arXiv subjects
Publications and source records attributed to Jiro Soda.
Recently, branes in supergravity have become an indispensable tool even for traditional relativists. The purpose of this manuscript is to provide a pedagogical account of the brane technology so that the relativists can use branes in their study. The type IIA supergravity theory is mainly discussed and other cases are briefly mentioned. The repulson singularity is also explained as an interesting application.
We investigate the effect of the bulk gravitational field on the cosmological perturbations on a brane embedded in the 5D Anti-de Sitter (AdS) spacetime. The effective 4D Einstein equations for the scalar cosmological perturbations on the brane are obtained by solving the perturbations in the bulk. Then the behaviour of the corrections induced by the bulk gravitational field to the conventional 4D Einstein equation are determined. Two types of the corrections are found. First we investigate the corrections which become significant at scales below the AdS curvature scales and in the high energy universe with the energy density larger than the tension of the brane. The evolution equation for the perturbations on the brane is found and solved. Another type of the corrections is induced on the brane if we consider the bulk perturbations which do not contribute to the metric perturbations but do contribute to the matter perturbations. At low energies, they have imaginary mass $m^2=-(2/3) \k^2$ in the bulk where $\k$ is the 3D comoving wave number of the perturbations. They diverge at the horizon of the AdS spacetime. The induced density perturbations behave as sound waves with sound velocity $1/\sqrt{3}$ in the low energy universe. At large scales, they are homogeneous perturbations that depend only on time and decay like radiation. They can be identified as the perturbations of the dark radiation. They produce isocurvature perturbations in the matter dominated era. Their effects can be observed as the shifts of the location and the height of the acoustic peak in the CMB spectrum.
The evolution of the cosmological perturbations is studied in the context of the Randall-Sundrum brane world scenario, in which our universe is realized on a three-brane in the five dimensional Anti-de Sitter(AdS) spacetime. We develop a formalism to solve the coupled dynamics of the cosmological perturbations in the brane world and the gravitational wave in the AdS bulk. Using our formalism, the late time evolution of the cosmological scalar perturbations at any scales larger than the AdS curvature scale $l$ is shown to be identical with the one obtained in the conventional 4D cosmology, provided the effect of heavy graviton modes may be neglected. Here the late time means the epoch when the Hubble horizon $H^{-1}$ in the 4D brane world is sufficiently larger than the AdS curvature scale $l$. If the inflation occurs sufficiently lower than $l^{-1}$, the scalar temperature anisotropies in the Cosmic Microwave Background at large scales can be calculated using the constancy of the Bardeen parameter as is done in the 4D cosmology. The assumption of the result is that the effect of the massive graviton with mass $m e^{-α_0}>l^{-1}$ in the brane world is negligible, where $e^{α_0}$ is the scale factor of the brane world. We also discuss the effect of these massive gravitons on the evolution of the perturbations.
We develop a formalism to calculate the effective action of the strongly coupled conformal field theory (CFT) in curved spacetime. The effective action of the CFT is obtained from AdS/CFT correspondence. The anti de-Sitter (AdS) spacetime has various slicing which give various curved spacetime on its boundary. We show the de Sitter spacetime and the Friedmann-Robertson-Walker (FRW) universe can be embedded in the AdS spacetime and derive the scalar two-point function of the conformal fields in those spacetime. In curved spacetime, the two-point function depends on the vacuum state of the CFT. A method to specify the vacuum state in AdS/CFT calculations is shown. Because the classical action in AdS spacetime diverges near the boundary, we need the counter terms to regulate the result. The simple derivation of the counter terms using the Hamilton-Jacobi equation is also presented in the appendix.
The classical central charge for the higher curvature gravity in 3-dimensions is calculated using the Legendre transformation method. The statistical entropy of BTZ black hole is derived by the Cardy's formula and the result completely coincides with the Iyer-Wald formula for the geometrical entropy. This coincidence suggests the generalized AdS/CFT correspondence.
We consider a model of an inhomogeneous universe including a massless scalar field, where the inhomogeneity is assumed to consist of many black holes. This model can be constructed by following Lindquist and Wheeler, which has already been investigated without including scalar field to show that an averaged scale factor coincides with that of the Friedmann model. In this work we construct the inhomogeneous universe with an massless scalar field, where we assume that the averaged scale factor and scalar field are given by those of the Friedmann model including a scalar field. All of our calculations are carried out in the framework of Brans-Dicke gravity. In constructing the model of an inhomogeneous universe, we define the mass of a black hole in the Brans-Dicke expanding universe which is equivalent to ADM mass if the mass evolves adiabatically, and obtain an equation relating our mass to the averaged scalar field and scale factor. As the results we find that the mass has an adiabatic time dependence in a sufficiently late stage of the expansion of the universe, and that the time dependence is qualitatively diffenrent according to the sign of the curvature of the universe: the mass increases decelerating in the closed universe case, is constant in the flat case and decreases decelerating in the open case. It is also noted that the mass in the Einstein frame depends on time. Our results that the mass has a time dependence should be retained even in the general scalar-tensor gravitiy with a scalar field potential. Furthermore, we discuss the relation of our results to the uniqueness theorem of black hole spacetime and gravitational memory effect.
The inflationary scenario for the brane world driven by the bulk inflaton is proposed. The quantum fluctuations of the inflaton is calculated and compared to those of the conventional 4-dimensional inflationary scenario. It is shown that the deviation of the primordial spectrum of this model from that of the conventional one is too small to be observed even if $AdS$ radius is very large. Hence, it turns out that the inflation caused by the bulk inflaton is viable in the context of brane world cosmology.
It appears difficult to construct a simple model for an open universe based on the one bubble inflationary scenario. The reason is that one needs a large mass to avoid the tunneling via the Hawking Moss solution and a small mass for successful slow-rolling. However, Rubakov and Sibiryakov suggest that the Hawking Moss solution is not a solution for the false vacuum decay process because it does not satisfy the boundary condition. Hence, we have reconsidered the arguments for the defect of the simple polynomial model. We point out the possibility that one of the valley bounce belonging to a valley line in the functional space represents the decay process instead of the Hawking Moss solution. Under this presumption, we show an open inflation model can be constructed within the polynomial form of the potential so that the fluctuations can be reconciled with the observations.
Birth of the brane world is studied using the Hamiltonian approach. It is shown that an inflating brane world can be created from nothing. The wave function of the universe obtained from the Wheeler de-Witt equation and the time-dependent Schr$\ddot{o}$dinger equation for quantized scalar fields on the brane are the same as in the conventional 4-dimensional quantum cosmology if the bulk is exactly the Anti-de Sitter spacetime. The effect of the massive objects in the bulk is also discussed. This analysis tells us the presence of the extra dimension imprints a nontrivial effect on the quantum cosmology of the brane world. This fact is important for the analysis of the quantum fluctuations in the inflationary scenario of the brane world.
It appears difficult to construct a simple model for an open universe based on the one bubble inflationary scenario. The reason is that one needs a large mass to avoid the tunneling via the Hawking Moss solution and a small mass for successful slow-rolling. However, Rubakov and Sibiryakov suggest that the Hawking Moss solution is not a solution for the false vacuum decay process since it does not satisfy the boundary condition. Hence, we have reconsidered the arguments for the defect of the simple polynomial model. We find the valley bounce belonging to a valley line in the functional space represents the decay process instead of the Hawking Moss solution. The point is that the valley bounce gives the appropriate initial condition for the inflation. We show an open inflation model can be constructed within the polynomial form of the potential so that the fluctuations can be reconciled with the observations.
For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated. It is equal to the Bekenstein-Hawking entropy. In this article, its statistical entropy in the higer curvature gravity is calculated and shown to be equal to one derived by using the Noether charge method. This suggests that the equivalence between the geometrical and statistical entropies of the black hole is retained in the general diffeomorphism invariant theories of gravity. A relation between the cosmic censorship conjecture and the unitarity of the conformal field theory on the boundary of AdS_3 is also discussed.
For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated to be equal to the Bekenstein-Hawking entropy. In this paper, the statistical entropy of the BTZ black hole in the higher curvature gravity is calculated and shown to be equal to the one derived by using the Noether charge method. This suggests that the equivalence of the geometrical and statistical entropies of the black hole is retained in the general diffeomorphism invariant theories of gravity. A relation between the cosmic censorship conjecture and the unitarity of the conformal field theory on the boundary of AdS is also discussed.
We consider constraints on the structure formation model based on non-Gaussian fluctuations generated during inflation, which have $χ_m^2$ distributions. Using three data sets, the abundance of the clusters at $z=0$, moderate $z$ and the correlation length, we show that constraints on the non-Gaussianity and the amplitude of fluctuations and the density parameter can be obtained. We obtain an upper bound for $Ω_m$ and a lower bound for the non-Gaussianity and the amplitude of the fluctuations. Using the abundance of clusters at $z \sim 0.6$, for the spectrum parameterized by cold dark matter (CDM) shape parameter $Γ=0.23$, we obtain an upper bound for the density parameter $Ω_m \sim 0.5$ and lower bounds for the amplitude $σ_8 \sim 0.7$ and for the non-Gaussianity of fluctuations $G \sim 2$ $(m \sim 200)$, where G=1 for Gaussian.
We propose novel structure formation scenarios based on a non-singular higher curvature cosmological model. The model is motivated by the $R^2$ coupling of a scalar field appearing in the string theory, and in our scenarios the universe has no beginning and no end. We give two examples with explicit parameter values which are consistent with present observations of the cosmological structure. In the first example, the origin of structures are generated as the adiabatic perturbation during the chaotic inflation, while in the second the isocurvature non-Gaussian perturbation from the superinflating era is responsible for the structure. In the second case it is possible to generate primordial supermassive blackholes whose scale is comparable to what is expected in the galactic nuclei.
We study the evolution of fluctuations in a universe dominated by a scalar field coupled to the Gauss-Bonnet term. During the graceful exit, we found non-negligible enhancements of both curvature perturbation and gravitational wave in the long wavelength limit, and we also found a short wavelength instability for steep background superinflation just after the completion of the graceful exit. This result for one possible graceful exit mechanism would provide a significant implication on the primordial spectrum from the string cos mology.
We propose a primeval baryon isocurvature model in the context of the Affleck-Dine (AD) baryogenesis mechanism. Quantum fluctuations of the AD field during inflation produce fluctuations in the baryon number. We obtain a model which gives both the appropriate baryon to entropy ratio of the order $10^{-11}$ and the gaussian baryon isocurvature perturbation of the order $10^{-3}$ at the break of the spectrum 1 Mpc with the steep spectrum $n=-1.5$ on large scales >1 Mpc.
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to Friedmann-like universe, via super inflation phase. We are interested in whether the non-singular nature of the solution would be stable or not in more general inhomogeneous case. Perturbative analysis is made for scalar, vector, and tensor linear perturbations, and instability is found for tensor-type perturbation.
Non-singular Bianchi type I solutions are found from the effective action with a superstring-motivated Gauss-Bonnet term. These anisotropic non-singular solutions evolve from the asymptotic Minkowski region, subsequently super-inflate, and then smoothly continue either to Kasner-type (expanding in two directions and shrinking in one direction) or to Friedmann-type (expanding in all directions) solutions. We also found a new kind of singularity which arises from the fact that the anisotropic expansion rates are multiple-valued function of time. The initial singularity in the isotropic limit of this model belongs to this new kind of singularity. In our analysis the anisotropic solutions are likely to be singular when the super-inflation is steep.