The Lemaitre Model and the Generalisation of the Cosmic Mass

We consider the spherically symmetric metric with a comoving perfect fluid and non-zero pressure -- the Lemaitre metric -- and present it in the form of a calculational algorithm. We use it to review the definition of mass, and to look at the apparent horizon relations on the observer's past null cone. We show that the introduction of pressure makes it difficult to separate the mass from other physical parameters in an invariant way. Under the usual mass definition, the apparent horizon relation, that relates the diameter distance to the cosmic mass, remains the same as in the Lemaitre-Tolman case.Comment: latex, 16 pages, Revision has minor changes due to referee's comments

Imitating accelerated expansion of the Universe by matter inhomogeneities - corrections of some misunderstandings

A number of misunderstandings about modeling the apparent accelerated expansion of the Universe, and about the `weak singularity' are clarified: 1. Of the five definitions of the deceleration parameter given by Hirata and Seljak (HS), only $q_1$ is a correct invariant measure of acceleration/deceleration of expansion. The $q_3$ and $q_4$ are unrelated to acceleration in an inhomogeneous model. 2. The averaging over directions involved in the definition of $q_4$ does not correspond to what is done in observational astronomy. 3. HS's equation (38) connecting $q_4$ to the flow invariants gives self-contradictory results when applied at the centre of symmetry of the Lema\^{\i}tre-Tolman (L-T) model. The intermediate equation (31) that determines $q_{3'}$ is correct, but approximate, so it cannot be used for determining the sign of the deceleration parameter. Even so, at the centre of symmetry of the L-T model, it puts no limitation on the sign of $q_{3'}(0)$. 4. The `weak singularity' of Vanderveld {\it et al.} is a conical profile of mass density at the centre - a perfectly acceptable configuration. 5. The so-called `critical point' in the equations of the `inverse problem' for a central observer in an L-T model is a manifestation of the apparent horizon - a common property of the past light cones in zero-lambda L-T models, perfectly manageable if the equations are correctly integrated.Comment: 15 pages. Completely rewritten to match the published version. We added discussion of 2 key papers cited by VFW and identified more clearly the assumptions, approximations and mistakes that led to certain misconceptions

Cosmological Backreaction from Perturbations

We reformulate the averaged Einstein equations in a form suitable for use with Newtonian gauge linear perturbation theory and track the size of the modifications to standard Robertson-Walker evolution on the largest scales as a function of redshift for both Einstein de-Sitter and Lambda CDM cosmologies. In both cases the effective energy density arising from linear perturbations is of the order of 10^-5 the matter density, as would be expected, with an effective equation of state w ~ -1/19. Employing a modified Halofit code to extend our results to quasilinear scales, we find that, while larger, the deviations from Robertson-Walker behaviour remain of the order of 10^-5.Comment: 15 pages, 8 figures; replaced by version accepted by JCA

Apparent and average acceleration of the Universe

In this paper we consider the relation between the volume deceleration parameter obtained within the Buchert averaging scheme and the deceleration parameter derived from the supernova observation. This work was motivated by recent findings that showed that there are models which despite $\Lambda=0$ have volume deceleration parameter $q^{vol} < 0$. This opens the possibility that backreaction and averaging effects may be used as an interesting alternative explanation to the dark energy phenomenon. We have calculated $q^{vol}$ in some Lema\^itre--Tolman models. For those models which are chosen to be realistic and which fit the supernova data, we find that $q^{vol} > 0$, while those models which we have been able to find which exhibit $q^{vol} < 0$ turn out to be unrealistic. This indicates that care must be exercised in relating the deceleration parameter to observations.Comment: 15 pages, 5 figures; matches published versio