arXiv subjects

Masato Tokutake

Publications and source records attributed to Masato Tokutake.

2 recordsLinked to original sources

arXiv2017

Observational Constraint on Spherical Inhomogeneity with CMB and Local Hubble Parameter

We derive an observational constraint on a spherical inhomogeneity of the void centered at our position from the angular power spectrum of the cosmic microwave background(CMB) and local measurements of the Hubble parameter. The late time behaviour of the void is assumed to be well described by the so-called $\Lambda$-Lema\^itre-Tolman-Bondi~($\Lambda$LTB) solution. Then, we restrict the models to the asymptotically homogeneous models each of which is approximated by a flat Friedmann-Lema\^itre-Robertson-Walker model. The late time $\Lambda$LTB models are parametrized by four parameters including the value of the cosmological constant and the local Hubble parameter. The other two parameters are used to parametrize the observed distance-redshift relation. Then, the $\Lambda$LTB models are constructed so that they are compatible with the given distance-redshift relation. Including conventional parameters for the CMB analysis, we characterize our models by seven parameters in total. The local Hubble measurements are reflected in the prior distribution of the local Hubble parameter. As a result of a Markov-Chains-Monte-Carlo analysis for the CMB temperature and polarization anisotropies, we found that the inhomogeneous universe models with vanishing cosmological constant are ruled out as is expected. However, a significant under-density around us is still compatible with the angular power spectrum of CMB and the local Hubble parameter.

astro-ph.CO↗

arXiv2016

Inverse Construction of the $\Lambda$LTB Model from a Distance-redshift Relation

Spherically symmetric dust universe models with a positive cosmological constant $\Lambda$, known as $\Lambda$-Lema\^itre-Tolman-Bondi($\Lambda$LTB) models, are considered. We report a method to construct the $\Lambda$LTB model from a given distance-redshift relation observed at the symmetry center. The spherical inhomogeneity is assumed to be composed of growing modes. We derive a set of ordinary differential equations for three functions of the redshift, which specify the spherical inhomogeneity. Once a distance-redshift relation is given, with careful treatment of possible singular points, we can uniquely determine the model by solving the differential equations for each value of $\Lambda$. As a demonstration, we fix the distance-redshift relation as that of the flat $\Lambda$CDM model with $(\Omega^{\rm dis}_{\rm m0}, \Omega^{\rm dis}_{\rm \Lambda 0})=(0.3,0.7)$, where $\Omega^{\rm dis}_{\rm m0}$ and $\Omega^{\rm dis}_{\rm \Lambda 0}$ are the normalized matter density and the cosmological constant, respectively. Then, we construct the $\Lambda$LTB model for several values of $\Omega_{\rm \Lambda 0}:=\Lambda/(3H_0^2)$, where $H_0$ is the present Hubble parameter observed at the symmetry center. We obtain void structure around the symmetry center for $\Omega_{\Lambda 0}<\Omega^{\rm dis}_{\Lambda 0}$. We show the relation between the ratio $\Omega_{\Lambda0}/\Omega^{\rm dis}_{\Lambda 0}$ and the amplitude of the inhomogeneity.

astro-ph.CO↗