Related papers: Spectral Representation and the Averaging Problem …

We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…

The energy density of the universe today may be dominated by the vacuum energy of a slowly rolling scalar field. Making a quantum expansion around such a time dependent solution is found to break fundamental symmetries of quantum field…

The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the…

The homogeneity of matter distribution at large scales, known as the cosmological principle, is a central assumption in the standard cosmological model. The case is testable though, thus no longer needs to be a principle. Here we perform a…

The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing…

A major goal of modern astrophysics is to understand the processes by which the universe evolved from its initial simplicity, as seen in measurements of the Cosmic Microwave Background, to the universe we see today, with complexity on all…

One of the main goals of modern observational cosmology is to map the large scale structure of the Universe. A potentially powerful approach for doing this would be to exploit three-dimensional spectral maps, i.e. the specific intensity of…

This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…

The exact solution of a two-scale Buchert average of the Einstein equations is derived for an inhomogeneous universe which represents a close approximation to the observed universe. The two scales represent voids, and the bubble walls…

We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we…

The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is…

Cosmic voids are low-mass-density regions on intergalactic scales. They are where cosmic expansion and acceleration are most dominant, important places to understand and analyze for cosmology. This entry summarises theoretical underpinnings…

Cosmology relies on the Cosmological Principle, i.e., the hypothesis that the Universe is homogeneous and isotropic on large scales. This implies in particular that the counts of galaxies should approach a homogeneous scaling with volume at…

The most fundamental premise to the standard model of the universe, the Cosmological Principle (CP), states that the large-scale properties of the universe are the same in all directions and at all comoving positions. Demonstrating this…

The standard model of cosmology assumes that the Universe can be described to hover around a homogeneous-isotropic solution of Einstein's general theory of relativity. This description needs (sometimes hidden) hypotheses that restrict the…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…

It is a fundamental unsolved question in general relativity how to unambiguously characterize the effective collective dynamics of an ensemble of fluid elements sourcing the local geometry, in the absence of exact symmetries. In a…

Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…

Aims: we propose that the condition of relative motion between us and the objects that we observe in the Universe should generate relativistic aberration on the photons that such objects emit, varying the observed flux similarly to the…