This article presents two caveats for the analysis of large-scale structure. Within distances for which the fractal structure of the distribution of galaxies obtains, fluctuations may be on the scale of the measurements themselves, as is typical of fractals. Second, within this region it is...

Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape, and connectivity. Here we point out that these scalar descriptors can be complemented by vector-valued curvature measures also known as Quermaß vectors. Using examples of...

We consider a toy metric in four-dimensional space–time defined in terms of a recursive hierarchical prescription. The matter distribution turns out to be extremely inhomogeneous. Surprisingly, for very large samples the average mass density tends (very slowly) to a constant. There is no trace...

A one-dimensional (1D) system obeying the Hubble expansion is studied numerically using an N-body code. The rescaling of both space and time changes the dynamics which, in the rescaled frame, is analogous to the dynamics of a 1D one-component plasma with the addition of a friction term. We start...

A critical review is given of the theory of cosmological natural selection. The successes of the theory are described, and a number of published criticisms are answered. An observational test is described which could falsify the theory.

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar kind of q-exponential distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those...

In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to propose the coherent access by a particle to the available...