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Masayuki Tanimoto

Publications and source records attributed to Masayuki Tanimoto.

At least 19 recordsLinked to original sources
arXiv2009

The Role of Anisotropy in the Void Models without Dark Energy

Void models provide a possible explanation of the "accelerated expansion" of the Universe without dark energy. To make the conventional void models more realistic, we allow the void, an underdense region around us, to be anisotropic and consider an average of the distance-redshift relations over the solid angle subtended at the observer. We first show that after taking the average of a form of the optical scalar equation (distance equation), the effective distance equation we obtain coincides with the one for the Lemaitre-Tolman-Bondi universe with a Dyer-Roeder-like extension. We then numerically solve the equation to compare with observational data of Type Ia supernovae. We find that anisotropy allows smaller size of void and larger Omega_m.

astro-ph.CO↗
arXiv2007

Luminosity distance-redshift relation for the LTB solution near the center

Motivated by the inverse problem for the Lemaitre-Tolman-Bondi dust solution, in which problem the luminosity distance function $D_L(z)$ is taken as an input to select a specific model, we compute the function $D_L(z)$ of the LTB solution up to the third order of $z$. To perform the otherwise cumbersome computation, we introduce a new convenient form of the LTB solution, in which the solution is explicit and unified. With this form of the LTB solution we obtain the luminosity distance function with the full generality. We in particular find that the function exactly coincides with that of a homogeneous and isotropic dust solution up to second order, if we demand that the solution be regular at the center.

gr-qc↗
arXiv2005

Accelerating Universe via Spatial Averaging

We present a model of an inhomogeneous universe that leads to accelerated expansion after taking spatial averaging. The model universe is the Tolman-Bondi solution of the Einstein equation and contains both a region with positive spatial curvature and a region with negative spatial curvature. We find that after the region with positive spatial curvature begins to re-collapse, the deceleration parameter of the spatially averaged universe becomes negative and the averaged universe starts accelerated expansion. We also discuss the generality of the condition for accelerated expansion of the spatially averaged universe.

gr-qc↗
arXiv2004

Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations

Using appropriate harmonics, we study the future asymptotic behavior of massless scalar fields on a class of cosmological vacuum spacetimes. The spatial manifold is assumed to be a circle bundle over a higher genus surface with a locally homogeneous metric. Such a manifold corresponds to the SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III type). After a technical preparation including an introduction of suitable harmonics for the circle-fibered Bianchi VIII to separate variables, we derive systems of ordinary differential equations for the scalar field. We present future asymptotic solutions for these equations in a special case, and find that there is a close similarity with those on the circle-fibered Bianchi III spacetime. We discuss implications of this similarity, especially to (gravitational) linear perturbations. We also point out that this similarity can be explained by the "fiber term dominated behavior" of the two models.

gr-qc↗
arXiv2004

Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model

To analyze linear field equations on a locally homogeneous spacetime by means of separation of variables, it is necessary to set up appropriate harmonics according to its symmetry group. In this paper, the harmonics are presented for a spatially compactified Bianchi II cosmological model -- the nilgeometric model. Based on the group structure of the Bianchi II group (also known as the Heisenberg group) and the compactified spatial topology, the irreducible differential regular representations and the multiplicity of each irreducible representation, as well as the explicit form of the harmonics are all completely determined. They are also extended to vector harmonics. It is demonstrated that the Klein-Gordon and Maxwell equations actually reduce to systems of ODEs, with an asymptotic solution for a special case.

gr-qc↗
arXiv2003

Linear perturbations of spatially locally homogeneous spacetimes

Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein's equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III (Thurston's H^2 x R) type, while the other is the Bianchi II (Thurston's Nil) type. With a brief summary of previous results on the Bianchi III perturbations, asymptotic solutions for the gauge-invariant variables for the Bianchi III are shown, with which (in)stability of the background solution is also examined. The issue of linear stability for a Bianchi II solution is still an open problem. To approach it, appropriate eigenfunctions are presented for an explicitly compactified Bianchi II manifold and based on that, some field equations on the Bianchi II background spacetime are studied. Differences between perturbation analyses for Bianchi class B (to which Bianchi III belongs) and class A (to which Bianchi II belongs) are stressed for an intention to be helpful for applications to other models.

gr-qc↗
arXiv2003

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.

gr-qc↗
arXiv2001

Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it generalized Gowdy models}), are characterized by the existence of two commuting spatial {\it local} Killing vectors. For systematic investigations we first present a classification of possible spatial topologies in this class. We stress the significance of the locally homogeneous limits (i.e., the Bianchi types or the `geometric structures') of the models. In particular, we show a method of reduction to the natural reduced manifold, and analyze the equivalences at the reduced level of the models as dynamical models. Based on these fundamentals, we examine the influence of spatial topologies on dynamics by obtaining translation and reflection operators which commute with the dynamical flow in the phase space.

gr-qc↗
arXiv1999

Criticality and Averaging in Cosmology

We propose comparing cosmological solutions in terms of their total spatial volumes $V(τ)$ as functions of proper time $τ$, assuming synchronous gauge, and with this intention evaluate the variations of $V(τ)$ about the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) solutions for dust. This can be done successfully in a simple manner without solving perturbation equations. In particular, we find that first variations vanish with respect to all directions which do not possess homogeneity and isotropy preserving components; in other words, every FLRW solution is a {\it critical point} for $V(τ)$ in the properly restricted subspace of the space of solutions. This property may support a validity of the interpretation of the FLRW solutions as constituting an averaged model. We also briefly investigate the second variations of $V(τ)$.

gr-qc↗
arXiv1999

Averaging from a global point of view

We study the averaging problem from a point of view of variation of spatial volume $V$. We show that in the space of spherically symmetric dust solutions which are regular on the spatial manifold $S^3$ the variation $δV$ vanishes at the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution in an appropriate sense, which supports the validity of the FLRW solution as the averaged solution. We also present the second variation $δ^2 V$, giving the leading effect of the deviation from the FLRW solution.

gr-qc↗
arXiv1998

New varieties of Gowdy spacetimes

Gowdy spacetimes are generalized to admit two commuting spatial "local" Killing vectors, and some new varieties of them are presented, which are all closely related to Thurston's geometries. Explicit spatial compactifications, as well as the boundary conditions for the metrics are given in a systematic way. A short comment on an implication to their dynamics toward the initial singularity is made.

gr-qc↗
arXiv1997

Hamiltonians for Compact Homogeneous Universes

We briefly show how we can obtain Hamiltonians for spatially compact locally homogeneous vacuum spacetimes. The dynamical variables are categorized into the curvature parameters and the Teichmüller parameters. While the Teichmüller parameters usually parameterise the covering group of the spatial sections, we utilise another suitable parameterization where the universal cover metric carries all the dynamical variables and with this we reduce the Hamiltonians. For our models, all dynamical variables possess their clear geometrical meaning, in contrast to the conventional open models.}

gr-qc↗
arXiv1997

Hamiltonian structures for compact homogeneous universes

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key ingredients of our arguments is a suitable mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variations, i.e., the covering group is fixed. We discuss general problems concerned with the use of this expression in the context of general relativity, and demonstrate the reduction of the Hamiltonians for some examples. For our models, all the dynamical degrees of freedom in Hamiltonian view are unambiguously interpretable as geometrical deformations, in contrast to the conventional open models.

gr-qc↗
arXiv1996

Dynamics of compact homogeneous universes

A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four dimensional spacetime with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the spacetime isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogenoeus universes. Some examples are demonstrated for Bianchi II, VI${}_0$, VII${}_0$, and I universal covers.

gr-qc↗
arXiv1994

Compact Homogeneous Universes

A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski-Sachs-Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorised into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.

gr-qc↗
arXiv1994

Static axisymmetric spacetimes with non-generic world-line SUSY

The conditions for the existence of Killing-Yano tensors, which are closely related to the appearance of non-generic world-line SUSY, are presented for static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set of solutions admitting Killing-Yano tensors is considered. In particular, it is shown that static, axisymmetric and asymptotically flat vacuum solutions admitting Killing-Yano tensors are only the Schwarzschild solution.

gr-qc↗