@misc{oai:ir.soken.ac.jp:00004066,
author = {齋藤, 惠樹 and サイトウ, ケイキ and SAITO, Keiki},
month = {2016-02-26, 2016-02-17},
note = {We study cosmological tests of models that can explain the apparent accelerated expansion of the present universe in terms of inhomogeneities. There are a number of models, such as dark energy models, modified matter models, modified gravity models, local void models, backreaction models, etc., and these models have to be tested by various observations other than the distance-redshift rela-tion of type Ia supernova. Therefore, in this thesis, we provide methods of testing these models by particularly focusing on inhomogeneities of the universe, because, practically, our universe is inho-mogeneous.
First, we consider the effective gravitational stress-energy tensor for short-wavelength perturbations in modified gravity theories. In general relativity, a consistent expansion scheme for short-wavelength perturbations and the corresponding effective stress-energy tensor were largely developed by Isaac-son, in which the small parameter, say ϵ, corresponds to the amplitude and at the same time the wave-length of perturbations. Isaacson’s expansion scheme is called the high frequency limit or the short-wavelength approximation. If the effective stress-energy tensor had a term proportional to the background spacetime metric, then it would correspond to adding a cosmological constant to the ef-fective Einstein equations for the background metric, thereby explaining possible origin of dark ener-gy from local inhomogeneities. It has been shown, however, that this effective gravitational stress-energy tensor is traceless and satisfies the weak energy condition, i.e. acts like radiation, and thus cannot provide any effects that imitate dark energy in general relativity. However, it is far from obvious if this traceless property of the effective gravitational stress-energy tensor is a nature specific only to the general relativity or is rather a generic property that can hold also in other types of gravity theories.
The purpose of the first test is to address this question in a simple, concrete model in the cosmologi-cal context. Since f(R) gravity contains higher order derivative terms, one can anticipate the effective gravitational stress-energy tensor to be generally modified in the high frequency limit. Our analysis can be performed, in principle, either (i) by first translating a given f(R) gravity into the corresponding scalar-tensor theory and then inspecting the stress-energy tensor for the scalar field ϕ, or (ii) by di-rectly dealing with metric perturbations of f(R) gravity. We may expect that the former approach is sufficient for our present purpose and much easier than the latter metric approach, as we have to deal with metric perturbations of complicated combinations of the curvature tensors in the latter case. Nevertheless we will take the both approaches. In fact, in the metric approach, by directly taking up perturbations of the scalar curvature, the Ricci tensor and the Riemann tensor involved in a given f(R) theory, we can learn how to generalize our present analysis of a specific class of f(R) gravity to anal-yses of other, different types of modified gravity theories that cannot even be translated into a sca-lar-tensor theory, such as the Gauss-Bonnet gravity. Then, we will make sure that the effective
stress-energy tensor in Brans-Dicke theory is consistent with that in our f(R) gravity.
Second, we discuss temperature anisotropies of cosmic microwave background (CMB) in local void models. Furthermore, those in the local void model and in the Λ-Lemaitre-Tolman-Bondi (Λ-LTB) spacetime are shown as a particular case. In order to justify the local void model as a viable alternative to the standard ΛCDM model, we have to test this model by various observations other than the SN Ia distance-redshift relation. Most of previous analyses were performed for various types of local void models by using numerical methods, and they do not seem to be straightforward to compare analyses for each different model so as to have a coherent understanding of the results. In order to have general consequences of the local void model and systematically examine its viability, it is desirable to de-velop some general, analytic methods that can apply, independently of the details of each specific model.
The purpose of the second test is to derive the analytic formulae for the dipole and quadrupole of the CMB anisotropy in general spherically symmetric spacetimes, including the Λ-LTB spacetime, and to give constraints on the local void model. Instead, we will exploit the key requirement of the local void model that we, observers, are restricted to be around very near the center of the spherical symmetry: Namely, we first note that the small distance between the symmetry center and an off-center observer gives rise to a corresponding deviation in the photon distribution function. Then, by taking ‘Taylor-expansions’ of the photon distribution function at the center with respect to the deviation, we can read off the CMB temperature anisotropy caused by the deviation in the photon distribution function. By doing so, we can, in principle, construct the l-th order multiple moment of the CMB temperature anisotropy from the (up to) l-th order expansion coefficients, with the help of the background null geodesic equations and the Boltzmann equation. We will do so for the first and second-order expansions to find the CMB dipole and quadrupole moments. We also provide the concrete expression of the corresponding formulae for the local void model. Our formulae are then checked to be consistent with the numerical analyses of the CMB temperature anisotropy in the local void model, previously made by Alnes and Amarzguioui. We apply our formulae to place the constraint on the distance between an observer and the symmetry center of the void, by using the latest Wilkinson Microwave Anisotropy Probe (WMAP) data, thereby updating the results of the previous analyses., 総研大甲第1589号},
title = {Cosmological tests of models for the accelerating universe in terms of inhomogeneities},
year = {}
}