113 research outputs found
The Effects of Inhomogeneities on Evaluating the mass parameter and the cosmological constant
Analytic expressions for distance-redshift relations which have been
corrected for the effects of inhomogeneities in the
Friedmann-Lema\^itre-Robertson-Walker (FLRW) mass density are given in terms of
Heun functions and are used to illustrate the significance of inhomogeneities
on a determination of the mass parameter and the cosmological
constant . The values of these parameters inferred from a given set of
observations depend on the fractional amount of matter in inhomogeneities and
can significantly differ from those obtained by using the standard
magnitude-redshift (-) result for pure dust FLRW models. As an example a
determination of made by applying the homogeneous distance-redshift
relation to SN 1997ap at could be as much as 50% lower than its true
value.Comment: 39 pages including 8 figures and captions. To appear in ApJ 507 (Nov.
1998
Luttinger theorem for a spin-density-wave state
We obtained the analog of the Luttinger relation for a commensurate
spin-density-wave state. We show that while the relation between the area of
the occupied states and the density of particles gets modified in a simple and
predictable way when the system becomes ordered, a perturbative consideration
of the Luttinger theorem does not work due to the presence of an anomaly
similar to the chiral anomaly in quantum electrodynamics.Comment: 4 pages, RevTeX, 1 figure embedded in the text, ps-file is also
available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.htm
Can Strong Gravitational Lensing Constrain Dark Energy?
We discuss the ratio of the angular diameter distances from the source to the
lens, , and to the observer at present, , for various dark
energy models. It is well known that the difference of s between the
models is apparent and this quantity is used for the analysis of Type Ia
supernovae. However we investigate the difference between the ratio of the
angular diameter distances for a cosmological constant,
and that for other dark energy models,
in this paper. It has been known that there is
lens model degeneracy in using strong gravitational lensing. Thus, we
investigate the model independent observable quantity, Einstein radius
(), which is proportional to both and velocity
dispersion squared, . values depend on the parameters
of each dark energy model individually. However, for the various dark energy models, is well within
the error of for most of the parameter spaces of the dark energy
models. Thus, a single strong gravitational lensing by use of the Einstein
radius may not be a proper method to investigate the property of dark energy.
However, better understanding to the mass profile of clusters in the future or
other methods related to arc statistics rather than the distances may be used
for constraints on dark energy.Comment: 15 pages, 13 figures, Accepted in PR
Observational constraints on inhomogeneous cosmological models without dark energy
It has been proposed that the observed dark energy can be explained away by
the effect of large-scale nonlinear inhomogeneities. In the present paper we
discuss how observations constrain cosmological models featuring large voids.
We start by considering Copernican models, in which the observer is not
occupying a special position and homogeneity is preserved on a very large
scale. We show how these models, at least in their current realizations, are
constrained to give small, but perhaps not negligible in certain contexts,
corrections to the cosmological observables. We then examine non-Copernican
models, in which the observer is close to the center of a very large void.
These models can give large corrections to the observables which mimic an
accelerated FLRW model. We carefully discuss the main observables and tests
able to exclude them.Comment: 27 pages, 7 figures; invited contribution to CQG special issue
"Inhomogeneous Cosmological Models and Averaging in Cosmology". Replaced to
match the improved version accepted for publication. Appendix B and
references adde
Development of Zeldovich’s approach for cosmological distances measurement in the Friedmann Universe
How does the cosmic large-scale structure bias the Hubble diagram?
The Hubble diagram is one of the cornerstones of observational cosmology. It
is usually analysed assuming that, on average, the underlying relation between
magnitude and redshift matches the prediction of a
Friedmann-Lema\^itre-Robertson-Walker model. However, the inhomogeneity of the
Universe generically biases these observables, mainly due to peculiar
velocities and gravitational lensing, in a way that depends on the notion of
average used in theoretical calculations. In this article, we carefully derive
the notion of average which corresponds to the observation of the Hubble
diagram. We then calculate its bias at second-order in cosmological
perturbations, and estimate the consequences on the inference of cosmological
parameters, for various current and future surveys. We find that this bias
deeply affects direct estimations of the evolution of the dark-energy equation
of state. However, errors in the standard inference of cosmological parameters
remain smaller than observational uncertainties, even though they reach percent
level on some parameters; they reduce to sub-percent level if an optimal
distance indicator is used.Comment: 19+7 pages, 10 figures, v2 accepted by JCAP; minor changes to improve
clarit
The Effect of Large-Scale Inhomogeneities on the Luminosity Distance
We study the form of the luminosity distance as a function of redshift in the
presence of large scale inhomogeneities, with sizes of order 10 Mpc or larger.
We approximate the Universe through the Swiss-cheese model, with each spherical
region described by the Tolman-Bondi metric. We study the propagation of light
beams in this background, assuming that the locations of the source and the
observer are random. We derive the optical equations for the evolution of the
beam area and shear. Through their integration we determine the configurations
that can lead to an increase of the luminosity distance relative to the
homogeneous cosmology. We find that this can be achieved if the Universe is
composed of spherical void-like regions, with matter concentrated near their
surface. For inhomogeneities consistent with the observed large scale
structure, the relative increase of the luminosity distance is of the order of
a few percent at redshifts near 1, and falls short of explaining the
substantial increase required by the supernova data. On the other hand, the
effect we describe is important for the correct determination of the energy
content of the Universe from observations.Comment: 27 pages, 5 figures Revised version. References added. Conclusions
clarifie
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