We study the cosmological implications of the one-loop terms in the string expansion. In particul... more We study the cosmological implications of the one-loop terms in the string expansion. In particular, we find non-singular solutions which interpolate between a contracting universe and an expanding universe, and show that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies. In addition, we perform numerical calculations to show that the non-singular cosmologies do not require a careful choice of initial conditions, and estimate the likely magnitude of higher order terms in the string expansion.
A black hole casts a shadow as an optical appearance because of its strong gravitational field. W... more A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.
Journal of Cosmology and Astroparticle Physics, Aug 25, 2011
We investigate the dynamics of a single spherical void embedded in a Friedmann-Lemaître universe,... more We investigate the dynamics of a single spherical void embedded in a Friedmann-Lemaître universe, and analyze the void shape in the redshift space. We find that the void in the redshift space appears as an ellipse shape elongated in the direction of the line of sight (i.e., an opposite deformation to the Kaiser effect). Applying this result to observed void candidates at the redshift z ∼ 1-2, it may provide us with a new method to evaluate the cosmological parameters, in particular the value of a cosmological constant.
We consider a superradiance effect around rotating dilatonic black holes. We analyze two cases: o... more We consider a superradiance effect around rotating dilatonic black holes. We analyze two cases: one is an exact solution with the coupling constant α = √ 3, which effective action is reduced from the 5-dimensional Kaluza-Klein theory, and the other is a slowly rotating dilatonic black holes with arbitrary coupling constant. We find that there exists a critical value (α ∼ 1), which is predicted from a superstring model, and the superradiant emission rate with coupling larger than the critical value becomes much higher than the Kerr-Newman case (α = 0) in the maximally charged limit. Consequently, 4-dimensional primordial black holes in higher dimensional unified theories are either rotating but almost neutral or charged but effectively non-rotating.
Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly... more Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems such as galaxies and interstellar molecular clouds. We study the origin of these properties using a onedimensional ring model which we newly propose in this paper. In this simple model, N particles are moving, on a circular ring fixed in three dimensional space, with mutual interaction of gravity. This model is suitable for the accurate symplectic integration method by which we argue the phase transition in this system. Especially, in between the extended-phase and the collapsed-phase, we find an interesting phase (halo-phase) which has negative specific heat at the intermediate energy scale. Moreover in this phase, there appear scaling properties and non-thermal and non-Gaussian velocity distributions. In contrast, these peculiar properties are never observed in other gas and core phases. Particles in each phase have a typical time scale of motions determined by the cutoff length ξ, the ring radius R, and the total energy E. Thus all relaxation patterns of the system are determined by these three time scales.
Using the covariant approach and conformal transformations, we present a gauge-invariant formalis... more Using the covariant approach and conformal transformations, we present a gauge-invariant formalism for cosmological perturbations in generalized Einstein theories (GETs), including the Brans-Dicke theory, theories with a non-minimally coupled scalar field and certain curvature-squared theories. We find an enhancement in the growth rate of density perturbations in the Brans-Dicke theory, and discuss attractive features of GETs in the structure formation process.
We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theorie... more We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact General Relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e. solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.
In one-loop string effective action, we study a generality of non-singular cosmological solutions... more In one-loop string effective action, we study a generality of non-singular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi I and IX type spacetimes. We find that nonsingular solutions still exist in Bianchi I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in Bianchi IX model. Non-existence of nonsingular Bianchi IX universe may be consistent with the analysis by Kawai, Sakagami and Soda, i.e. the tensor mode perturbations against nonsingular flat Friedmann universe are unstable, because Bianchi IX model can be regarded as a closed Friedmann universe with a single gravitational wave. So based on these facts, we may conclude the nonsingular universe is found in isotropic case is generally unstable, a singularity avoid
We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational ... more We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time t constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite time-t interval, t being the cosmological time, i.e. the time of an observer located far away from the collapsing cloud. The presence of this vanishing lapse endpoint implies the necessity of a UV completion to describe the physics inside the resulting black hole. On the other hand, since the corresponding cosmic time t is infinite, VCDM can safely describe the whole history of the universe at larg...
We study cosmological dynamics of the Cuscuta–Galileon gravity with a potential term by using the... more We study cosmological dynamics of the Cuscuta–Galileon gravity with a potential term by using the dynamical system approach. This model is galileon generalization of the cuscuton gravity where we add a potential term to the theory in order to obtain the radiation and matter dominated eras. The exponential potential can provide the sequence of the thermal history of the Universe correctly, i.e. starting from radiation dominance, passing through matter dominant era, and then approaching de Sitter expansion stage. This model has no ghosts and the Laplacian instability for both scalar and tensor perturbations. We also discuss the observational constraints on the model parameters. It turns out that the model actually has three degrees of freedom unlike the original cuscuton theory.
Primordial Nucleosynthesis and Evolution of Early Universe, 1991
The cosmology resulting from two coupled scalar fields, one which is either a new or chaotic type... more The cosmology resulting from two coupled scalar fields, one which is either a new or chaotic type inflaton and the other which has an exponentially decaying potential, is studied. Such a potential arises in superstring theories and in the conformally transformed frame of generalized Einstein theories like the Jordan-Brans-Dicke theory. The constraints necessary for successful inflation are examined. Conventional GUT models such as SU(5) are compatible with new inflation, while restrictions on the self-coupling constant are significantly loosened for chaotic inflation when the exponential potential is fundamental, but no significant improvement for the latter occurs when in the conformal frame.
We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface... more We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Hořava-Lifshitz theory, which is composed of the z = 2 Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. While, if three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns to be a spacelike singularity.
We study the dynamics of the universe with a scalar field and an SU(2) non-Abelian Gauge (Yang-Mi... more We study the dynamics of the universe with a scalar field and an SU(2) non-Abelian Gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary solution is a stable attractor in a certain range of coupling parameters. Unlike the case with multiple Abelian gauge fields, the power-law inflationary solution with the dominant electric component is unstable because of the existence of non-linear coupling of the Yang-Mills field. We also analyze the dynamics for the non-inflationary regime, and find several attractor solutions.
We investigate two Type-IIa minimally modified gravity theories, namely V ðφÞ Cold Dark Matter (V... more We investigate two Type-IIa minimally modified gravity theories, namely V ðφÞ Cold Dark Matter (VCDM) and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact general relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e., solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.
We study the Hawking radiation in a monopole black hole background in SO(3) Einstein-Yang-Mills-H... more We study the Hawking radiation in a monopole black hole background in SO(3) Einstein-Yang-Mills-Higgs system. We only consider a massless scalar field which does not couple with the Yang-Mills field or Higgs field around the black hole. Starting from a Reissner-Nortström black hole, and assuming that it transits into a monopole black hole at a critical point, we find that the evaporation rate will increase continuously or discontinuously according to the type of phase transition, that is either second order or first order, respectively. We also discuss differences in evaporating rate between a monopole black hole and a Reissner-Nortström black hole. The results are such that although the transmission amplitude Γ for a monopole black hole becomes smaller than electronic mail:tamaki@gravity.phys.waseda.ac.jp electronic mail:maeda@gravity.phys.waseda.ac.jp
We study gravitational waves from a particle moving around a system of a point mass with a disk i... more We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase of the orbit in which particle motion becomes to be nearly regular (the so-called ``stagnant motion'') for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviours affect on observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different ch...
We study statistical mechanics of the self--gravitating system applying the cluster expansion met... more We study statistical mechanics of the self--gravitating system applying the cluster expansion method developed in solid state physics. By summing infinite series of diagrams, we derive a complex free energy whose imaginary part is related to the relaxation time of the system. Summation of another series yields two--point correlation function whose correlation length is essentially given by the Jeans wavelength of the system.
Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 1998
Using a metric perturbation method, we study gravitational waves from a test particle scattered b... more Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius R < ∼ 3M ), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole).
We consider the internal structure of the Skyrme black hole under a static and spherically symmet... more We consider the internal structure of the Skyrme black hole under a static and spherically symmetric ansatz. @u8(Be concentrate on solutions with the node number one and with the "winding" number zero, where there exist two solutions for each horizon radius; one solution is stable and the other is unstable against linear perturbation. We find that a generic solution exhibits an oscillating behavior near the sigularity, as similar to a solution in the Einstein-Yang-Mills (EYM) system, independently to stability of the solution. Comparing it with that in the EYM system, this oscillation becomes mild because of the mass term of the Skyrme field. We also find Schwarzschild-like exceptional solutions where no oscillating behavior is seen. Contrary to the EYM system where there is one such solution branch if the node number is fixed, there are two branches corresponding to the stable and the unstable ones.
We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a ga... more We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models, which include Bianchi type I, II, VI0, VII0, VIII and IX. The linear stability of isotropic inflationary solution with background magnetic field is shown, which generalizes the known results for U(1) gauge fields. We also study anisotropic inflationary solutions, all of which turn out to be unstable. Then nonlinear stability for the isotropic inflationary solution is examined by numerically investigating the dependence of the late-time behaviour on the initial conditions. We present a number of novel features that may well affect physical predictions and viability of the models. First, in the absence of spatial curvature, strong initial anisotropy leads to a rapid oscillation of gauge field, thwarting convergence to the inflationary attractor. Secondly, the inclusion of spatial curvature destabilizes the oscillatory attractor and t...
We study the cosmological implications of the one-loop terms in the string expansion. In particul... more We study the cosmological implications of the one-loop terms in the string expansion. In particular, we find non-singular solutions which interpolate between a contracting universe and an expanding universe, and show that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies. In addition, we perform numerical calculations to show that the non-singular cosmologies do not require a careful choice of initial conditions, and estimate the likely magnitude of higher order terms in the string expansion.
A black hole casts a shadow as an optical appearance because of its strong gravitational field. W... more A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.
Journal of Cosmology and Astroparticle Physics, Aug 25, 2011
We investigate the dynamics of a single spherical void embedded in a Friedmann-Lemaître universe,... more We investigate the dynamics of a single spherical void embedded in a Friedmann-Lemaître universe, and analyze the void shape in the redshift space. We find that the void in the redshift space appears as an ellipse shape elongated in the direction of the line of sight (i.e., an opposite deformation to the Kaiser effect). Applying this result to observed void candidates at the redshift z ∼ 1-2, it may provide us with a new method to evaluate the cosmological parameters, in particular the value of a cosmological constant.
We consider a superradiance effect around rotating dilatonic black holes. We analyze two cases: o... more We consider a superradiance effect around rotating dilatonic black holes. We analyze two cases: one is an exact solution with the coupling constant α = √ 3, which effective action is reduced from the 5-dimensional Kaluza-Klein theory, and the other is a slowly rotating dilatonic black holes with arbitrary coupling constant. We find that there exists a critical value (α ∼ 1), which is predicted from a superstring model, and the superradiant emission rate with coupling larger than the critical value becomes much higher than the Kerr-Newman case (α = 0) in the maximally charged limit. Consequently, 4-dimensional primordial black holes in higher dimensional unified theories are either rotating but almost neutral or charged but effectively non-rotating.
Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly... more Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems such as galaxies and interstellar molecular clouds. We study the origin of these properties using a onedimensional ring model which we newly propose in this paper. In this simple model, N particles are moving, on a circular ring fixed in three dimensional space, with mutual interaction of gravity. This model is suitable for the accurate symplectic integration method by which we argue the phase transition in this system. Especially, in between the extended-phase and the collapsed-phase, we find an interesting phase (halo-phase) which has negative specific heat at the intermediate energy scale. Moreover in this phase, there appear scaling properties and non-thermal and non-Gaussian velocity distributions. In contrast, these peculiar properties are never observed in other gas and core phases. Particles in each phase have a typical time scale of motions determined by the cutoff length ξ, the ring radius R, and the total energy E. Thus all relaxation patterns of the system are determined by these three time scales.
Using the covariant approach and conformal transformations, we present a gauge-invariant formalis... more Using the covariant approach and conformal transformations, we present a gauge-invariant formalism for cosmological perturbations in generalized Einstein theories (GETs), including the Brans-Dicke theory, theories with a non-minimally coupled scalar field and certain curvature-squared theories. We find an enhancement in the growth rate of density perturbations in the Brans-Dicke theory, and discuss attractive features of GETs in the structure formation process.
We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theorie... more We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact General Relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e. solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.
In one-loop string effective action, we study a generality of non-singular cosmological solutions... more In one-loop string effective action, we study a generality of non-singular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi I and IX type spacetimes. We find that nonsingular solutions still exist in Bianchi I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in Bianchi IX model. Non-existence of nonsingular Bianchi IX universe may be consistent with the analysis by Kawai, Sakagami and Soda, i.e. the tensor mode perturbations against nonsingular flat Friedmann universe are unstable, because Bianchi IX model can be regarded as a closed Friedmann universe with a single gravitational wave. So based on these facts, we may conclude the nonsingular universe is found in isotropic case is generally unstable, a singularity avoid
We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational ... more We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time t constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite time-t interval, t being the cosmological time, i.e. the time of an observer located far away from the collapsing cloud. The presence of this vanishing lapse endpoint implies the necessity of a UV completion to describe the physics inside the resulting black hole. On the other hand, since the corresponding cosmic time t is infinite, VCDM can safely describe the whole history of the universe at larg...
We study cosmological dynamics of the Cuscuta–Galileon gravity with a potential term by using the... more We study cosmological dynamics of the Cuscuta–Galileon gravity with a potential term by using the dynamical system approach. This model is galileon generalization of the cuscuton gravity where we add a potential term to the theory in order to obtain the radiation and matter dominated eras. The exponential potential can provide the sequence of the thermal history of the Universe correctly, i.e. starting from radiation dominance, passing through matter dominant era, and then approaching de Sitter expansion stage. This model has no ghosts and the Laplacian instability for both scalar and tensor perturbations. We also discuss the observational constraints on the model parameters. It turns out that the model actually has three degrees of freedom unlike the original cuscuton theory.
Primordial Nucleosynthesis and Evolution of Early Universe, 1991
The cosmology resulting from two coupled scalar fields, one which is either a new or chaotic type... more The cosmology resulting from two coupled scalar fields, one which is either a new or chaotic type inflaton and the other which has an exponentially decaying potential, is studied. Such a potential arises in superstring theories and in the conformally transformed frame of generalized Einstein theories like the Jordan-Brans-Dicke theory. The constraints necessary for successful inflation are examined. Conventional GUT models such as SU(5) are compatible with new inflation, while restrictions on the self-coupling constant are significantly loosened for chaotic inflation when the exponential potential is fundamental, but no significant improvement for the latter occurs when in the conformal frame.
We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface... more We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Hořava-Lifshitz theory, which is composed of the z = 2 Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. While, if three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns to be a spacelike singularity.
We study the dynamics of the universe with a scalar field and an SU(2) non-Abelian Gauge (Yang-Mi... more We study the dynamics of the universe with a scalar field and an SU(2) non-Abelian Gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary solution is a stable attractor in a certain range of coupling parameters. Unlike the case with multiple Abelian gauge fields, the power-law inflationary solution with the dominant electric component is unstable because of the existence of non-linear coupling of the Yang-Mills field. We also analyze the dynamics for the non-inflationary regime, and find several attractor solutions.
We investigate two Type-IIa minimally modified gravity theories, namely V ðφÞ Cold Dark Matter (V... more We investigate two Type-IIa minimally modified gravity theories, namely V ðφÞ Cold Dark Matter (VCDM) and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact general relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e., solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.
We study the Hawking radiation in a monopole black hole background in SO(3) Einstein-Yang-Mills-H... more We study the Hawking radiation in a monopole black hole background in SO(3) Einstein-Yang-Mills-Higgs system. We only consider a massless scalar field which does not couple with the Yang-Mills field or Higgs field around the black hole. Starting from a Reissner-Nortström black hole, and assuming that it transits into a monopole black hole at a critical point, we find that the evaporation rate will increase continuously or discontinuously according to the type of phase transition, that is either second order or first order, respectively. We also discuss differences in evaporating rate between a monopole black hole and a Reissner-Nortström black hole. The results are such that although the transmission amplitude Γ for a monopole black hole becomes smaller than electronic mail:tamaki@gravity.phys.waseda.ac.jp electronic mail:maeda@gravity.phys.waseda.ac.jp
We study gravitational waves from a particle moving around a system of a point mass with a disk i... more We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase of the orbit in which particle motion becomes to be nearly regular (the so-called ``stagnant motion'') for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviours affect on observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different ch...
We study statistical mechanics of the self--gravitating system applying the cluster expansion met... more We study statistical mechanics of the self--gravitating system applying the cluster expansion method developed in solid state physics. By summing infinite series of diagrams, we derive a complex free energy whose imaginary part is related to the relaxation time of the system. Summation of another series yields two--point correlation function whose correlation length is essentially given by the Jeans wavelength of the system.
Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 1998
Using a metric perturbation method, we study gravitational waves from a test particle scattered b... more Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius R < ∼ 3M ), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole).
We consider the internal structure of the Skyrme black hole under a static and spherically symmet... more We consider the internal structure of the Skyrme black hole under a static and spherically symmetric ansatz. @u8(Be concentrate on solutions with the node number one and with the "winding" number zero, where there exist two solutions for each horizon radius; one solution is stable and the other is unstable against linear perturbation. We find that a generic solution exhibits an oscillating behavior near the sigularity, as similar to a solution in the Einstein-Yang-Mills (EYM) system, independently to stability of the solution. Comparing it with that in the EYM system, this oscillation becomes mild because of the mass term of the Skyrme field. We also find Schwarzschild-like exceptional solutions where no oscillating behavior is seen. Contrary to the EYM system where there is one such solution branch if the node number is fixed, there are two branches corresponding to the stable and the unstable ones.
We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a ga... more We study anisotropic cosmologies of a scalar field interacting with an SU(2) gauge field via a gauge-kinetic coupling. We analyze Bianchi class A models, which include Bianchi type I, II, VI0, VII0, VIII and IX. The linear stability of isotropic inflationary solution with background magnetic field is shown, which generalizes the known results for U(1) gauge fields. We also study anisotropic inflationary solutions, all of which turn out to be unstable. Then nonlinear stability for the isotropic inflationary solution is examined by numerically investigating the dependence of the late-time behaviour on the initial conditions. We present a number of novel features that may well affect physical predictions and viability of the models. First, in the absence of spatial curvature, strong initial anisotropy leads to a rapid oscillation of gauge field, thwarting convergence to the inflationary attractor. Secondly, the inclusion of spatial curvature destabilizes the oscillatory attractor and t...
Uploads
Papers by Kei-ichi Maeda