Related papers: Spectral Representation and the Averaging Problem …
The Hubble constant problem is the discrepancy between different measurements of the Hubble constant in different scales. We show that this problem can be resolved within the general relativistic framework of the perturbation theory in the…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann-Lemaitre-Robertson-Walker (FLRW) line…
The problems of coarse-graining and averaging of inhomogeneous cosmologies, and their backreaction on average cosmic evolution, are reviewed from a physical viewpoint. A particular focus is placed on comparing different notions of average…
We present a new approach for averaging in general relativity and cosmology. After a short review of the theory originally taken from the equivalence problem, we consider two ways how to deal with averaging based on Cartan scalars. We apply…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
Structure occurs over a vast range of scales in the universe. Our large-scale cosmological models are coarse-grained representations of what exists, which have much less structure than there really is. An important problem for cosmology is…
Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced…
The cosmological principle is fundamental to the standard cosmological model. It assumes that the Universe is homogeneous and isotropic on very large scales. As the basic assumption, it must stand the test of various observations. In this…
The methods of obtaining the average spectral shape in a low statistics regime are presented. Different approaches to averaging are extensively tested with simulated spectra, based on the ASCA responses. The issue of binning up the spectrum…
In this paper we outline the framework of mathematical statistics with which one may study the properties of galaxy distance estimators. We describe, within this framework, how one may formulate the problem of distance estimation as a…
Bayesian model averaging is a procedure to obtain parameter constraints that account for the uncertainty about the correct cosmological model. We use recent cosmological observations and Bayesian model averaging to derive tight limits on…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
Several cosmological measurements have attained significant levels of maturity and accuracy over the last decade. Continuing this trend, future observations promise measurements of the statistics of the cosmic mass distribution at an…
The strong equivalence principle is extended in application to averaged dynamical fields in cosmology to include the role of the average density in the determination of inertial frames. The resulting cosmological equivalence principle is…
The Hubble tension cast a blight on the standard cosmology. As a possible attitude to the problem, the local variation of the expansion rate in an inhomogeneous cosmology has been proposed where the spatial averaging over a finite domain…
The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann…
The timescape cosmology represents a potentially viable alternative to the standard homogeneous cosmology, without the need for dark energy. Although average cosmic evolution in the timescape scenario only differs substantially from that of…
It is necessary to make assumptions in order to derive models to be used for cosmological predictions and comparison with observational data. In particular, in standard cosmology the spatial curvature is assumed to be constant and zero (or…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…