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Hajime Aoki

Publications and source records attributed to Hajime Aoki.

At least 19 recordsLinked to original sources
arXiv2019

Large-scale inhomogeneity of dark energy produced in the ancestor vacuum

We investigate large-scale inhomogeneity of dark energy in the bubble nucleation scenario of the universe. In this scenario, the present universe was created by a bubble nucleation due to quantum tunneling from a metastable ancestor vacuum, followed by a primordial inflationary era. During the bubble nucleation, supercurvature modes of some kind of a scalar field are produced, and remain until present without decaying; thus they can play a role of the dark energy, if the mass of the scalar field is sufficiently light in the present universe. The supercurvature modes fluctuate at a very large spatial scale, much longer than the Hubble length in the present universe. Thus they create large-scale inhomogeneities of the dark energy, and generate large-scale anisotropies in the cosmic microwave background (CMB) fluctuations. This is a notable feature of this scenario, where quantum fluctuations of a scalar field are responsible for the dark energy. In this paper, we calculate imprints of the scenario on the CMB anisotropies through the integrated Sachs-Wolfe (ISW) effect, and give observational constraints on the curvature parameter $Ω_K$ and on an additional parameter $ε$ describing some properties of the ancestor vacuum.

astro-ph.CO↗
arXiv2018

Observational signatures of dark energy produced in an ancestor vacuum: Forecast for galaxy surveys

We study observational consequences of the model for dark energy proposed in [1] (Aoki et al., Phys.Rev. D97 (2018) no.4, 043517). We assume our universe has been created by bubble nucleation, and consider quantum fluctuations of an ultralight scalar field. Residual effects of fluctuations generated in an ancestor vacuum (de Sitter space in which the bubble was formed) is interpreted as dark energy. Its equation of state parameter w(z) has a characteristic form, approaching -1 in the future, but -1/3 in the past. A novel feature of our model is that dark energy effectively increases the magnitude of the negative spatial curvature in the evolution of the Hubble parameter, though it does not alter the definition of the angular diameter distance. We perform Fisher analysis and forecast the constraints for our model from future galaxy surveys by Square Kilometre Array and Euclid. Due to degeneracy between dark energy and the spatial curvature, galaxy surveys alone can determine these parameters only for optimistic choices of their values, but combination with other independent observations, such as CMB, will greatly improve the chance of determining them.

astro-ph.CO↗
arXiv2018

Vacuum fluctuations in an ancestor vacuum: A possible dark energy candidate

We consider an open universe created by bubble nucleation, and study possible effects of an "ancestor vacuum" (de Sitter space in which bubble nucleation occurred) on the present universe. We compute vacuum expectation values of energy-momentum tensor for a minimally coupled scalar field, carefully taking into account the effect of the ancestor vacuum by the Euclidean prescription. In the study of the time evolution, an important role is played by the so-called supercurvature mode, which is non-normalizable on a spatial slice of open universe and decays in time most slowly. We point out that vacuum energy of a quantum field can be regarded as dark energy if mass of the field is of order the present Hubble parameter or smaller. We obtain preliminary results for the dark energy equation of state w(z) as a function of the redshift.

hep-th↗
arXiv2015

Evolution of Vacuum Fluctuations of an Ultra-Light Massive Scalar Field generated during and before Inflation

We consider an ultra-light scalar field with a mass comparable to (or lighter than) the Hubble parameter of the present universe, and calculate the time evolution of the energy-momentum tensor of the vacuum fluctuations generated during and before inflation until the late-time radiation-dominated and matter-dominated universe. The equation of state changes from $w=1/3$ in the early universe to $w=-1$ at present, and it can give a candidate for the dark energy that we observe today. It then oscillates between $w=-1$ and $1$ with the amplitude of the energy density decaying as $a^{-3}$. If the fluctuations are generated during ordinary inflation with the Hubble parameter $H_I \lesssim 10^{-5} M_{\rm Pl}$, where $M_{\rm Pl}$ is the reduced Planck scale, we need a very large e-folding number $N \gtrsim 10^{12}$ to explain the present dark energy of the order of $10^{-3} {\rm eV}$. If a Planckian universe with a large Hubble parameter $H_P \sim M_{\rm Pl}$ existed before the ordinary inflation, an e-folding number $N \sim 240$ of the Planckian inflation is sufficient.

gr-qc↗
arXiv2014

Evolution of vacuum fluctuations generated during and before inflation

We calculate the time evolution of the expectation value of the energy-momentum tensor for a minimally-coupled massless scalar field in cosmological spacetimes, with an application to dark energy in mind. We first study the evolution from inflation until the present, fixing the Bunch-Davies initial condition. The energy density of a quantum field evolves as $ρ\sim 3(H_I H)^2 /32 π^2 $ in the matter-dominated (MD) period, where $H_I$ and $H$ are the Hubble parameters during inflation and at each moment. Its equation of state, $w=ρ/p$, changes from a negative value to $w=1/3$ in the radiation-dominated period, and from $1/3$ to $w=0$ in the MD period. We then consider possible effects of a Planckian universe, which may have existed before inflation, by assuming there was another inflation with the Hubble parameter $H_P (> H_I)$. In this case, modes with wavelengths longer than the current horizon radius are mainly amplified, and the energy density of a quantum field grows with time as $ρ\sim (a/a_0)(H_P H)^2/32$ in the MD period, where $a$ and $a_0$ are the scale factors at each time and at present. Hence, if $H_P$ is of the order of the Planck scale $M_P$, $ρ$ becomes comparable to the critical density $3(M_P H)^2$ at the present time. The contribution to $ρ$ from the long wavelength fluctuations generated before the ordinary inflation has $w=-1/3$ in the free field approximation. We mention a possibility that interactions further amplify the energy density and change the equation of state.

hep-th↗
arXiv2014

Realizing three generations of the Standard Model fermions in the type IIB matrix model

We discuss how the Standard Model particles appear from the type IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. In particular, we are concerned with a constructive definition of the theory, in which we start with finite-N matrices and take the large-N limit afterwards. In that case, it was pointed out recently that realizing chiral fermions in the model is more difficult than it had been thought from formal arguments at N=infinity and that introduction of a matrix version of the warp factor is necessary. Based on this new insight, we show that two generations of the Standard Model fermions can be realized by considering a rather generic configuration of fuzzy S^2 and fuzzy S^2 * S^2 in the extra dimensions. We also show that three generations can be obtained by squashing one of the S^2's that appear in the configuration. Chiral fermions appear at the intersections of the fuzzy manifolds with nontrivial Yukawa couplings to the Higgs field, which can be calculated from the overlap of their wave functions.

hep-th↗
arXiv2014

Phenomenological studies in the matrix models

Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability distribution of their appearance. This article mainly addresses studies in toroidal compactifications with magnetic fluxes.

hep-th↗
arXiv2013

Probability distribution over some phenomenological models in the matrix model compactified on a torus

We study some phenomenological models in a matrix model corresponding to the IIB matrix model compactified on a six-dimensional torus with magnetic fluxes. Extending our previous works, we examine a wider class of models: a Pati-Salam-like model with a gauge group U(4)*U_L(2)*U_R(2), and models where the gauge group U(4) is broken down to U_c(3)*U(1) and/or U_R(2) is broken down to U(1)^2. We find all the matrix configurations that yield matter content of all the phenomenological models whose gauge group is a subgroup of U(8). We then estimate semiclassically a probability distribution for the appearance of the phenomenological models.

hep-th↗
arXiv2013

Probability of the Standard Model Appearance from a Matrix Model

The standard model of particle physics lies in an enormous number of string vacua. In a nonperturbative formulation of string theory, various string vacua can, in principle, be compared dynamically, and the probability distribution over the vacuum space could be calculated. In this paper, we consider situations where the IIB matrix model is compactified on a six-dimensional torus with various gauge groups and various magnetic fluxes, find matrix configurations that provide the standard model matter content, and estimate semiclassically the probability of their appearance.

hep-th↗
arXiv2012

Revisiting the Naturalness Problem -- Who is afraid of quadratic divergences? --

It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences, which can always be absorbed into a position of the critical surface, should be simply subtracted in model constructions. Such a picture gives another justification to the argument that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.

hep-ph↗
arXiv2010

Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter

We formulate a Ginsparg-Wilson relation on a fuzzy 2-sphere for matter in the adjoint representation of the gauge group. Because of the Ginsparg-Wilson relation, an index theorem is satisfied. Our formulation is applicable to topologically nontrivial configurations as monopoles. It gives a solid basis for obtaining chiral fermions, which are an important ingredient of the standard model, from matrix model formulations of the superstring theory, such as the IIB matrix model, by considering topological configurations in the extra dimensions. We finally discuss whether this mechanism really works.

hep-th↗
arXiv2009

Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation

We construct a topological charge of gauge field configurations on a fuzzy S^2xS^2 by using a Dirac operator satisfying the Ginsparg-Wilson relation. The topological charge defined on the fuzzy S^2xS^2 can be interpreted as a noncommutative (or matrix) generalization of the 2nd Chern character on S^2xS^2. We further calculate the number of chiral zero modes of the Dirac operator in topologically nontrivial gauge configurations. Generalizations of our formulation to fuzzy (S^2)^k are also discussed.

hep-th↗
arXiv2009

Dominance of a single topological sector in gauge theory on non-commutative geometry

We demonstrate a striking effect of non-commutative (NC) geometry on topological properties of gauge theory by Monte Carlo simulations. We study 2d U(1) NC gauge theory for various boundary conditions using a new finite-matrix formulation proposed recently. We find that a single topological sector dictated by the boundary condition dominates in the continuum limit. This is in sharp contrast to the results in commutative space-time based on lattice gauge theory, where all topological sectors appear with certain weights in the continuum limit. We discuss possible implications of this effect in the context of string theory compactifications and in field theory contexts.

hep-th↗
arXiv2009

Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions

We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our formulation is based on the algebraic characterization of the configuration space. This enables us to describe the twisted boundary conditions in terms of finite matrices and hence to realize the Morita equivalence at a fully regularized level. Matter fields in the fundamental representation turn out to be represented by rectangular matrices for twisted boundary conditions analogously to the matrix spherical harmonics on the fuzzy sphere with the monopole background. The corresponding Ginsparg-Wilson Dirac operator defines an index, which can be used to classify gauge field configurations into topological sectors. We also perform Monte Carlo calculations for the index as a consistency check. Our formulation is expected to be useful for applications of non-commutative geometry to various problems related to topological aspects of field theories and string theories.

hep-th↗
arXiv2008

Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere

We consider a gauge-Higgs system on a fuzzy 2-sphere and study the topological structure of gauge configurations, when the U(2) gauge symmetry is spontaneously broken to U(1) times U(1) by the vev of the Higgs field. The topology is classified by the index of the Dirac operator satisfying the Ginsparg-Wilson relation, which turns out to be a noncommutative analog of the topological charge introduced by 't Hooft. It can be rewritten as a form whose commutative limit becomes the winding number of the Higgs field. We also study conditions which assure the validity of the formulation, and give a generalization of the admissibility condition. Finally we explicitly calculate the topological charge of a one-parameter family of configurations.

hep-th↗
arXiv2007

Probability distribution of the index in gauge theory on 2d non-commutative geometry

We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index nu of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of nu by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under nu -> -nu, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.

hep-th↗
arXiv2007

Index Theorem in Finite Noncommutative Geometry

Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological aspects in gauge theory is also shown.

hep-th↗