Related papers: The Center is Everywhere
In his paper "On the Schlafli differential equality", J. Milnor conjectured that the volume of n-dimensional hyperbolic and spherical simplices, as a function of the dihedral angles, extends continuously to the closure of the space of…
Rohatgi and the author recently proved a shuffling theorem for lozenge tilings of `doubly-dented hexagons' (arXiv:1905.08311). The theorem can be considered as a hybrid between two classical theorems in the enumeration of tilings:…
We study the impact of the expansion of the universe on a broad class of objects, including black holes, neutron stars, white dwarfs, and others. Using metrics that incorporate primordial inhomogeneities, the effects of a hypothetical…
Homogeneity is a crucial, but poorly tested, assumption in cosmology. We introduce a new approach which allows us to place limits on the presence of localized structures within essentially our entire observable volume, using cosmic…
According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here,…
General Relativity allows for a cosmological constant ($\Lambda$) which has inspired models of cosmic Inflation and Dark Energy. We show instead that $r_\Lambda = \sqrt{3/\Lambda}$ corresponds to an event horizon: a causal boundary term in…
The papers included in this Focus Point collection are devoted to the studies on the cosmological tensions and challenges stimulated by the latest observational data. The first results of the LARES-2 laser ranging satellite on the high…
Fluctuations in the intensity and polarization of the cosmic microwave background (CMB) and the large-scale distribution of matter in the universe each contain clues about the nature of the earliest moments of time. The next generation of…
Galaxy Surveys are enjoying a renaissance thanks to the advent of multi-object spectrographs on ground-based telescopes. The last 15 years have seen the fruits of this experimental advance, including the 2-degree Field Galaxy Redshift…
We revisit textbook claims that entropy must increase and show that, under time-reversal invariant microscopic dynamics, no universal trajectory-wise or statistical assertion that the coarse-grained entropy $S(t)$ is non-decreasing can…
This paper is a major revision of our previous work on the HST model of inflation. We identify the local fluctuations of the metric with fluctuations of the mass and angular momentum of black holes, and show that the consistency conditions…
Inflation is a bold and expansive extension of the Standard Cosmology. It holds the promise to extend our understanding of the Universe to within 10^{-32}sec of the big bang and answer most of the pressing questions in cosmology. Its…
This review summarizes a few of the frontiers of Galactic center research that are currently the focus of considerable activity and attention. It is aimed at providing a necessarily incomplete sketch of some of the timely work being done on…
I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous…
The ${\rm SL}_3$-skein algebra $\mathscr{S}_{\bar{q}}(\mathfrak{S})$ of a punctured oriented surface $\mathfrak{S}$ is a quantum deformation of the coordinate algebra of the ${\rm SL}_3$-character variety of $\mathfrak{S}$. When $\bar{q}$…
The ``Century Survey'' (CS hereafter) is a complete redshift survey of a 1$^\circ$-wide strip. It covers 0.03 steradians to a limiting m$_R$ = 16.13. The survey is 98.4% complete and contains 1762 galaxies. Large-scale features in the…
Typical cosmological models are based on the postulate that space is homogeneous. Space however contains overdense regions in which matter is concentrating, leaving underdense regions of almost void. The evolution of the scale factor of the…
Using the 2MASS Photometric Redshift catalogue we perform a number of statistical tests aimed at detecting possible departures from statistical homogeneity and isotropy in the large-scale structure of the Universe. Making use of the angular…
This study investigates a generalisation of the Pythagorean theorem to the lengths of conic arcs constructed symmetrically on the sides of a right triangle. It is demonstrated that the theorem remains valid whenever the conic eccentricity…
The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal…