相关论文: Scale Symmetry in the Universe

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution $\mathrm{d} N/\mathrm{d} M\propto M^{-2}$ which (to first order) describes stars, protostellar…

We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement…

New measurements of galaxy clustering and background radiations provide improved constraints on the isotropy and homogeneity of the Universe on large scales. In particular, the angular distribution of radio sources and the X-Ray Background…

The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…

Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…

We consider a Yang-Mills type gauge theory of gravity based on the conformal group SO(4,2) coupled to a conformally invariant real scalar field. The goal is to generate fundamental dimensional constants via spontaneous breakdown of the…

The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…

We give a review of the theory of random fields defined on the observable part of the Universe that satisfy the cosmological principle, i.e., invariant with respect to the 6-dimensional group $\mathcal{G}$ of the isometries of the time…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…

A scale invariant, Weyl geometric, Lagrangian approach to cosmology is explored, with a a scalar field phi of (scale) weight -1 as a crucial ingredient besides classical matter \cite{Tann:Diss,Drechsler:Higgs}. For a particularly simple…

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to…

Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental…

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…

Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of the…

Symmetries in the Physical Laws of Nature lead to observable effects. Beyond regularities and conserved magnitudes, the last decades in Particle Physics have seen the identification of symmetries, and their well defined breaking, as the…

Unless there is evidence for fractal scaling with a single exponent over distances .1 <= r <= 100 h^-1 Mpc then the widely accepted notion of scale invariance of the correlation integral for .1 <= r <= 10 h^-1 Mpc must be questioned. The…

In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal…

Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the…

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…