Large Scale Astrophysics and Cosmology

The debate

This web page is dedicated to the debate on fractal versus homogenous universe. You can find here the basic references and opinions of different authors. Comments are welcomed.

Staff

• Luciano Pietronero La Sapienza University of Rome
• Marco Montuori INFM SMC, UdR RM1 (Rome)
• Francesco Sylos Labini Universite' de Paris Orsey Cedex France
• Andrea Gabrielli Fermi Center of Rome

International collaborations

• Luca Amendola Osservatorio Astronomico di Monte Mario (Roma)
• P.W. Anderson Princeton University (USA)
• Robin Ball Warwick University (Great Britain)
• Yuri Baryshev Astronomical Institute of St. Petersburg State University (Russia)
• Roberto Capuzzo Dolcetta La Sapienza University (Rome)
• Helene Di Nella Observatory of Lyon (France)
• Ruth Durrer and Jean-Pierre Eckmann Geneva University (Switzerland)
• Michael Joyce M.A. Orsey (France)
• Benoit Mandelbrot and Paul Coleman Yale University (Ney York)
• Norma Sanchez Observatory of Paris DEMIRM (France)
• Pekka Teerikorpi Turola Observatoty (Turku, Finlad)

Research Activity

The first galaxy catalogues were only angular, namely they defined the two angles corresponding to the galaxy positions in the sky. These angular distributions show structures at small scales but appear rather smooth at large angular scales in agreement to the theoretical expectations of a homogeneous universe. In the late seventies however the first redshift measurements begun to appear and permitted the identification of the absolute distance of galaxies. In this way it became possible to obtain the complete three dimensional distribution of galaxies. These distributions showed a more irregular structure with respect to the angular data with the appearance of superclusters and large voids. This three dimensional picture did not show any more a clear tendency towards homogenization and was in contrast with the angular data. This conflictual situation found an apparent solution with the first statistical analysis of the CfA1 galaxy catalogue. In fact, this analysis identified a small correlation length of only 5 Mpc in a catalogue that showed structures of much larger sizes. The statistical analysis appeared therefore to provide a way out such that large structures can be compatible with small correlation lengths.

In the following years the situation evolved in a dramatic way because deeper and deeper surveys showed larger and larger structures that appeared difficult to reconcile with such a small correlation length. In addition the catalogues of clusters gave a correlation length of 25 Mpc, five times larger than the one of galaxies, even though the clusters are made themselves of galaxies. In the end the most popular picture is that clusters and galaxy structures require different theories because their correlation show different amplitudes. A linear theory is necessary for clusters while a non linear theory should be adopted for galaxies. The large scale structures can be compatible with small correlation lengths and with a large scale homogeneity because the amplitudes of the structures becomes smaller the larger is the structure.

In the past years we have challenged this picture by showing that it arises from a mathematical inconsistency in the characterization of the galaxy and cluster correlations. Our main result is that a correct analysis of the data shows fractal correlations up to the present observational limits. The galaxy-cluster mismatch disappears and the visible universe is characterized by a multifractal distribution of matter when the galaxy masses are also included. This requires a radical change of perspective for the properties of the universe and for the theoretical methods that one should use to describe it.

We have extended the results of Coleman & Pietronero (1992) by analyzing new and deeper redshift surveys such as Perseus Pisces, Stromlo-APM, SSRS1, IRAS, Las Campanas, LEDA and ESP for galaxies and various subsamples fo the Abell and ACO catalogs for clusters. These new analysis are in complete agreement with those of Coleman & Pietronero (1992): the fractal structure with D=2 extends up to 150 Mpc in Perseus-Pisces and LEDA, while it arrives up to 900 Mpc in the ESP survey.

We have studied in detail the possible correlation between the space and the luminosity properties of visible matter, finding in particular that the Schechter luminosity function can be naturally explained considering the multifractal nature of galaxy distribution. Moreover we have considered the finite size effects due to the lower cut-off of the fractal structure, for the determination of various observable quantities such as the number counts and the angular correlation function. Such an analysis allows us to explain the main features of these observational relations. In particular, we can re-interpret the experimental situation of the galaxy counts and show that it represents a clear evidence that the visible matter is fractal distributed up to the deepest probed scale.

We have clarified also the problem of the determination of the power spectrum in the case of self-similar distributions. Moreover we have considered in detail the consequences of the fractal distribution of matter in relation to the various cosmological scenarios. Finally we have developed a stochastic model. to study a mechanism that can lead to the observed fractal and multifractal distribution.

The natural evolution of these studies in the near future will be along the following lines:

On one hand we would like to put our observational conclusions on a firm basis by analyzing the new catalogs that may become available in the next months (CfA2 , SSRS2)

On the other hand we have already started a study of the theoretical consequences of our new picture. In particular this will require more cooperation of interdisciplinary type between astrophysics and statistical physics. For example, apart from the problem of the eventual crossover towards homogeneity, galaxy structures are certainly fractal. This imply a change of perspective from the theoretical side that should focus more on the critical exponent rather than the amplitude of correlations. In fact, the main theoretical consequence is that one should not discuss a self-similar structure in terms of amplitude of correlation, but the only meaningful quantity is the exponent that characterizes the power law behavior.

An important point in the theoretical investigation concerns the distribution of the newtonian graviational force inside a fractal structure. This problem has never been investiaged so far. We are attempting to describe such a distribution using both numerical simulations and an analytical approach (in collaboration with Prof.R. Durrer). Another related point is the amplitude of the fluctuations of the gravitational potential.

Finally it is important to mentiion that a very contraversial point in debate about fractal versus homogeneous universe is represented by the angular properteis of fractal sets. We are studying this problem also in collaboration with Prof. R. Durrer and Prof. J-P. Eckmann,

References

Before 1997

• L. Pietronero, "The Fractal Structure of the Universe: correlations of galaxies and clusters and the average mass density", Physica A. 144, 257 (1987).
• P.H. Coleman, L. Pietronero, Sanders R.H. " Absence of any characteristic length in the CFA catalogue", Astron.& Astrophys. 245, 1 (1988)
• P.H. Coleman e L. Pietronero "The Fractal Structure of the Universe", Physics Reports 213, 311 (1992)
• F. Sylos Labini "Isotropy, homogeneity and dipole saturation" Astrophys. J. 433, 464-67, (1994)
• Yu. V. Baryshev, F. Sylos Labini, M. Montuori and L. Pietronero "Facts and ideas in modern cosmology" Vistas in Astronomy, 38, 419-500, (1994)
• L. Pietronero and F. Sylos Labini "Cosmological Principle and the debate on Large Scale Structures distribution" Proc. of the workshop: "Birth of the Universe and fundamental Physics" F. Occhionero editor, Springer Verlag, 17, (1995)
• F. Sylos Labini and L. Pietronero "Stochastic aggregation model for the multifractal distribution of matter" Proc. of the workshop: "Birth of the Universe and fundamental Physics" F. Occhionero editor, Springer Verlag, 317, (1995) 1996
• F. Sylos Labini, A. Gabrielli, M. Montuori and L. Pietronero "Finite size effects on the galaxy number counts: evidence for fractal behavior up to the deepest scale" Physica A, 266, 195 (1996)
• H. Di Nella, M. Montuori, G. Paturel L. Pietronero F. Sylos Labini "Long-range (fractal) correlations in the LEDA database" Astronom. & Astrophys. Lett 308, L33 (1996)
• F. Sylos Labini & L. Amendola "The power spectrum in a strongly inhomogeneous Universe" Astrophys.J.Lett., 468, L1 (1996)
• F. Sylos Labini and L. Pietronero " Multifractal properties of visible matter" Astrophysical Letters and Communications 36, 49 (1996)
• F. Sylos Labini & L. Pietronero "Multifractality as a link between space and luminosity distributions" Astrophys. J., 469 28 (1996)
• F. Sylos Labini, M. Montuori and L. Pietronero "Statistical analysis of the Perseus-Pisces redshift survey: spatial and luminosity properties" Physica A, 230, 336-358 (1996)
• F. Sylos Labini and L. Pietronero "Statistical properties of galaxy distributions" Non Linear Process in Geophysics 3, 274-283 (1996)

1997

• H. Di Nella and F. Sylos Labini "How can we measure a correlation length of 5-10 Mpc when observations show structures extended over 150 Mpc ?" Astrophysical Letters and Communications 36, 33-39 (1997)
• L. Pietronero, M. Montuori and F. Sylos Labini "The debate of galaxy correlations and its theoretical implications" Astrophysical Letters and Communications 36, 65-73 (1997) F. Sylos Labini and L. Amendola "Power Spectrum for fractal fractal distributions" Astrophysical Letters and Communications 36, 50-63 (1997)
• F. Sylos Labini, M. Montuori and L. Pietronero "Scaling Properties of the Perseus-Pisces Redshift Survey Astrophysical Letters and Communications 36, 265-271 (1997)
• L. Pietronero, M. Montuori and F. Sylos Labini "On the Fractal structure of the visible Universe" Proc. of the Conference "Critical Dialogues in Cosmology" Ed. N. Turok, World Scientific , 24-29 (1997)
• F. Sylos Labini, L. Pietronero, Montuori M. "Frequently asked questions about fractals" in the Proceedings of the Ringberg Conference, Eds. T. Buchert, P. Schneider and F.v. Feilzsch 109-136 (1997)
• M. Montuori, F. Sylos Labini, A. Amici "Correlation Properties of Cluster Distribution" Physica A 246 1-17 (1997)
• R.Durrer, J.-P. Eckmann, F. Sylos Labini, M. Montuori, L.Pietronero "Angular Projection of Fractal Sets"
• Eurpohys. Lett. 40, 491-496 (1997) M. Montuori, F. Sylos Labini, A. Gabrielli, A. Amici and L. Pietronero " Galaxy number counts and fractal correlations"; Europhys Letters 39, 103-108 (1997)
• M. Montuori and F. Sylos Labini, " Angular correlations of galaxy distribution"; Astrophys. J. Letters 487, L1-L4 (1997).
• L. Amendola, H. Di Nella, M. Montuori, and F. Sylos Labini " Statistical properties of the LEDA redshift database " Fractals 5 No. 4 (1997)
• L. Pietronero, M. Montuori and F. Sylos Labini "An intorduction to the statistical properties of galaxy distribution" " Proc. of the Conf. "Generation of Cosmological Large Scale Structures"
• D.N. Schramm nd P. Galeotti Eds. Dorotech: Kluwer Academy, p.105-122 (1997)

1998

• F. Sylos Labini, M. Montuori and L. Pietronero "Scale Invariance of galaxy clustering" Physics Reports, 293, 61-226 (1998)
• F. Sylos Labini and M. Montuori " Scale Invariance properties of the Stromlo-APM catalog"; Astron & Astrophys 331, 809.
• L. Pietronero, F. Sylos Labini and M. Montuori "Correlation properties of the large scale matter distribution and galaxy number counts Proc. of the Conference Erice Chalonge Course" N. Sanchez and A. Zichichi Eds. World Scientific. NATO-ASI Series, pp.603-646 (1998)
• M. Montuori, F. Sylos Labini and L. Pietronero " On the Average Density of Galaxies" Proc. of the Conference "Birth of the Universe II" Ed. F. Occhionero. Kluwer (1998)
• L. Pietronero, F. Sylos Labini and M. Montuori " The Visible Universe at the Light of Modern Statistical Physics " Proc. of the "4eme Colloque cosmologie Observatoire de Paris" N. Sanchez and H. de Vega Editors. (1998)
• L. Pietronero, M. Montuori and F. Sylos Labini " Statistical properties of galaxy distribution " Proc. of the Conf. "Topological Difects in Cosmology" F. Melchiorri and M. Signore Eds. World Scientific, pp.225-239 (1998)
• L. Pietronero, M. Montuori and F. Sylos Labini "The fractal structure of the Universe" Italian Edition of "Scientific American" 354, 41 (1998)
• F. Sylos Labini, M. Montuori and L. Pietronero "Multifractality in the large scale distribution of galaxies" Proceedings of Conference "Dirsorder and Chaos" A. Vulpiani Ed. Journal de Physique, in press (1998)
• F. Sylos Labini, M. Montuori and L. Pietronero " Comment on the paper by L. Guzzo 'Is the Universe homogeneous� Submitted to New Astronomy , (1998)
• Yu. Baryshev, F. Sylos Labini, M. Montuori, L. Pietronero and P. Teerikorpi "the fractal structure of galaxy distribution and its implication for cosmology " Fractals 6 231-244 , (1998)
• R. Durrer and F. Sylos Labini, " A Fractal galaxy distribution in an homogeneous universe ?" Astron. Astrophys. Lett., 339, L85-L88 (1998)
• F. Sylos Labini. "Galaxy distributions: introduction to the basic properties " Proceedings of the Erice-course, "New Vistas in Astrophysics" Science and Culture Series - Astrophysics. Editors Wefel and Shapiro (1999) In the press.
• F. Sylos Labini, " Fractals and the galaxy distribution " To appear in the Proceedings of the 2nd Intas Meeting "Fundamental problems in classical, quantum and string gravity" (1999)
• L. Pietronero & F. Sylos Labini, "Scale invariance in galaxy structures: general concepts and application to the most recent data " To appear in the Proceedings "VI Colloque de Cosmologie" Paris 4-6 June (1998)
• F. Sylos Labini, " On the fractal structure of the universe: methods, results and theoretical implication. " In the Proceedings of the conference "Dark Matter 1998", Editors H.V. Klapdor-Kleingrothaus and L. Baudis (1999)
• F. Sylos Labini, " Scale invariance of galaxy clustering: implications for Dark Matter" Proc. of the conference "2nd International Workshop on the Identification of Dark Matter" World Scientific, p.42-49 (1999)

1999

• A. Gabrielli, F. Sylos Labini, S. Pellegrini. " Gravitational force distribution in fractal structures " Europhysics Letters (1999), 46, 127-133
• M. Joyce, M. Montuori, F. Sylos Labini " Fractal correlations in the CfA2 -south galaxy redshift survey" Astrophys.J.Letters, 514, L5-l8 (1999)
• M. Joyce, M. Montuori, F. Sylos Labini and L. Pietronero "Comment on the paper 'The ESO Slice Project galaxy redshift survey: V. Evidence for a D=3 sample dimensionality'" Astron.Astrophys., 344, 387-392 (1999)
• Luciano Pietronero, Francesco Sylos Labini " Reconstructing the cosmological puzzle " In the proceedings of the "VI Colloque de Cosmologie" Paris 16-18 June 1999

2000

• A. Gabrielli, F. Sylos Labini and R. Durrer " Biasing in Gaussian random fields and galaxy correlations " Astrophysical Journal Letters 531, L1-L4, (2000)
• M. Joyce, P. W. Anderson, M. Montuori, L. Pietronero and F. Sylos Labini " Fractal Cosmology in an Open Universe " Europhysics Letters 49 (2000) 416-422
• L. Pietronero, M. Joyce, M. Montuori and F. Sylos Labini " Complexity in Cosmology " In the Proceedings of the "ASPEN WINTER CONFERENCE IN CONDENSED MATTER 'FIFTY YEARS OF CONDENSED MATTER PHYSICS' " January 9-15, 2000 (Aspen, USA) (2000)
• Luciano Pietronero, Francesco Sylos Labini "Fractal structures and the large scale distribution of galaxies" In the proceedings of the 7th Course in astrofundamental physics, Nato Advanced Study Institute,International Euroconference Erice, 5-16 December 1999
• F. Sylos Labini and A. Gabrielli " Scaling and fluctuations in galaxy distribution: two tests to probe large scale structures " Proceedings from ``Virtual Observatories of the Future'' edited by R. J. Brunner, S. G. Djorgovski, A. Szalay
• F. Sylos Labini and A. Gabrielli "Correlation and clustering " To appear proceedings of the NATO Advanced Study Institute ``Astrophysical Sources of High Energy Particles & Radiation'' Erice (Italy) 11-21 November 2000
• L. Pietronero and F. Sylos Labini "Fractals Universe" in the Proceedings of "Statistical mechanics and strongly correlated systems" conference in Rome (Italy), September 27-29 (1999) - Physica A, 280, 125, (2000)

2001

• F. Sylos Labini and L. Pietronero " Complexity in Cosmology" In the proceedings of the Erice Course in astrofundamental physics, Nato Advanced Study Institute, International Euroconference Erice, Ettore Majorana Centre December 2000 N. Sanchez and A. Zichichi Editors.NATO-ASI (2001)
• M. Joyce and F. Sylos Labini "Luminosity density estimation from redshift surveys and the mass density of the Universe " Astrophysical Journal Letters In The Press (2001)
• A. Gabrielli and F. Sylos Labini "Fluctuations in galaxy counts: a new test for homogeneity versus fractality" Europhys. Lett. 54 (3), pp. 286-292 (2001)

2002

• M. Montuori and L. Pietronero The debate of galxy space distribution: an overview in "Modern Cosmology" edited by Bonometto S., Gorini V., Moschella U., IoP (2002)
• M. Montuori, L. Pietronero and M. Bottaccio Clustering in galaxy distributions: comparison between redshift surveys Physica A 305 (1-2), 242 (2002)
• F. Pompilio and M. Montuori "An inhomogeneous cosmological fractal model" Class. and Quant. Cosmol., 19, 203 (2002)
• L. Pietronero, A. Gabrielli and F. Sylos Labini "Statistical Physics for Cosmic Structures" Proceedings of the Conference "StatsPhys21" Cancun (Mexico) July 15-21 2001; Phys. A 306, 395 (2002)

2003

• A. Gabrielli, M. Joice and F. Sylos Labini "Real Space statistical properties of standard cosmological models" to appear in the 7th Granada Seminar on Computational Physics - AIP Conference Proceedings (2003)
• F. Sylos Labini, T. Baertschinger, A. Gabrielli and M. Joyce "Initial conditions, Discreteness and non-linear structure formation in cosmology" to appear in Proceedings of 9th Course on Astrofundamental Physics, International School D. Chalonge, Kluwer, ed. N. G. Sanchez and Y. M. Pariiski (2003)

Contact

Luciano Pietronero

Fermi building, room n.108 phone +39-06-4991-3488

Marco Montuori ; Francesco Sylos Labini

Fermi building, room n. 206 (003) phone +39-06-4991-3450 (or -3442)