Related papers: Resolving the universe with multifractals
Cosmography and galaxy clusters are discussed in the framework of f(R)-gravity giving a comprehensive review of recent results.
On the scale of the cosmic horizon, signatures that are unique to general relativity are concealed within the statistics of the large scale distribution of galaxies. These were thought to be beyond the reach of all but the most ambitious…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
The question of the nature of galaxy clustering and the possible homogeneity of galaxy distribution is one of the fundamental problem of cosmology. It is well established that galaxy structures are characterized, up to a certain scale, by…
I review some results of estimation of the power spectrum of density fluctuations from galaxy redshift surveys and discuss advances that may be possible with the Sloan Digital Sky Survey. I then examine the realities of power spectrum…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
Weak lensing surveys exploit measurements of galaxy ellipticities. These measurements are subject to errors which degrade the cosmological information that can be extracted from the surveys. Here we propose a way of using the galaxy data…
Despite consistent progress in numerical simulations, the observable properties of galaxy clusters are difficult to predict ab initio. It is therefore important to compare both theoretical and observational results to a direct measure of…
These are advanced lecture notes covering recent developments in the methodology used to analyse galaxy surveys. The focus is particularly on direct measurements of the galaxy power spectrum although I also discuss its Fourier transform,…
The clustering amplitude of galaxies depends on their intrinsic luminosity. We compare the properties of publicly available galaxy formation models with clustering measurements from the two-degree field galaxy redshift survey. The model…
One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determine the shape of the correlation function, its possible evolution…
Combining different observational probes, such as galaxy clustering and weak lensing, is a promising technique for unveiling the physics of the Universe with upcoming dark energy experiments. Whilst this strategy significantly improves…
We present the second-order general relativistic description of the observed galaxy number density in a cosmological framework. The observed galaxy number density is affected by the volume and the source effects, both of which arise due to…
We consider cosmological applications of galaxy number density correlations to be inferred from future deep and wide multi-band optical surveys. We mostly focus on very large scales as a probe of possible features in the primordial power…
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…
After exactly a century since the formulation of the general theory of relativity, the phenomenon of gravitational lensing is still an extremely powerful method for investigating in astrophysics and cosmology. Indeed, it is adopted to study…
Various cosmological applications of galaxy clusters are presented. Clusters are used to determine the baryon fraction, dark matter distribution and the matter density of the universe. They also contain a wealth of information about…
Galaxy redshift surveys are one of the key probes in modern cosmology. In the data analysis of galaxy surveys, the precision of the statistical measurement is primarily limited by the cosmic variance on large scales. Fortunately, this…