Related papers: The Center is Everywhere
A new method for constructing exact inhomogeneous universes is presented, that allows variation in 3 dimensions. The resulting spacetime may be statistically uniform on average, or have random, non-repeating variation. The construction…
The assumption of a flat Universe that follows the cosmological principle, i.e., that the universe is statistically homogeneous and isotropic at large scales, comprises one of the core foundations of the standard cosmological model --…
We use the scaled counts in spherical caps $\mathcal{N}(<\theta)$ and the fractal correlation dimension $ \mathcal{D}_{2}(\theta) $ procedures to search for a transition scale to homogeneity in the local universe as given by the ALFALFA…
The so-called 'Galactic Center' Lobe (GCL) is an extended (~1 deg) radio continuum feature situated above the Galactic Plane, for which the literature contains varying claims about both its nature and location. Using new optical integral…
Black hole entropy appears to be ``universal''--many independent calculations, involving models with very different microscopic degrees of freedom, all yield the same density of states. I discuss the proposal that this universality comes…
There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…
We point out that the horizon problem encountered in standard text-books or review papers on cosmology is, in general, derived for world models based on Robertson-Walker line element where homogeneity and isotropy of the universe -- \`a la…
The purpose of the present work is based on two main observations: the tensions encountered by the standard $\Lambda$CDM model when confronted to precision small scale cosmological data and the finding that the matter distribution and the…
Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of…
Barycenters (aka Fr\'echet means) were introduced in statistics in the 1940's and popularized in the fields of shape statistics and, later, in optimal transport and matrix analysis. They provide the most natural extension of linear…
Cosmological density fields are assumed to be translational and rotational invariant, avoiding any special point or direction, thus satisfying the Copernican Principle. A spatially inhomogeneous matter distribution can be compatible with…
Quantum theory, general relativity, the standard model of particle physics, and the $\Lambda$CDM model of cosmology have all been spectacularly successful within their respective regimes of applicability, but many central problems remain…
Astronomical observations have shown that the expansion of the universe is at present accelerating, in a way consistent with the presence of a positive cosmological constant. This is a major puzzle, because we do not understand: why the…
The cosmological principle (CP), assuming spatially homogeneous and isotropic background geometry in the cosmological scale, is a fundamental assumption in modern cosmology. Recent observations of the galaxy redshift survey provide relevant…
The "cosmic web", the filamentary large-scale structure in a cold dark matter Universe, is readily apparent via galaxy tracers in spectroscopic surveys. However, the underlying dark matter structure is as of yet unobservable and mapping the…
The present work describes an immersion in 5D of the interior Schwarzschild solution of the general relativity equations. The model theory is defined in the context of a flat 5D space time matter Minkowski model, using a Tolman like…
Assuming the Central Limit Theorem, experimental uncertainties in any data set are expected to follow the Gaussian distribution with zero mean. We propose an elegant method based on Kolmogorov-Smirnov statistic to test the above; and apply…
The future evolution of the universe suggested by the cosmological model proposed earlier at this meeting by the authors is explored. The fundamental role played by the positive "cosmological constant" is emphasized. Dyson's 1979 paper…
These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…
The Cosmological Constant Lambda, a concept introduced by Einstein in 1917, has been with us ever since in different variants and incarnations, including the broader concept of Dark Energy. Current observations are consistent with a value…