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A fundamental spacetime scale in the universe leads to noncommutative spacetime and thence to a modified energy - momentum dispersion relation or equivalently to a modification of Lorentz symmetry as shown by the author and others. This…

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a…

The fine-structure constant alpha approximately 1/137 is traditionally regarded as a fundamental dimensionless parameter. I argue instead that alpha is a scaled quantity that arises only where the structural scales contributed by classical…

The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients…

We study cosmological solutions for the very early universe beginning at the Planck scale for a universe containing radiation, curvature and, as a simplification of a possible scalar field potential, a cosmological constant term. The…

Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…

In the debate about galaxy correlation there are different questions which can be addressed separately: Which are the statistical methods able to properly detect scale invariance and describe, in general, the properties of irregular and…

A standard paradigm is now available for the recent evolution (z < 10) of structure on galactic and larger scales. Most of the matter is assumed to be dark and dissipationless and to cluster hierarchically from gaussian initial conditions.…

The laws of physics have a set of fundamental constants, and it is generally admitted that only dimensionless combinations of constants have physical significance. These combinations include the electromagnetic and gravitational fine…

We investigate whether a mass scale for elementary particles can be derived from interactions of particles with distant matter in the Universe, the mechanism of the interaction being the classical vector potential, propagating in a space of…

This work describes underlying features of the universe such as fundamental constants and cosmological parameters, conservation laws, baryon and lepton asymmetries, etc. in the context of local gauge theories for fundamental forces under…

The Planck mass and the cosmological constant determine the minimum and the maximum distances in the physical universe. A relativistic theory that takes into account a fundamental distance limit $\ell$ on par with the fundamental speed…

Using considerations from the Quantum Zero Point Field and Thermodynamics, we show that the Planck Scale is the minimum (maximum mass) and the Photon Scale is the maximum (minimum mass) Scale in the universe. The arguments also deduce the…

We consider the properties of an ensemble of universes as function of size, where size is defined in terms of the asymptotic value of the Hubble constant (or, equivalently, the value of the cosmological constant). We assume that standard…

We suggest discovery targets for the Higgs boson, dark matter, and quantum gravity mass scales, motivated by the Dirac equation for the electron in deSitter space, and a sixth-order constraint between the electron QED parameters and the…

Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the…

Astrophysical observations suggest that the fine structure constant (alpha) may (or may not) be evolving over the cosmological time scale. This raises a much debated question: is alpha variation due to the variation of the speed of light…

In a large scale view of the universe, galaxies are the basic unit of structure. A typical bright galaxy may contain 100 billion stars and span tens of thousands of light years, but the empty expanses between the galaxies are much larger…

Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…

We study structure formation in a set of cosmological simulations to uncover the scales in the initial density field that gave rise to the formation of present-day structures. Our simulations share a common primordial power spectrum (here…