Related papers: Spectral Representation and the Averaging Problem …
The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. A rigorous mathematical definition of averaging in a cosmological model is necessary. In general, a spacetime is…
We study a fundamental issue in cosmology: Whether we can rely on a cosmological model to understand the real history of the Universe. This fundamental, still unresolved issue is often called the ``model-fitting problem (or averaging…
We investigate the representation of the geometrical information of the universe in terms of the eigenvalues of the Laplacian defined on the universe. We concentrate only on one specific problem along this line: To introduce a concept of…
The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. We review cosmological observations and discuss some of the issues regarding averaging. We present a precise definition of…
We derive the evolution equations for the spectra of the Universe. Here "spectra" means the eigenvalues of the Laplacian defined on a space, which contain the geometrical information on the space. These equations are expected to be useful…
Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not…
This thesis deals with the averaging problem in cosmology, which has gained considerable interest in recent years, and is concerned with correction terms (after averaging inhomogeneities) that appear in the Einstein equations when working…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of…
Averaged inhomogeneous cosmologies lie at the forefront of interest, since cosmological parameters like the rate of expansion or the mass density are to be considered as volume-averaged quantities and only these can be compared with…
We analyze two theoretical approaches to ensemble averaging for integrable systems in quantum chaos - spectral averaging and parametric averaging. For spectral averaging, we introduce a new procedure - rescaled spectral averaging. Unlike…
The interpretation of cosmological observations relies on a notion of an average Universe, which is usually considered as the homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) model. However, inhomogeneities may…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are…
This paper presents a general averaging procedure for a set of observers which are tilted with respect to the cosmological matter fluid. After giving the full set of equations describing the local dynamics, we define the averaging procedure…
In the context of the averaging problem in relativistic cosmology, we provide a key to the interpretation of cosmological parameters by taking into account the actual inhomogeneous geometry of the Universe. We discuss the relation between…
Observational cosmology provides us with a large number of high precision data which are used to derive models trying to reproduce ``on the mean'' our observable patch of the Universe. Most of these attempts are achieved in the framework of…
The question of the averaging of inhomogeneous spacetimes in cosmology is important for the correct interpretation of cosmological data. In this paper we suggest a conceptually simpler approach to averaging in cosmology based on the…
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an…
Context. The Spectroscopy Made Easy (SME) package has become a popular tool for analyzing stellar spectra, often in connection with large surveys or exoplanet research. SME has evolved significantly since it was first described in 1996, but…
The Averaging problem in general relativity and cosmology is discussed. The approach of macroscopic gravity to resolve the problem is presented. An exact cosmological solution to the equations of macroscopic gravity is given and its…