00214-3 · Cited by 132
Semiclassical universe from first principles
Jan Ambjørn, A., Jurkiewicz, J., & Loll, R. (2004) · Physics Letters B · doi:10.1016/j.physletb.2004.12.067 · Cited by 131
Self-citationQuantum Gravity at Astrophysical Distances?Preprint
Reuter, M., & Weyer, H. (2004) · Cited by 121
Nonperturbative 3D Lorentzian quantum gravity
Ambjørn, J., Jurkiewicz, J., & Loll, R. (2001) · Physical Review D · doi:10.1103/physrevd.64.044011 · Cited by 116
Self-citationA proper-time cure for the conformal sickness in quantum gravity
Dasgupta, A., & Loll, R. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00227-9 · Cited by 115
Self-citationScaling in four-dimensional quantum gravity
Jan Ambjørn, A., & Jurkiewicz, J. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00303-a · Cited by 113
Self-citationWorld-sheet geometry and baby universes in 2D quantum gravity
Jain, S., & Mathur, S. D. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)91769-6 · Cited by 105
Scaling exponents in quantum gravity near two-dimensionsPreprint
Kawai, H., Kitazawa, Y., & Masao Ninomiya, C. (1993) · Cited by 104
The appearance of critical dimensions in regulated string theories (II)
Jan Ambjørn, A., Durhuus, B., & Fröhlich, J. M. (1986) · Nuclear Physics B · doi:10.1016/0550-3213(86)90594-8 · Cited by 99
Critical behavior of dynamically triangulated quantum gravity in four dimensions
Agishtein, M. E., & Migdal, A. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90106-l · Cited by 96
Summing over all genera for d > 1: a toy model
Jan Ambjørn, A., Durhuus, B., & Jónsson, T. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)90337-6 · Cited by 93
Newtonian potential in quantum Regge gravity
Hamber, H. W., & Williams, R. M. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(94)00495-z · Cited by 85
Renormalizability of quantum gravity near two dimensions
Kawai, H., Kitazawa, Y., & Ninorniya, M. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00119-8 · Cited by 81
Baby universes in 2d quantum gravity
Jan Ambjørn, A., Jain, S., & Þorleifsson, G. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)90188-n · Cited by 81
The spectral dimension of the branched polymer phase of two-dimensional quantum gravity
Jónsson, T., & WHEATER, J. F. (1998) · Nuclear Physics B · doi:10.1016/s0550-3213(98)00027-3 · Cited by 78
Phase structure of four dimensional simplicial quantum gravity
Catterall, S., Kogut, J. B., & Renken, R. L. (1994) · Physics Letters B · doi:10.1016/0370-2693(94)91480-x · Cited by 78
Gravitational scaling dimensions
Hamber, H. W. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.124008 · Cited by 77
Three-dimensional simplicial quantum gravity
Jan Ambjørn, A., & Varsted, S. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90444-g · Cited by 72
Matter fields with c > 1 coupled to 2d gravity
Jan Ambjørn, A., Durhuus, B., Jónsson, T., & Þorleifsson, G. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90604-n · Cited by 68
Phases of simplical quantum gravity in four dimensions estimates for the critical exponents
Hamber, H. W. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90409-i · Cited by 68
Elementary moves and ergodicity in D-dimensional simplicial quantum gravity
Gross, M., & Varsted, S. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90012-z · Cited by 66
The vacuum in three-dimensional simplicial quantum gravity
Jan Ambjørn, A., Boulatov, D. V., Krzywicki, A., & Varsted, S. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)91663-t · Cited by 66
Quantum geometry of 2D gravity coupled to unitary matter
Jan Ambjørn, A., & Anagnostopoulos, K. N. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00259-9 · Cited by 64
Appearance of mother universe and singular vertices in random geometries
Białas, P., Burda, Z., Petersson, B., & Tabaczek, J. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00226-5 · Cited by 62
Lorentzian 3d gravity with wormholes via matrix models
Ambjørn, J., Jurkiewicz, J., Loll, R., & Vernizzi, G. (2001) · Journal of High Energy Physics · doi:10.1088/1126-6708/2001/09/022 · Cited by 62
Self-citationA Lorentzian cure for Euclidean troubles
Jan Ambjørn, A., Dasgupta, A., Jurkiewicz, J., & Loll, R. (2002) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(01)01903-x · Cited by 60
Self-citationObserving 4d baby universes in quantum gravity
Jan Ambjørn, A., Jain, S., Jurkiewicz, J., & Kristjansen, C. F. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)90109-u · Cited by 57
Self-citationScaling and the fractal geometry of two-dimensional quantum gravity
Catterall, S., Thorleifsson, G., Bowick, M. J., & John, V. (1995) · Physics Letters B · doi:10.1016/0370-2693(95)00623-s · Cited by 56
Curvature and scaling in 4D dynamical triangulation
de Bakker, B. V., & Jan Smit, A. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00026-o · Cited by 45
The quantum space-time of c = −2 gravity
Jan Ambjørn, A., Anagnostopoulos, K. N., Ichihara, T., Jensen, L., Kawamoto, N., Watabiki, Y., & Yotsuji, K. (1998) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00659-7 · Cited by 43
Counting a black hole in Lorentzian product triangulations
Dittrich, B., & Loll, R. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/11/012 · Cited by 43
Self-citationSingular vertices and the triangulation space of the D-sphere
Catterall, S. M., Þorleifsson, G., Kogut, J. B., & Renken, R. L. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00130-7 · Cited by 42
Bistellare �quivalenz kombinatorischer Mannigfaltigkeiten
Pachner, U. (1978) · Archiv der Mathematik · doi:10.1007/bf01226024 · Cited by 36
Singular structure in 4D simplicial gravity
Catterall, S., Renken, R., & Kogut, J. (1998) · Physics Letters B · doi:10.1016/s0370-2693(97)01349-x · Cited by 34
Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity
Catterall, S. M., Thorleifsson, G., Bowick, M. J., & John, V (1995) · Syracuse University Libraries (Syracuse University) · Cited by 31
Jurkiewicz, J., & Krzywicki, A. (1997) · Physics Letters B · doi:10.1016/s0370-2693(96)01559-6 · Cited by 30
Self-citationRenormalization of 3d quantum gravity from matrix models
Ambjørn, J., Jurkiewicz, J., & Loll, R. (2004) · Physics Letters B · doi:10.1016/j.physletb.2003.11.068 · Cited by 29
Self-citationGravitational binding in 4D dynamical triangulation
de Bakker, B. V., & Jan Smit, A. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(96)00616-5 · Cited by 27
Effective sampling of random surfaces by baby universe surgery
Jan Ambjørn, A., Białas, P., Jurkiewicz, J., Burda, Z., & Petersson, B. (1994) · Physics Letters B · doi:10.1016/0370-2693(94)90022-1 · Cited by 23
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Codello, A., Percacci, R., & Rahmede, C. (2009) · Annals of Physics · doi:10.1016/j.aop.2008.08.008 · Cited by 538
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Ambjørn, J., Görlich, A., Jurkiewicz, J., & Loll, R. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.03.007 · Cited by 383
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Metadata
- Authors
- Ambjørn, J., Jurkiewicz, J., & Loll, R.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2005-09-22
- Volume
- 72
- Issue
- 6
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2167377764
- Cited by
- 422
- References
- 83
- FWCI
- 11.26
- Type
- journal article
- Language
- en
- Open access
- green
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