Related papers: Distance measures in cosmology
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
We discuss how inhomogeneities of the universe affect observations of the gravitational lensing; (1) the bending angle, (2) the lensing statistics and (3) the time delay. In order to take account of the inhomogeneities, the Dyer-Roeder…
Revolutionary advances in both theory and technology have launched cosmology into its most exciting period of discovery yet. Unanticipated components of the universe have been identified, promising ideas for understanding the basic features…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
The standard $\Lambda$ Cold Dark Matter cosmological model provides an amazing description of a wide range of astrophysical and astronomical data. However, there are a few big open questions, that make the standard model look like a…
In the standard cosmological theory one uses the Einstein concepts of space and time as were originally introduced for the special theory of relativity and the general relativity theory. According to this approach all physical quantities…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
In recent years the possibility of measuring the temporal change of radial and transverse position of sources in the sky in real time have become conceivable thanks to the thoroughly improved technique applied to new astrometric and…
Cosmography is the tool that makes possible to untie the interpretation of cosmological observations from the definition of any dynamical prior. We review the constraints on the cosmographic parameter obtained using the most thorough data…
The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The…
The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time…
The advent of large data-set in cosmology has meant that in the past 10 or 20 years our knowledge and understanding of the Universe has changed not only quantitatively but also, and most importantly, qualitatively. Cosmologists rely on data…
This is the dawning of the age of precision cosmology, when all the important parameters will be established to one significant figure or better, within the cosmological model. In the age of accurate cosmology the model, which nowadays…
In this review, the status of measurements of the matter density (Omega), the vaccuum energy density or cosmological constant (Lambda), the Hubble constant (H0), and ages of the oldest measured objects (t0) are summarized. Measurements of…
Quantum cosmology offers a unique stage to address questions of time related to its underlying (and perhaps truly quantum dynamical) meaning as well as its origin. Some of these issues can be analyzed with a general scheme of quantum…
As is well known, classical systems approximate quantum ones -- but how well? We introduce a definition of a "distance" on classical and quantum phase spaces that offers a measure of their separation. Such a distance scale provides a means…
This is a review article for The Review of Particle Physics 2014 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2014. Topics included are Parametrizing the Universe;…
These lecture notes aim to provide an introduction to dark matter from the perspective of astrophysics/cosmology. We start with a rapid overview of cosmology, including the evolution of the Universe, its thermal history and structure…