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In homogeneous cosmological models the wavelength $\lambda$ of a photon exchanged between two fundamental observers changes in proportion to expansion of the space $D$ between them, so $\Delta\log(\lambda / D) = 0$. This is exactly the same…
Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that…
The increase in mass of our observed expansive and isotropic relativistic Universe in the present relativistic cosmology is explained by the extensive assumption of the matter objects emerging on the horizon (of the most remote visibility).…
We examine the observational viability of a class of $f(\mathcal{R})$ gravity cosmological models. Particular attention is devoted to constraints from the recent observational determination of the redshift of the cosmological…
In this contribution to the conference "Beyond Einstein: Historical Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century", we give a critical status report of attempts to explain the late accelerated expansion of the…
Recent observations of the Universe have led to a conclusion suppressing an up-to-now supposed deceleration of the Universe caused by attractive gravitational forces. Contrary, there is a renaissance of the cosmological member lambda and…
This is a short overview of spatially flat (or open) four-dimensional accelerating cosmologies for some simple exponential potentials obtained by string or M theory compactification on some non-trivial curved spaces, which may lead to some…
It is shown that for Robertson-Walker models with flat or closed space sections, all of the cosmological spectral shift can be attributed to the non-flat connection (and thus indirectly to space-time curvature). For Robertson-Walker models…
Cosmology is undergoing an explosive period of activity, fueled both by new, accurate astrophysical data and by innovative theoretical developments. Cosmological parameters such as the total density of the Universe and the rate of…
In this series of lectures we review observational evidence for, and theoretical investigations into, cosmic acceleration and dark energy. The notes are in four sections. First I review the basic cosmological formalism to describe the…
The observed late-time acceleration of the cosmic expansion constitutes a fundamental problem in modern theoretical physics and cosmology. In an attempt to weight the validity of a large number of dark energy models, I use the recent…
This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $\ell^{1}$. We also point…
We investigate what current cosmological data tells us about the cosmological expansion rate in a model independent way. Specifically, we study if the expansion was decelerating at high redshifts and is accelerating now, without referring…
There are now several analyses reporting quantized differences in the redshifts between pairs of galaxies. In the simplest cases, these differential redshifts are found to be harmonics of fundamental periods of approximately 72 km/s and…
It is widely believed that the cosmological redshift is not a Doppler shift. However, Bunn & Hogg have recently pointed out that to settle properly this problem, one has to transport parallelly the velocity four-vector of a distant galaxy…
While general relativity ties together the cosmic expansion history and growth history of large scale structure, beyond the standard model these can have independent behaviors. We derive expressions for cosmologies with identical growth…
Cosmography is an ideal tool to investigate the cosmic expansion history of the Universe in a model-independent way. The equations of motion in modified theories of gravity are usually very complicated; cosmography may select practical…
We define a new observable that depends on finite redshift differences of the spin-weighted angular moments of the two point function of the three dimensional cosmic shear and on luminosity distance. It is shown that precise measurements of…
In this paper I examine how well Ryskin's model of emergent cosmic acceleration fits several sets of cosmological observations. I find that while Ryskin's model is somewhat compatible with the standard model of cosmological acceleration…
We consider a single field governed expansion of the universe from a five dimensional (5D) vacuum state. Under an appropiate change of variables the universe can be viewed in a effective manner as expanding in 4D with an effective equation…