arXiv subjects

F. Sylos Labini

Publications and source records attributed to F. Sylos Labini.

At least 37 records · Page 2Linked to original sources

arXiv2000

Fractal Cosmology in an Open Universe

The clustering of galaxies is well characterized by fractal properties, with the presence of an eventual cross-over to homogeneity still a matter of considerable debate. In this letter we discuss the cosmological implications of a fractal distribution of matter, with a possible cross-over to homogeneity at an undetermined scale R_{homo}. Contrary to what is generally assumed, we show that, even when R_{homo} -> \infty, this possibility can be treated consistently within the framework of the expanding universe solutions of Friedmann. The fractal is a perturbation to an open cosmology in which the leading homogeneous component is the cosmic background radiation (CBR). This cosmology, inspired by the observed galaxy distributions, provides a simple explanation for the recent data which indicate the absence of deceleration in the expansion (q_o \approx 0). Correspondingly the `age problem' is also resolved. Further we show that the model can be extended back from the curvature dominated arbitrarily deep into the radiation dominated era, and we discuss qualitatively the modifications to the physics of the anisotropy of the CBR, nucleosynthesis and structure formation.

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arXiv1999

Comment on the paper ``The ESO Slice Project galaxy redshift survey: V. Evidence for a D=3 sample dimensionality''

In a recent analysis of number counts in the ESP survey Scaramella et al. (1998) claim to find evidence for a cross-over to homogeneity at large scales, and against a fractal behaviour with dimension $D \approx 2$. In this comment we note firstly that, if such a cross-over exists as described by the authors, the scale characterizing it is ~ 100 - 300 Mpc/h. This invalidates the ``standard'' analysis of the same catalogue given elsewhere by the authors which results in a ``correlation length'' of only r_0 = 4 Mpc/h. Furthermore we show that the evidences for a cross-over to homogeneity rely on the choice of cosmological model, and most crucially on the so called K corrections. We show that the D ~ 3 behaviour seen in the K-corrected data of Scaramella et al. is in fact unstable, increasing systematically towards D=4 as a function of the absolute magnitude limit. This behaviour can be quantitatively explained as the effect of an unphysical K-correction in the relevant range of red-shift (z ~ 0.1- 0.3). A more consistent interpretation of the number counts is that D is in the range 2 - 2.5, depending on the cosmological model, consistent with the continuation of the fractal D ~ 2 behaviour observed at scales up to ~100 Mpc/h. This implies a smaller K-correction. Given, however, the uncertainty in the effect of intrinsic fluctuations on the number counts statistic, and its sensitivity on these large scales to the uncertain K corrections, we conclude that it is premature to put a definitive constraint on the galaxy distribution using the ESP data alone.

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arXiv1999

Fractal correlations in the CfA2-South redshift survey

We report our analysis of the properties of galaxy clustering for a new redshift sample of galaxies, the CfA2-South catalog, using statistical methods which do not rely on the assumption of homogeneity. We find that, up to ~ 20 Mpc/h, which is the largest scale to which correlation properties can be reliably inferred, the galaxy clustering is scale-invariant and characterized by a fractal dimension D=1.9 \pm 0.1. Further there is no statistical evidence for homogeneity at any of the larger scales (up to ~150 Mpc/h) probed more weakly by the catalog. These results means that characteristic ``correlation lengths'' for the clustering of galaxies derived using standards methods of analysis are not meaningful. Further the results are very consistent with those obtained from many other catalogs using the methods adopted here, which show the D =2 fractal continuing to beyond 100 Mpc/h. The incompleteness of the relevant data conjectured by various authors to give rise to such behaviour is therefore proved to have no significant effect (up to 20 Mpc/h) on the measured correlations.

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arXiv1999

Gravitational force distribution in fractal structures

We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size effects. For dimensions smaller than d-1 (being $d$ the space dimension) the convergence of the net gravitational force is assured by the fast decaying of the density, while for fractal dimension D>d-1 the morphological properties of the structure determine the eventual convergence of the force as a function of distance. We clarify the role played by the cut-offs of the distribution. Some cosmological implications are discussed.

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arXiv1998

Comment on the paper by L. Guzzo "Is the Universe homogeneous ?"

This comment is in response to the paper by L. Guzzo recently appeared in ``New Astronomy'' related to our work. The subject of the discussion concerns the correlation properties of galaxy distribution in the available 3-d samples. There is a general agreement that galaxy structures exhibit fractal properties, at least up to some scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are still matter of debate. Here we briefly summarize our point of view by discussing three main topics. The first one is methodological, i.e. we clarify which are the correct methods to detect the real correlations properties of the 3-d galaxy distribution. Then we discuss the results of the analysis of several samples in two ranges of scales. In the first range of scale, below $100 ÷200 \hmp$, the statistical quality of the data is rather good, and we find that galaxy distribution has fractal properties with $D \approx2$. At larger distances the statistical robustness of the present data is weaker, but, we show that there is evidence for a continuation of the fractal behavior, without any tendency towards homogenization.

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arXiv1997

Statistical properties of the LEDA redshift database

We present the statistical properties of large scale galaxy distribution in the LEDA redshift database. This catalog contains more than 40,000 redshifts over all the sky. We find that LEDA, although seriously affected by incompleteness, shows quite stable statistical properties. In particular, we have considered the behaviour of the two points correlation function and of the power spectrum of the density fluctuations, and we have done several tests to check whether the incompleteness of the catalog affect these statistical quantities. Our conclusion is that galaxy distribution in this catalog has fractal properties up to the distance 200 Mpc with D = 2.1 \pm 0.2, with no sign towards homogeneity: this result is statistically stable. We analyze also the properties of the angular distributions, finding a complete agreement with the results obtained in redshift space. Finally, we compare these results with those obtained in other redshift surveys, finding that this sample well reproduces the properties of galaxy distribution found in the different catalogs.

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arXiv1997

Scale-invariant properties of the APM-Stromlo survey

We investigate the statistical properties of the APM-Stromlo redshift survey by using the concepts and methods of modern Statistical Physics. We find that galaxy distribution in this survey exhibits scale invariant properties with fractal dimension $D = 2.1 \pm 0.1$, up to $\sim 40 \hmp$, i.e. the limit of its statistical validity, without any tendency towards homogenization. No intrinsic characteristic scales are definitely found in this galaxy sample. We present several tests to study the statistical reliability of the results. \

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arXiv1997

Scale-invariance of galaxy clustering

Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not homogeneous up to the limits of the available catalogs. The usual statistical methods, which are based on the assumption of homogeneity, are therefore inconsistent for all the length scales probed so far, and a new, more general, conceptual framework is necessary to identifythe real physical properties of these structures. In the last few years the 3-d catalogs have been significatively improved and we have extended our methods to the analysis of number counts and angular catalogs. This has led to a complete analysis of all the available data that we present in this review. The result is that galaxy structures are highly irregular and self-similar: all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed so far ($1000 \hmp$) and even more as indicated from the new interpretation of the number counts. The evidence for scale-invariance of galaxy clustering is very strong up to $150 \hmp$ due to the statistical robustness of the data but becomes progressively weaker (statistically) at larger distances due to the limited data. In These facts lead to fascinating conceptual implications about our knowledge of the universe and to a new scenario for the theoretical challenge in this field.

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arXiv1997

Correlation properties of the large scale matter distribution and galaxy number counts

We introduce the basic techniques used for the analysis of three dimensional and two dimensional galaxy samples. We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension $D \simeq 2$) up to the present observational limits without any tendency towards homogenization. This result points to a new interpretation of the galaxy number counts. We show that an analysis of the small scale fluctuations allows us to reconcile the correlation analysis and the number counts in a new perspective which has a number of important implications.

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arXiv1997

On the Average Density of Galaxies

The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a crossover to an homogeneous one at large scale. However up to now, the quantitative determination of this presumed homogeneity scale is still lacking. Contrary to such expectations, observational results show, in fact, a very inhomogeneous galaxy distribution. Some years ago we criticise the standard statistical approach and proposed a new one based on the concepts and methods of modern statistical analysis. The main result of new analysis is that, contrary to the conclusion of standard methods, the distribution of galaxies in the available samples, does not show any crossover to homogeneity, but has fractal correlations (with dimension $D \approx 2$) up to the limits of present three dimensional catalogs ($\approx 1000 h^{-1} Mpc$). The very first consequence of this result is that the standard approach is incorrect for all the length scale probed until now; moreover it calls for fascinating conceptual implication for the theoretical challenge in this field.

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arXiv1997

The Visible Universe at the Light of Modern Statistical Physics

In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop spontaneously correlations with power law behaviour both in space and time. Pattern formation, aggregation phenomena, biological systems, geological systems, disordered materials, clustering of matter in the universe are just some of the fields in which scale invariance has been observed as a common and basic feature. However, the fact that certain structures exhibit fractal and complex properties does not tell us why this happens. A crucial point to understand is therefore the origin of the general scale-invariance of natural phenomena. This would correspond to the understanding of the origin of fractal structures and of the properties of Self- Organized Criticality (SOC) from the knowledge of the microscopic physical processes at the basis of these phenomena. Fractal geometry can play a crucial role in extracting the correct physical properties from experimental data. In particular, the recent availability of complete three dimensional samples of galaxies and clusters permits a direct study of their spatial properties. We present a brief review of galaxy correlations based on the methods of modern Statistical Physics. These methods are able to identify self-similar and non-analytical properties, and allow us to test the usual homogeneity assumption of luminous matter distribution. The new analysis shows that all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed until now ($1000 \hmp$)

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arXiv1997

Galaxy number counts and Fractal correlations

We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension $D \simeq 2$) up to the present observational limits ($\approx 150 \hmp$) without any tendency towards homogenization. This result points to a new interpretation of the number counts that represents the main subject of this letter. We show that an analysis of the small scale fluctuations allows us to reconcile the correlation analysis and the number counts in a new perspective which has a number of important implications.

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arXiv1997

Correlation Properties of Cluster Distribution

We analyze subsamples of Abell and ACO cluster catalogs, in order to study the spatial properties of the large scale matter distribution. The subsamples analyzed are estimated to be nearly complete and are the standard ones used in the correlation analysis by various authors. The statistical analysis of cluster correlations is performed without any assumptions on the nature of the distribution itself. The cluster samples show fractal correlations up to sample limits ($\approx 70 h^{-1} Mpc$) with fractal dimension $D \approx 2$, without any tendency towards homogenization. Our analysis shows that the standard correlation methods are incorrect, since they give a finite correlation length for a distribution that does not possess one. In particular, the so called correlation length $r_{0}$ is shown to be simply a fraction of the sample size. Moreover we conclude that galaxies and clusters are two different representations of the same self similar structure and that the correlations of clusters are the continuation of those of galaxies to larger scales.

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arXiv1997

Frequently asked questions about fractals

In this lecture we will try to address the "frequently asked questions about fractals" in the field of large scale galaxy distribution. This paper takes its origin from a very interesting discussion we had at this meeting. A lot of points were raised, and we try to make clear the fundamental ones.

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arXiv1996

On the Fractal Structure of the Visible Universe

Some years ago we proposed a new approach for the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical physics. This led to the surprising result that galaxy correlations are fractal and not homogeneous up to the limits of the available catalogues. In the meantime many more redshifts have been measured and we have extended our methods also to the analysis of number counts and angular catalogues. This has led to a complete analysis of all the available data that we are going to present in detail in this lecture. In particular we will discuss the properties of the following catalogues: CfA, Perseus-Pisces, SSRS, IRAS, LEDA, Las Campanas and ESP for galaxies and Abell and ACO for clusters. The usual statistical methods, that are based on the assumption of homogeneity, are therefore inconsistent for all the length scales probed until now. A new, more general, conceptual framework is necessary to identify the real physical properties of these structures. In the range of self-similarity theories should shift from "amplitudes" to "exponents". The new analysis shows that all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed until now ($1000 h^{-1}Mpc$) and even more as indicated from the new interpretation of the number counts. The distribution of luminous matter in the universe is therefore fractal and not homogeneous. The evidence for this being very strong up to $150 h^{-1}Mpc$ due to the statistical roboustness of the data and progressively weaker (statistically) at larger distances due to the limited data. These facts lead to fascinating conceptual implications about our knowledge of the universe and to a new scenario for the theoretical challenge in this field.

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arXiv1996

Finite size effects on the galaxy number counts: evidence for fractal behavior up to the deepest scale

We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various data that are considered as pointing to a homogenous distribution are all affected by these spurious effects and their interpretation should be completely changed. In particular, we show that finite size effects strongly affect the determination of the galaxy number counts, namely the number versus magnitude relation ($N(<m)$) as computed from the origin. When one computes $N(<m)$ averaged over all the points of a redshift survey one observes an exponent $α= D/5 \approx 0.4$ compatible with the fractal dimension $D \approx 2$ derived from the full correlation analysis. Instead the observation of an exponent $α\approx 0.6$ at relatively small scales, where the distribution is certainly not homogeneous, is shown to be related to finite size effects. We conclude therefore that the observed counts correspond to a fractal distribution with dimension $D \approx 2$ in the entire range $12 \ltapprox m \ltapprox 28$, that is to say the largest scales ever probed for luminous matter. In addition our results permit to clarify various problems of the angular catalogs, and to show their compatibility with the fractal behavior. We consider also the distribution of Radio-galaxies, Quasars and $γ$ ray burst, and we show their compatibility with a fractal structure with $D \approx 1.6 ÷1.8$. Finally we have established a quantitative criterion that allows us to define and {\em predict} the statistical validity of a galaxy catalog (angular or three dimensional).

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arXiv1996

Long-range (fractal) correlations in the LEDA database

All the recent redshift surveys show highly irregular patterns of galaxies on scales of hundreds of megaparsecs such as chains, walls and cells. One of the most powerful catalog of galaxies is represented by the LEDA database that contains more than 36,000 galaxies with redshift. We study the correlation properties of such a samplefinding that galaxy distribution shows well defined fractal nature up to R$_s \sim 150 h^{-1}Mpc $ with fractal dimension $D \approx 2$. We test the consistency of these results versus the incompleteness in the sample.

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arXiv1995

The debate of galaxy correlations and its theoretical implications

We discuss the problem of galaxy correlations by considering the various methods by which this information can be obtained. We focus in particular on the volume limited three dimensional samples and discuss a new way to increase the scale of their statistical validity. From our previous results and the most recent ones on all the available catalogues we conclude that galaxy correlations show fractal properties with dimension $ D \approx 2$ up to the present observational limits ($200-800 \hmp$ depending on the catalogue) without any tendency towards homogenization. We also discuss the compatibility of this result with the galaxy counts as a function of magnitude and the angular catalogues. A new picture emerges which changes the standard ideas about the properties of the universe and requires a corresponding change in the theoretical concepts that one should use to describe it.

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