Fractal structures and the large scale distribution of galaxies

Pietronero, L.; Labini, Francesco Sylos

doi:10.1007/978-94-010-0748-1_19

Cited by 3 publications

(2 citation statements)

References 38 publications

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“…It is now well-established that the universe is fractal at small scales (r < lOh-1Mpc) (Durrer and Labini, 1998;Sylos Labini, 1999;Joyce et al , 1999;Pietronero and Sylos Labini, 2001). It is now well-established that the universe is fractal at small scales (r < lOh-1Mpc) (Durrer and Labini, 1998;Sylos Labini, 1999;Joyce et al , 1999;Pietronero and Sylos Labini, 2001).…”

Section: Introductionmentioning

confidence: 99%

Astronomical Image and Data Analysis

Starck

Murtagh

2002

Astronomy and Astrophysics Library

185

162

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Cover picture: Five-minute exposure (five 60-second dithered and stacked images), R filter, taken with CFH12K wide-field camera (100 million pixels) at the primary focus ofthe CFHT in July 2000. The image is from an extremely rich zone of our Galaxy, containing star formation regions, dark nebulae (molecular c10uds and dust regions), emission nebulae (Ha regions), and evolved stars which are scattered throughout the field in their two-dimensiona1 projection effect. This zone is in the constellation of Sagittarius. (©Canada-France-Hawaii Telescope, J.-C. Cuillandre,

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Section: Introductionmentioning

confidence: 99%

Astronomical Image and Data Analysis

Starck

Murtagh

2002

Astronomy and Astrophysics Library

185

162

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“…The large-scale structure of the Universe has been extensively studied since the publication of the first galaxy surveys. Some analysis with high-redshift samples show the existence of fractal correlations [8,25,23,31], where the large network of matter filaments that connect galaxies is characterized by fractal structures [34,21,45,46]. In a cosmological context, fractals were introduced into a model by Mandelbrot as a hypothesis to solve the Olbers paradox [32].…”

Section: Introductionmentioning

confidence: 99%

Effect of observational holes in fractal analysis of galaxy survey masks

García-Farieta

Casas-Miranda

2018

Chaos, Solitons & Fractals

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Cosmological observations reveal that the Universe has a hierarchy of galaxy clustering with a transition to homogeneity on large scales according to the ΛCDM model. On the other hand some observational estimates suggest a multifractal behavior where galactic clustering is based on generalization of the correlation dimension. From this point of view, we study the influence of veto areas on fractal measurements in masks of galaxy surveys. Particularly we investigate if these holes can produce fractal behaviors or modify the scale of cosmic homogeneity. From the footprint of the Baryon Oscillation Spectroscopic Survey (BOSS) data release (DR12), we build a homogeneous sample following the radial selection function for 73, 412 points limited to the redshift range 0.002 < z < 0.2. Different percentages of observational holes were created cumulatively in right ascension and declination on the sample. For the synthetic sample and for a real sample of galaxies we determined the fractal dimension D q (r) in the range 2 ≤ q ≤ 6 using the sliding window technique to characterize the spatial point distribution. Our results show that generalized dimension varies with the scale, for low scales there are a fractal behavior with fluctuations for all hole percentages studied and for larger scales than 113 M pc/h the statistical homogeneity is achieved in concordance with other analysis. We find that observational holes cause a shift in the homogeneity scale r H , in particular for all synthetic samples with percentages of holes between 0 − 10% the homogeneity scale is reached at (83 ± 1)Mpc/h while the fractal dimension changes as 2.83 ±0.09 ≤ D q ≤ 2.855 ±0.09 . For synthetic samples with percentages of holes greater than 10%, we find that the value of r H increases proportionally. Consequently future results about homogeneity scale based in fractal analyses must be corrected by observational holes and regions of incompleteness in the geometry of the galaxy catalogue if the size of the veto mask is significant.

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Modified Friedmann equations and fractal Black Hole thermodynamics

Davood Sadatian,

Gholame

2024

Int. J. Geom. Methods Mod. Phys.

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The general relativity unification and quantum theory is a significant open problem in theoretical physics. This problem arises from the fact that these two fundamental theories, which describe gravity and the behavior of particles at the microscopic level, respectively, are currently incompatible. The unification of these theories is crucial for a complete comprehension of the fundamental forces and the nature of the universe. In this regard, the quantum properties of a Black Hole result in fundamental importance. By analyzing such properties in quantum field theory, in the first step, the gravity enters as a classical background. In semi-classical approximation, Black Holes will emit Hawking radiation with an almost thermal spectrum, while Black Hole’s entropy is proportional to the Black Hole’s horizon. Besides, Hawking’s temperature and Black Hole entropy should follow the first law of Black Hole thermodynamics. Also, Jacobson [Thermodynamics of spacetime: The Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260, https://doi.org/10.1103/PhysRevLett.75.1260 ] showed shown that there is a connection between Black Hole thermodynamics and Einstein’s equation that opens the root of a potential thermodynamic nature of gravity. This issue opened a new impressive research framework in which the Einstein field equation can be expressed as a form of the first law of thermodynamics and vice versa. In this study, it is assumed that the universe has a fractal structure. Accordingly, modified Friedmann’s equations and the Black Holes thermodynamics in a fractal universe have been examined. The fractal framework shows what features and changes occur in the description of the universe, particularly in studying the thermodynamics of a Black Hole. However, the paper strategy is organized as follows: in the beginning, we consider the first thermodynamic law in a fractal universe. Then, we investigate the Friedmann equation of the fractal universe in the form of the entropy balance, this means [Formula: see text], where [Formula: see text] and [Formula: see text] are the thermal energy and horizon temperature. We consider the entropy [Formula: see text] have two terms; (1) obeys the usual area law and (2) the entropy production term due to the non-equilibrium thermodynamics of a fractal universe. Therefore, in a fractal universe, a term with non-equilibrium thermodynamics of spacetime may be needed. Also, we study the generalized second law of thermodynamics in a fractal universe. When the temperature of the apparent horizon and the temperature of the matter fields inside the horizon are equal, i.e. [Formula: see text], the second law of generalized thermodynamics can be obtained according to the state parameter range equation, which is consistent with the recent observations. Finally, in Sec. 6, based on the mathematical calculations, we study the various cosmological parameters such as the Hubble parameter, scale factor, deceleration parameter and equation of state parameter.

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Fractal structures and the large scale distribution of galaxies

Cited by 3 publications

References 38 publications

Astronomical Image and Data Analysis

Astronomical Image and Data Analysis

Effect of observational holes in fractal analysis of galaxy survey masks

Modified Friedmann equations and fractal Black Hole thermodynamics

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