Apparent horizons in the quasi-spherical Szekeres models

The notion of an apparent horizon (AH) in a collapsing object can be carried over from the Lema\^{\i}tre -- Tolman (L--T) to the quasispherical Szekeres models in three ways: 1. Literally by the definition -- the AH is the boundary of the region, in which every bundle of null geodesics has negative expansion scalar. 2. As the locus, at which null lines that are as nearly radial as possible are turned toward decreasing areal radius $R$. These lines are in general nongeodesic. The name "absolute apparent horizon" (AAH) is proposed for this locus. 3. As the boundary of a region, where null \textit{geodesics} are turned toward decreasing $R$. The name "light collapse region" (LCR) is proposed for this region (which is 3-dimensional in every space of constant $t$); its boundary coincides with the AAH. The AH and AAH coincide in the L--T models. In the quasispherical Szekeres models, the AH is different from (but not disjoint with) the AAH. Properties of the AAH and LCR are investigated, and the relations between the AAH and the AH are illustrated with diagrams using an explicit example of a Szekeres metric. It turns out that an observer who is already within the AH is, for some time, not yet within the AAH. Nevertheless, no light signal can be sent through the AH from the inside. The analogue of the AAH for massive particles is also considered.Comment: 14 pages, 9 figures, includes little extensions and style corrections made after referee's comments, the text matches the published versio

Geometry of the quasi-hyperbolic Szekeres models

Geometric properties of the quasi-hyperbolic Szekeres models are discussed and related to the quasi-spherical Szekeres models. Typical examples of shapes of various classes of 2-dimensional coordinate surfaces are shown in graphs; for the hyperbolically symmetric subcase and for the general quasi-hyperbolic case. An analysis of the mass function $M(z)$ is carried out in parallel to an analogous analysis for the quasi-spherical models. This leads to the conclusion that $M(z)$ determines the density of rest mass averaged over the whole space of constant time.Comment: 19 pages, 13 figures. This version matches the published tex

The ergodicity bias in the observed galaxy distribution

The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy -- the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy distribution. The resultant difference between observed statistics (volume average) and the true cosmic value (ensemble average) is termed as the ergodicity bias. We perform explicit numerical investigation of the effect for a set of galaxy survey depths and near-end distance cuts. It is found that the ergodicity bias in observed two- and three-point correlation functions in most cases is insignificant for modern analysis of samples from galaxy surveys and thus close a loophole in precision cosmology. However, it may become non-negligible in certain circumstances, such as those applications involving three-point correlation function at large scales of local galaxy samples. Thus one is reminded to take extra care in galaxy sample construction and interpretation of the statistics of the sample, especially when the characteristic redshift is low.Comment: Revised version published as JCAP08(2010)01

Volume averaging in the quasispherical Szekeres model

This paper considers the volume averaging in the quasispherical Szekeres model. The volume averaging became of considerable interest after it was shown that the volume acceleration calculated within the averaging framework can be positive even though the local expansion rate is always decelerating. This issue was intensively studied within spherically symmetric models. However, since our Universe is not spherically symmetric similar analysis is needed in non symmetrical models. This papers presents the averaging analysis within the quasispherical Szekeres model which is a non-symmetrical generalisation of the spherically symmetric Lema\^itre--Tolman family of models. Density distribution in the quasispherical Szekeres has a structure of a time-dependent mass dipole superposed on a monopole. This paper shows that when calculating the volume acceleration, $\ddot{a}$, within the Szekeres model, the dipole does not contribute to the final result, hence $\ddot{a}$ only depends on a monopole configuration. Thus, the volume averaging within the Szekeres model leads to literally the same solutions as obtained within the Lema\^itre--Tolman model.Comment: 8 pages; calculation of the spatial Ricci scalar added; accepted for publication in Gen. Rel. Gra

Pressure gradients, shell crossing singularities and acoustic oscillations - application to inhomogeneous cosmological models

Inhomogeneous cosmological models have recently become a very interesting alternative to standard cosmology. This is because these models are able to fit cosmological observations without the need for dark energy. However, due to inhomogeneity and pressure-less matter content, these models can suffer from shell crossing singularities. These singularities occur when two shell of dust collide with each other leading to infinite values of the density. In this Letter we show that if inhomogeneous pressure is included then these singularities can be prevented from occurring over the period of structure formation. Thus, a simple incorporation of a gradient of pressure allows for more comprehensive studies of inhomogeneous cosmological models and their application to cosmology.Comment: 5 pages, 3 figures. Accepted for publication in MNRA

Redshift Drift in LTB Void Universes

We study the redshift drift, i.e., the time derivative of the cosmological redshift in the Lema\^itre-Tolman-Bondi (LTB) solution in which the observer is assumed to be located at the symmetry center. This solution has often been studied as an anti-Copernican universe model to explain the acceleration of cosmic volume expansion without introducing the concept of dark energy. One of decisive differences between LTB universe models and Copernican universe models with dark energy is believed to be the redshift drift. The redshift drift is negative in all known LTB universe models, whereas it is positive in the redshift domain $z \lesssim 2$ in Copernican models with dark energy. However, there have been no detailed studies on this subject. In the present paper, we prove that the redshift drift of an off-center source is always negative in the case of LTB void models. We also show that the redshift drift can be positive with an extremely large hump-type inhomogeneity. Our results suggest that we can determine whether we live near the center of a large void without dark energy by observing the redshift drift.Comment: 16 pages, 2 figure