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==Fractals in observational cosmology== |
==Fractals in observational cosmology== |
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The first attempt to model the distribution of galaxies with a fractal pattern was made by [[Luciano Pietronero]] and his team in 1987,<ref>{{cite journal |author=Pietronero, L. |date=1987 |title=The Fractal Structure of the Universe: Correlations of Galaxies and Clusters |journal=Physica A |volume=144 |issue=144 |pages=257–284 | doi = 10.1016/0378-4371(87)90191-9 |bibcode = 1987PhyA..144..257P }}</ref> and a more detailed view of the |
The first attempt to model the distribution of galaxies with a fractal pattern was made by [[Luciano Pietronero]] and his team in 1987,<ref>{{cite journal |author=Pietronero, L. |date=1987 |title=The Fractal Structure of the Universe: Correlations of Galaxies and Clusters |journal=Physica A |volume=144 |issue=144 |pages=257–284 | doi = 10.1016/0378-4371(87)90191-9 |bibcode = 1987PhyA..144..257P }}</ref> and a more detailed view of the universe's [[large-scale structure of the universe|large-scale structure]] emerged over the following decade, as the number of cataloged galaxies grew larger. Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a [[fractal dimension]] of about 2.<ref>{{cite journal |author1=Joyce, M. |author2=Labini, F.S. |author3=Gabrielli, A. |author4=Montouri, M. |author5=Pietronero, L. |date=2005 |title=Basic Properties of Galaxy Clustering in the light of recent results from the Sloan Digital Sky Survey |journal=Astronomy and Astrophysics |volume=443 |issue=11 |pages=11–16 |arxiv=astro-ph/0501583 | doi= 10.1051/0004-6361:20053658 |bibcode=2005A&A...443...11J}}</ref> The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3. |
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The universe has been observed to be homogeneous and [[isotropic]] (i.e. is smoothly distributed) at very large scales, as is expected in a standard [[Big Bang]] or [[FLRW]] cosmology, and in most interpretations of the [[Lambda-CDM model|Lambda-Cold Dark Matter model]]. The [[scientific consensus]] interpretation is that the [[Sloan Digital Sky Survey]] (SDSS) suggests that things do indeed smooth out above 100 Megaparsecs. |
The universe has been observed to be homogeneous and [[isotropic]] (i.e. is smoothly distributed) at very large scales, as is expected in a standard [[Big Bang]] or [[FLRW]] cosmology, and in most interpretations of the [[Lambda-CDM model|Lambda-Cold Dark Matter model]]. The [[scientific consensus]] interpretation is that the [[Sloan Digital Sky Survey]] (SDSS) suggests that things do indeed smooth out above 100 Megaparsecs. |
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One study of the SDSS data in 2004 found "The power spectrum is not well-characterized by a single power law but unambiguously shows curvature...thereby driving yet another nail into the coffin of the fractal universe hypothesis and any other models predicting a power-law power spectrum".<ref>{{cite journal |author=Tegmark |display-authors=etal |title=The Three-Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey |journal=The Astrophysical Journal |volume=606 |issue=2 |pages=702–740 |date=10 May 2004 |doi=10.1086/382125|arxiv = astro-ph/0310725 |bibcode = 2004ApJ...606..702T }}</ref> Another analysis of luminous red galaxies (LRGs) in the SDSS data calculated the fractal dimension of galaxy distribution (on a scales from 70 to 100 [[Parsec#Megaparsecs and gigaparsecs|Mpc/h]]) at 3, consistent with homogeneity; but that the fractal dimension is 2 "out to roughly 20 Mpc/h".<ref>{{cite journal |author1=Hogg, David W. |author2=Eisenstein, Daniel J. |author3=Blanton, Michael R. |author4=Bahcall, Neta A. |author5=Brinkmann, J. |author6=Gunn, James E. |author7=Schneider, Donald P. |date=2005 |title=Cosmic homogeneity demonstrated with luminous red galaxies |journal=[[The Astrophysical Journal]] |volume=624 |issue= 1|pages=54–58 |arxiv=astro-ph/0411197 |doi= 10.1086/429084 |pmid= |pmc= |bibcode=2005ApJ...624...54H}}</ref> |
One study of the SDSS data in 2004 found "The power spectrum is not well-characterized by a single power law but unambiguously shows curvature...thereby driving yet another nail into the coffin of the fractal universe hypothesis and any other models predicting a power-law power spectrum".<ref>{{cite journal |author=Tegmark |display-authors=etal |title=The Three-Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey |journal=The Astrophysical Journal |volume=606 |issue=2 |pages=702–740 |date=10 May 2004 |doi=10.1086/382125|arxiv = astro-ph/0310725 |bibcode = 2004ApJ...606..702T }}</ref> Another analysis of luminous red galaxies (LRGs) in the SDSS data calculated the fractal dimension of galaxy distribution (on a scales from 70 to 100 [[Parsec#Megaparsecs and gigaparsecs|Mpc/h]]) at 3, consistent with homogeneity; but that the fractal dimension is 2 "out to roughly 20 Mpc/h".<ref>{{cite journal |author1=Hogg, David W. |author2=Eisenstein, Daniel J. |author3=Blanton, Michael R. |author4=Bahcall, Neta A. |author5=Brinkmann, J. |author6=Gunn, James E. |author7=Schneider, Donald P. |date=2005 |title=Cosmic homogeneity demonstrated with luminous red galaxies |journal=[[The Astrophysical Journal]] |volume=624 |issue= 1|pages=54–58 |arxiv=astro-ph/0411197 |doi= 10.1086/429084 |pmid= |pmc= |bibcode=2005ApJ...624...54H}}</ref> In 2012, Scrimgeour et al. definitively showed that large-scale structure of galaxies was homogeneous beyond a scale around 70 Mpc/h.<ref>{{cite journal |last=Scrimgeour|first=M. |display-authors=etal |date=September 2012 |title=The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity |journal=Mon. Not. R. Astron. Soc. |volume=425 |issue=1 |pages=116–134 |doi=10.1111/j.1365-2966.2012.21402.x |bibcode=2012MNRAS.425..116S |arxiv = 1205.6812 }}</ref> |
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In a paper of 2008 entitled "Parabolic drift towards homogeneity in large-scale structures of galaxies" (Physica, A, 387: 3641-3646) D. Queiros-Conde showed that large-scale structure of galaxies are much better described by a scale-dependent fractal dimension drifting from zero to three at a scale around 55 Mpc/h in the context of a "scale-entropy diffusion equation". It gives a way to estimate the number of galaxies in the universe in agreement with Hubble measurements. Moreover, fractal dimension is varying linearly with scale-logarithm. This means that the geometry of galaxy distribution is a "parabolic fractal". Two years later, the same author with M. Feidt showed that the fractal dimension 2 found in numerous studies can be explained as being a problem of measurement. In 2012, Scrimgeour et al. definitively showed that large-scale structure of galaxies was homogeneous beyond a scale around 70 Mpc/h, close to the value found by D. Queiros-Conde.<ref>{{cite journal |last=Scrimgeour|first=M. |display-authors=etal |date=September 2012 |title=The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity |journal=Mon. Not. R. Astron. Soc. |volume=425 |issue=1 |pages=116–134 |doi=10.1111/j.1365-2966.2012.21402.x |bibcode=2012MNRAS.425..116S |arxiv = 1205.6812 }}</ref> |
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In 2013, astronomers discovered a [[large quasar group]] (LQG) that is 1.6 billion light-years in diameter, far larger than allowed by the [[cosmological principle]], which asserts that the universe should be homogeneous at scales this large.<ref name="largestructure">{{cite web|url=https://news.yahoo.com/largest-structure-universe-discovered-093416167.html|title=Largest Structure in Universe Discovered}}</ref> |
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==Fractals in theoretical cosmology== |
==Fractals in theoretical cosmology== |
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In the realm of theory, the first appearance of fractals in cosmology was likely with [[Andrei Linde|Andrei Linde’s]] "Eternally Existing Self-Reproducing Chaotic Inflationary Universe"<ref>{{cite journal |author=Linde, A.D. |date=August 1986 |title=Eternally Existing Self-Reproducing Chaotic Inflationary Universe |journal= Physica Scripta|volume= 15|issue= |pages= 169–175|url= |doi= 10.1088/0031-8949/1987/T15/024|pmid= |pmc= |bibcode = 1987PhST...15..169L }}</ref> theory (see [[Chaotic inflation theory]]), in 1986. In this theory, the evolution of a scalar field creates peaks that become nucleation points which cause inflating patches of space to develop into "bubble universes," making the universe fractal on the very largest scales. [[Alan Guth|Alan Guth's]] 2007 paper on "Eternal Inflation and its implications"<ref>{{cite journal |author=Guth, Alan |date=22 June 2007 |title=Eternal inflation and its implications |journal=J. Phys. A: Math. Theor. |volume=40 |issue=25 |pages=6811–6826 |arxiv=hep-th/0702178 |doi= 10.1088/1751-8113/40/25/S25|pmid= |pmc= |bibcode = 2007JPhA...40.6811G }}</ref> shows that this variety of [[Cosmic inflation|Inflationary universe]] theory is still being seriously considered today. And inflation, in some form or other, is widely considered to be our best available cosmological model. |
In the realm of theory, the first appearance of fractals in cosmology was likely with [[Andrei Linde|Andrei Linde’s]] "Eternally Existing Self-Reproducing Chaotic Inflationary Universe"<ref>{{cite journal |author=Linde, A.D. |date=August 1986 |title=Eternally Existing Self-Reproducing Chaotic Inflationary Universe |journal= Physica Scripta|volume= 15|issue= |pages= 169–175|url= |doi= 10.1088/0031-8949/1987/T15/024|pmid= |pmc= |bibcode = 1987PhST...15..169L }}</ref> theory (see [[Chaotic inflation theory]]), in 1986. In this theory, the evolution of a scalar field creates peaks that become nucleation points which cause inflating patches of space to develop into "bubble universes," making the universe fractal on the very largest scales. [[Alan Guth|Alan Guth's]] 2007 paper on "Eternal Inflation and its implications"<ref>{{cite journal |author=Guth, Alan |date=22 June 2007 |title=Eternal inflation and its implications |journal=J. Phys. A: Math. Theor. |volume=40 |issue=25 |pages=6811–6826 |arxiv=hep-th/0702178 |doi= 10.1088/1751-8113/40/25/S25|pmid= |pmc= |bibcode = 2007JPhA...40.6811G }}</ref> shows that this variety of [[Cosmic inflation|Inflationary universe]] theory is still being seriously considered today. And inflation, in some form or other, is widely considered to be our best available cosmological model. |
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Since 1986, however, quite a large number of different cosmological theories exhibiting fractal properties have been proposed. And while Linde’s theory shows fractality at scales likely larger than the observable universe, theories like [[ |
Since 1986, however, quite a large number of different cosmological theories exhibiting fractal properties have been proposed. And while Linde’s theory shows fractality at scales likely larger than the observable universe, theories like [[causal dynamical triangulation]]<ref name="Ambjorn, J.; Jurkiewicz, J.; Loll, R. 2005">{{cite journal |author1=Ambjorn, J. |author2=Jurkiewicz, J. |author3=Loll, R. |date=2005 |title=Reconstructing the Universe |journal=Phys. Rev. D |volume=72 |issue= 6|pages= 064014|arxiv=hep-th/0505154 |doi= 10.1103/PhysRevD.72.064014|pmid= |pmc= |bibcode = 2005PhRvD..72f4014A }}</ref> and the [[asymptotic safety in quantum gravity|asymptotic safety]] approach to [[quantum gravity]]<ref>{{cite journal |author1=Lauscher, O. |author2=Reuter, M. |date=2005 |title=Asymptotic Safety in Quantum Einstein Gravity |journal= |volume= |issue= |pages= 11260|arxiv=hep-th/0511260 |doi= |pmid= |pmc= |bibcode = 2005hep.th...11260L }}</ref> are fractal at the opposite extreme, in the realm of the ultra-small near the [[Planck scale]]. These recent theories of quantum gravity describe a fractal structure for [[spacetime]] itself, and suggest that the dimensionality of [[space]] evolves with [[time]]. Specifically; they suggest that reality is 2D at the Planck scale, and that spacetime gradually becomes 4D at larger scales. |
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⚫ | French mathematician [[Alain Connes]] has been working for a number of years to reconcile |
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==Publications== |
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On the 10th of March, 2007, the weekly science magazine [[New Scientist]] featured an article entitled "Is the Universe a Fractal?"<ref>Gefter, Amanda - Is the Universe a Fractal? - New Scientist - March 10, 2007: issue 2594</ref> on its cover. The article by [[Amanda Gefter]] focused on the contrasting views of Pietronero and his colleagues, who think that the universe appears to be fractal (rough and lumpy) with those of David W. Hogg of [[NYU]] and others who think that the universe will prove to be relatively homogeneous and isotropic (smooth) at a still larger scale, or once we have a large and inclusive enough sample (as is predicted by Lambda-CDM). Gefter gave experts in both camps an opportunity to explain their work and their views on the subject, for her readers. {{Citation needed|date=April 2013}} |
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This was a follow-up of an earlier article in that same publication on August 21 of 1999, by [[Marcus Chown]], entitled "Fractal Universe.".<ref>Chown, Marcus - Fractal Universe - New Scientist - August 21, 1999</ref> Back in November 1994, [[Scientific American]] featured an article on its cover written by physicist Andrei Linde, entitled "The Self-Reproducing Inflationary Universe"<ref>Linde, Andrei - The Self-Reproducing Inflationary Universe - Scientific American - November 1994 pp. 48-55</ref> whose heading stated that "Recent versions of the inflationary scenario describe the universe as a self-generating fractal that sprouts other inflationary universes," and which described Linde's theory of chaotic eternal inflation in some detail. |
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⚫ | French mathematician [[Alain Connes]] has been working for a number of years to reconcile general relativity with quantum mechanics using [[noncommutative geometry]]. Fractality also arises in this approach to quantum gravity. An article by Alexander Hellemans in the August 2006 issue of ''[[Scientific American]]''<ref>Hellemans, Alexander — The Geometer of Particle Physics — Scientific American - August, 2006</ref> quotes Connes as saying that the next important step toward this goal is to "try to understand how space with fractional dimensions couples with gravitation." The work of Connes with physicist [[Carlo Rovelli]]<ref>{{cite journal |author1=Connes, A. |author2=Rovelli, C. |date=1994 |title=Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation |journal=Class. Quantum Grav. |volume=11 |issue= 12|pages=2899–2918 |arxiv=gr-qc/9406019 |doi= 10.1088/0264-9381/11/12/007|pmid= |pmc= |bibcode = 1994CQGra..11.2899C }}</ref> suggests that time is an emergent property or arises naturally, in this formulation, whereas in causal dynamical triangulation,<ref name="Ambjorn, J.; Jurkiewicz, J.; Loll, R. 2005"/> choosing those configurations where adjacent building blocks share the same direction in time is an essential part of the 'recipe.' Both approaches suggest that the fabric of space itself is fractal, however. |
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In July 2008, Scientific American featured an article on [[Causal dynamical triangulation]],<ref>Ambjorn, J.; Jurkiewicz, J.; Loll, R. - The Self-Organizing Quantum Universe - Scientific American - July 2008 pp. 42-49</ref> written by the three scientists who propounded the theory, which again suggests that the universe may have the characteristics of a fractal. |
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==See also== |
==See also== |
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{{Portal|Physics}} |
{{Portal|Physics}} |
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*[[Causal dynamical triangulation]] |
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*[[Chaotic inflation theory]] |
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*[[Dirac large numbers hypothesis]] |
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*[[Invariant set postulate]] |
*[[Invariant set postulate]] |
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⚫ | |||
*[[Hoag's Object]] |
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*[[Holographic principle]] |
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⚫ | |||
*[[Nebular hypothesis]] |
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*[[Scale invariance]] |
*[[Scale invariance]] |
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*[[Scale relativity]] |
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*[[Self-organized criticality]] |
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*[[Shape of the universe]] |
*[[Shape of the universe]] |
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Revision as of 21:08, 2 February 2020
In physical cosmology, fractal cosmology is a set of minority cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is a fractal across a wide range of scales (see also: multifractal system). More generally, it relates to the usage or appearance of fractals in the study of the universe and matter. A central issue in this field is the fractal dimension of the universe or of matter distribution within it, when measured at very large or very small scales.
Fractals in observational cosmology
The first attempt to model the distribution of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987,[1] and a more detailed view of the universe's large-scale structure emerged over the following decade, as the number of cataloged galaxies grew larger. Pietronero argues that the universe shows a definite fractal aspect over a fairly wide range of scale, with a fractal dimension of about 2.[2] The fractal dimension of a homogeneous 3D object would be 3, and 2 for a homogeneous surface, whilst the fractal dimension for a fractal surface is between 2 and 3.
The universe has been observed to be homogeneous and isotropic (i.e. is smoothly distributed) at very large scales, as is expected in a standard Big Bang or FLRW cosmology, and in most interpretations of the Lambda-Cold Dark Matter model. The scientific consensus interpretation is that the Sloan Digital Sky Survey (SDSS) suggests that things do indeed smooth out above 100 Megaparsecs.
One study of the SDSS data in 2004 found "The power spectrum is not well-characterized by a single power law but unambiguously shows curvature...thereby driving yet another nail into the coffin of the fractal universe hypothesis and any other models predicting a power-law power spectrum".[3] Another analysis of luminous red galaxies (LRGs) in the SDSS data calculated the fractal dimension of galaxy distribution (on a scales from 70 to 100 Mpc/h) at 3, consistent with homogeneity; but that the fractal dimension is 2 "out to roughly 20 Mpc/h".[4] In 2012, Scrimgeour et al. definitively showed that large-scale structure of galaxies was homogeneous beyond a scale around 70 Mpc/h.[5]
Fractals in theoretical cosmology
In the realm of theory, the first appearance of fractals in cosmology was likely with Andrei Linde’s "Eternally Existing Self-Reproducing Chaotic Inflationary Universe"[6] theory (see Chaotic inflation theory), in 1986. In this theory, the evolution of a scalar field creates peaks that become nucleation points which cause inflating patches of space to develop into "bubble universes," making the universe fractal on the very largest scales. Alan Guth's 2007 paper on "Eternal Inflation and its implications"[7] shows that this variety of Inflationary universe theory is still being seriously considered today. And inflation, in some form or other, is widely considered to be our best available cosmological model.
Since 1986, however, quite a large number of different cosmological theories exhibiting fractal properties have been proposed. And while Linde’s theory shows fractality at scales likely larger than the observable universe, theories like causal dynamical triangulation[8] and the asymptotic safety approach to quantum gravity[9] are fractal at the opposite extreme, in the realm of the ultra-small near the Planck scale. These recent theories of quantum gravity describe a fractal structure for spacetime itself, and suggest that the dimensionality of space evolves with time. Specifically; they suggest that reality is 2D at the Planck scale, and that spacetime gradually becomes 4D at larger scales.
French mathematician Alain Connes has been working for a number of years to reconcile general relativity with quantum mechanics using noncommutative geometry. Fractality also arises in this approach to quantum gravity. An article by Alexander Hellemans in the August 2006 issue of Scientific American[10] quotes Connes as saying that the next important step toward this goal is to "try to understand how space with fractional dimensions couples with gravitation." The work of Connes with physicist Carlo Rovelli[11] suggests that time is an emergent property or arises naturally, in this formulation, whereas in causal dynamical triangulation,[8] choosing those configurations where adjacent building blocks share the same direction in time is an essential part of the 'recipe.' Both approaches suggest that the fabric of space itself is fractal, however.
See also
- Invariant set postulate
- Large-scale structure of the Universe
- Scale invariance
- Shape of the universe
Notes
- ^ Pietronero, L. (1987). "The Fractal Structure of the Universe: Correlations of Galaxies and Clusters". Physica A. 144 (144): 257–284. Bibcode:1987PhyA..144..257P. doi:10.1016/0378-4371(87)90191-9.
- ^ Joyce, M.; Labini, F.S.; Gabrielli, A.; Montouri, M.; Pietronero, L. (2005). "Basic Properties of Galaxy Clustering in the light of recent results from the Sloan Digital Sky Survey". Astronomy and Astrophysics. 443 (11): 11–16. arXiv:astro-ph/0501583. Bibcode:2005A&A...443...11J. doi:10.1051/0004-6361:20053658.
- ^ Tegmark; et al. (10 May 2004). "The Three-Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey". The Astrophysical Journal. 606 (2): 702–740. arXiv:astro-ph/0310725. Bibcode:2004ApJ...606..702T. doi:10.1086/382125.
- ^ Hogg, David W.; Eisenstein, Daniel J.; Blanton, Michael R.; Bahcall, Neta A.; Brinkmann, J.; Gunn, James E.; Schneider, Donald P. (2005). "Cosmic homogeneity demonstrated with luminous red galaxies". The Astrophysical Journal. 624 (1): 54–58. arXiv:astro-ph/0411197. Bibcode:2005ApJ...624...54H. doi:10.1086/429084.
- ^ Scrimgeour, M.; et al. (September 2012). "The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity". Mon. Not. R. Astron. Soc. 425 (1): 116–134. arXiv:1205.6812. Bibcode:2012MNRAS.425..116S. doi:10.1111/j.1365-2966.2012.21402.x.
- ^ Linde, A.D. (August 1986). "Eternally Existing Self-Reproducing Chaotic Inflationary Universe". Physica Scripta. 15: 169–175. Bibcode:1987PhST...15..169L. doi:10.1088/0031-8949/1987/T15/024.
- ^ Guth, Alan (22 June 2007). "Eternal inflation and its implications". J. Phys. A: Math. Theor. 40 (25): 6811–6826. arXiv:hep-th/0702178. Bibcode:2007JPhA...40.6811G. doi:10.1088/1751-8113/40/25/S25.
- ^ a b Ambjorn, J.; Jurkiewicz, J.; Loll, R. (2005). "Reconstructing the Universe". Phys. Rev. D. 72 (6): 064014. arXiv:hep-th/0505154. Bibcode:2005PhRvD..72f4014A. doi:10.1103/PhysRevD.72.064014.
- ^ Lauscher, O.; Reuter, M. (2005). "Asymptotic Safety in Quantum Einstein Gravity": 11260. arXiv:hep-th/0511260. Bibcode:2005hep.th...11260L.
{{cite journal}}
: Cite journal requires|journal=
(help) - ^ Hellemans, Alexander — The Geometer of Particle Physics — Scientific American - August, 2006
- ^ Connes, A.; Rovelli, C. (1994). "Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation". Class. Quantum Grav. 11 (12): 2899–2918. arXiv:gr-qc/9406019. Bibcode:1994CQGra..11.2899C. doi:10.1088/0264-9381/11/12/007.
References
- Rassem,M. and Ahmed E., "On Fractal Cosmology", Astro. Phys. Lett. Commun. (1996), 35, 311.