Related papers: The Apparent Fractal Conjecture
We apply the property of selfsimilarity that corresponds to the concept of a fractal universe, to the dimension of time. It follows that any interval of time, given by any tick of any clock, is proportional to the age of the universe. The…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
The Hubble diagram is one of the cornerstones of observational cosmology. It is usually analysed assuming that, on average, the underlying relation between magnitude and redshift matches the prediction of a…
An important part of cosmological model fitting relies on correlating distance indicators of objects (for example type Ia supernovae) with their redshift, often illustrated on a Hubble diagram. Comparing the observed correlation with a…
The Cosmological Principle is the assumption that the universe is spatially homogeneous and isotropic in the large-scale average. In year 1998 the author, together with his two colleagues, has shown that the BATSE's short gamma-ray bursts…
The universe is not isotropic or spatially homogeneous on local scales. The averaging of local inhomogeneities in general relativity can lead to significant dynamical effects on the evolution of the universe and on the interpretation of…
The presence of dark energy in the Universe is inferred directly and indirectly from a large body of observational evidence. The simplest and most theoretically appealing possibility is the vacuum energy density (cosmological constant).…
Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the…
Hierarchical theories of structure formation predict that clusters of galaxies should be embedded in a web like structure, with filaments emanating from them to large distances. The amount of mass contained within such filaments near a…
The cosmological implications from a new estimate of the local X-ray galaxy cluster abundance are summarized. The results are then compared to independent observations. It is suggested that `low' values for the mean cosmic matter density…
The paper uses geometrical arguments to derive equations with relevance for cosmology; 5-dimensional spacetime is assumed because it has been shown in other works to provide a setting for significant unification of different areas of…
From a fractal perspective, the entropy bound of gravitational systems undergoes changes. Furthermore, in the cosmological setting, the conservation law of a perfect fluid is also altered in such systems, affecting spatial elements like…
While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a non-trivial topology will generate pairs of matching circles of…
The quantum model of homogeneous and isotropic universe filled with the uniform scalar field is considered. This model predicts effective inverse square-law dependence of the mean total energy density <\rho> on the expectation value of…
This paper summarizes the physical mechanisms that encode the type and quantity of cosmological matter in the properties of large-scale structure, and reviews the application of such tests to current datasets. The key lengths of the horizon…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
In this article the cosmological constant problems, as well as the astronomical evidence for a cosmologically significant homogeneous exotic energy density with negative pressure (quintessence), are reviewed for a broad audience of…
The previous version of this article was a first attempt to confront the Dark Gravity theory to cosmological data. However, more recent developments lead to the conclusion that the cosmological principle is probably not valid in Dark…
The observational evidence for the existence of a non-zero cosmological constant is getting stronger. It is therefore timely to address the question of its eventual effect on the dynamics of galaxies, clusters and larger structures in the…
To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice…