Comparison of two approximation schemes for solving perturbations in a Lemaître-Tolman-Bondi cosmological model

Abstract

Recently, the present authors studied perturbations in the Lemaître-Tolman-Bondi cosmological model by applying the second-order perturbation theory in the dust Friedmann-Lemaître-Robertson-Walker universe model. Before this work, the same subject was studied in some papers by analyzing linear perturbations in the Lemaître-Tolman-Bondi cosmological model under the assumption proposed by Clarkson, Clifton and February, in which two of perturbation variables are negligible. However, it is a non-trivial issue in what situation the Clarkson-Clifton-February assumption is valid. In this paper, we investigate differences between these two approaches. It is shown that, in general, these two approaches are not compatible with each other. That is, in our perturbative procedure, the Clarkson-Clifton-February assumption is not valid at the order of our interest. *

Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models

“…These results are in agreement with previous considerations of February et al (2014) [39] as they find maximum deviations of the amplitudes of ϕ of around 30% well within deep voids at late times. Analytical treatments in the framework of second order FLRW perturbations (see [28]) predict a non-negligible coupling as well.…”

“…The void itself is modelled by isotropic first-order perturbations and general second order perturbations are placed "on top" of these. However, a full analysis of this formalism with cosmological initial conditions has not yet been performed in RW gauge and therefore only general arguments about the growing and decaying modes of second order perturbations are known (see [47] for details). Although one can argue that, at second order, the influence of non-scalar perturbations on the scalar potential or density contrast are present and even growing in time, this does not allow any direct quantitative comparison with the exact treatment of linear perturbations in voids so far.…”

“…Alonso et al (2010) [25] managed to set-up a Newtonian N-body simulation in the gravitational potential of a large Gpc void and studied Newtonian perturbations by comparing simulations with the theoretically predicted void profile of [14]. Nishikawa et al (2012) (see [26] and also [27,28]) studied the linear density evolution in void models by applying secondary linear perturbations on a primary non-linearly perturbed FLRW model that accounts for the void. Zibin (2008) (see [29] and further application in [30]) used a covariant 1+1+2 formalism for scalar perturbations in LTB spacetimes and obtained evolution equations and matter transfer functions in the, so-called, silent approximation by neglecting the magnetic part of the Weyl tensor and effectively the coupling of scalar to tensor modes.…”

Newtonian self-gravitating system in a relativistic huge void universe model

“…Growth of the large-scale structures in the universe can be thought of as one of the most useful tools to examine the huge void universe model, because the evolution of perturbations is expected to reflect the tidal force field in the background spacetime: the tidal force comes from the Weyl curvature, and hence there is the tidal force field, or simply, the tidal field in the huge void universe model but not in the homogeneous and isotropic universe model. Recently, linear perturbations in the LTB cosmological model and the observations related to them have been studied by several researchers [43,[59][60][61][62][63][64][65][66][67].…”