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Tsutomu Kobayashi

Publications and source records attributed to Tsutomu Kobayashi.

At least 37 records · Page 2Linked to original sources
arXiv2022

Cosmological gravity probes: connecting recent theoretical developments to forthcoming observations

Since the discovery of the accelerated expansion of the present Universe, significant theoretical developments have been made in the area of modified gravity. In the meantime, cosmological observations have been providing more high-quality data, allowing us to explore gravity on cosmological scales. To bridge the recent theoretical developments and observations, we present an overview of a variety of modified theories of gravity and the cosmological observables in the cosmic microwave background and large-scale structure, supplemented with a summary of predictions for cosmological observables derived from cosmological perturbations and sophisticated numerical studies. We specifically consider scalar-tensor theories in the Horndeski and DHOST family, massive gravity/bigravity, vector-tensor theories, metric-affine gravity, and cuscuton/minimally-modified gravity, and discuss the current status of those theories with emphasis on their physical motivations, validity, appealing features, the level of maturity, and calculability. We conclude that the Horndeski theory is one of the most well-developed theories of modified gravity, although several remaining issues are left for future observations. The paper aims to help to develop strategies for testing gravity with ongoing and forthcoming cosmological observations.

astro-ph.CO↗
arXiv2022

Testing gravity with the cosmic microwave background: constraints on modified gravity with two tensorial degrees of freedom

We provide a cosmological test of modified gravity with two tensorial degrees of freedom and no extra propagating scalar mode. The theory of gravity we consider admits a cosmological model that is indistinguishable from the $Λ$CDM model at the level of the background evolution. The model has a single modified-gravity parameter $β$, the effect of which can be seen in linear perturbations, though no extra scalar mode is propagating. Using the Boltzmann code modified to incorporate the present model, we derive the constraints $-0.047 < β< -0.028$ at 68$\%$ confidence from Planck CMB data. Since our modified gravity model can hardly be constrained by the Solar System tests and gravitational-wave propagation, our result offers the first observational test on the model.

astro-ph.CO↗
arXiv2022

Goal-Aware RSS for Complex Scenarios via Program Logic

We introduce a goal-aware extension of responsibility-sensitive safety (RSS), a recent methodology for rule-based safety guarantee for automated driving systems (ADS). Making RSS rules guarantee goal achievement -- in addition to collision avoidance as in the original RSS -- requires complex planning over long sequences of manoeuvres. To deal with the complexity, we introduce a compositional reasoning framework based on program logic, in which one can systematically develop RSS rules for smaller subscenarios and combine them to obtain RSS rules for bigger scenarios. As the basis of the framework, we introduce a program logic dFHL that accommodates continuous dynamics and safety conditions. Our framework presents a dFHL-based workflow for deriving goal-aware RSS rules; we discuss its software support, too. We conducted experimental evaluation using RSS rules in a safety architecture. Its results show that goal-aware RSS is indeed effective in realising both collision avoidance and goal achievement.

cs.RO↗
arXiv2021

The isotropic attractor solution of axion-SU(2) inflation: Universal isotropization in Bianchi type-I geometry

SU(2) gauge fields coupled to an axion field can acquire an isotropic background solution during inflation. We study homogeneous but anisotropic inflationary solutions in the presence of such (massless) gauge fields. A gauge field in the cosmological background may pose a threat to spatial isotropy. We show, however, that such models $\textit{generally}$ isotropize in Bianchi type-I geometry, and the isotropic solution is the attractor. Restricting the setup by adding an axial symmetry, we revisited the numerical analysis presented in Wolfson et.al (2020). We find that the reported numerical breakdown in the previous analysis is an artifact of parametrization singularity. We use a new parametrization that is well-defined all over the phase space. We show that the system respects the cosmic no-hair conjecture and the anisotropies always dilute away within a few e-folds.

gr-qc↗
arXiv2021

Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling

We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made non-dynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity. Focusing on a class of such modified gravity theories characterized by three functions of time, we discuss how modified gravity with two tensorial degrees of freedom can be distinguished observationally or phenomenologically from general relativity. It is checked that the theory gives the same predictions as general relativity for weak gravitational fields and the propagation speed of gravitational waves. We also find that there is no modification to asymptotically flat black hole solutions. Due to a large degree of freedom to choose the time-dependent functions in the theory, the homogeneous and isotropic cosmological dynamics can be made close to or even identical to that of the $Λ$CDM model. We investigate the behavior of cosmological perturbations in the long and short wavelength limits and show that in both limits the effects of modified gravity appear only through the modification of the background evolution. Finally, it is remarked that in the presence of a galileon field in the matter sector, the scalar degree of freedom is revived, ruining the essential feature of the theory.

gr-qc↗
arXiv2021

Dynamics of inflation with mutually orthogonal vector fields in a closed universe

We study the dynamics of a homogeneous, isotropic, and positively curved universe in the presence of a SU(2) gauge field or a triplet of mutually orthogonal vector fields. In the SU(2) case we use the previously known ansatz for the gauge-field configuration, but the case without non-abelian symmetries is more nontrivial and we develop a new ansatz. We in particular consider axion-SU(2) inflation and inflation with vector fields having U(1)$\times$U(1)$\times$U(1) symmetry, and analyze their dynamics in detail numerically. Novel effects of the spatial curvature come into play through vector fields, which causes unconventional pre-inflationary dynamics. It is found that the closed universe with vector fields is slightly more stable against collapse than that filled solely with an inflaton field.

gr-qc↗
arXiv2021

Robustifying Controller Specifications of Cyber-Physical Systems Against Perceptual Uncertainty

Formal reasoning on the safety of controller systems interacting with plants is complex because developers need to specify behavior while taking into account perceptual uncertainty. To address this, we propose an automated workflow that takes an Event-B model of an uncertainty-unaware controller and a specification of uncertainty as input. First, our workflow automatically injects the uncertainty into the original model to obtain an uncertainty-aware but potentially unsafe controller. Then, it automatically robustifies the controller so that it satisfies safety even under the uncertainty. The case study shows how our workflow helps developers to explore multiple levels of perceptual uncertainty. We conclude that our workflow makes design and analysis of uncertainty-aware controller systems easier and more systematic.

cs.SE↗
arXiv2021

Stars disformally coupled to a shift-symmetric scalar field

We investigate static and spherically symmetric stars disformally coupled to a scalar field. The scalar field is assumed to be shift symmetric, and hence the conformal and disformal factors of the metric coupled to matter are dependent only on the kinetic term of the scalar field. Assuming that the scalar field is linearly dependent on time, we consider a general shift-symmetric scalar-tensor theory and a general form of the matter energy-momentum tensor that allows for the anisotropic pressure and the heat flux in the radial direction. This is a natural starting point in light of how the gravitational field equations and the energy-momentum tensor transform under a disformal transformation. By inspecting the structure of the hydrostatic equilibrium equation in the presence of the derivative-dependent conformal and disformal factors, we show that the energy density and tangential pressure must vanish at the surface of a star. This fact is used to prove the disformal invariance of the surface of a star, which was previously subtle and unclear. We then focus on the shift-symmetric k-essence disformally coupled to matter, and study the interior and exterior metric functions and scalar-field profile in more detail. It is found that there are two branches of the solution depending on the velocity of the scalar field. The disformally-related metric functions of the exterior spacetime are also discussed.

gr-qc↗
arXiv2021

Architecture-Guided Test Resource Allocation Via Logic

We introduce a new logic named Quantitative Confidence Logic (QCL) that quantifies the level of confidence one has in the conclusion of a proof. By translating a fault tree representing a system's architecture to a proof, we show how to use QCL to give a solution to the test resource allocation problem that takes the given architecture into account. We implemented a tool called Astrahl and compared our results to other testing resource allocation strategies.

cs.SE↗
arXiv2021

Gravitational waves in Kasner spacetimes and Rindler wedges in Regge-Wheeler gauge: Unruh effect

We derive the solutions of gravitational waves in the future (F) expanding and the past (P) shrinking Kanser spacetimes as well as in the left (L) and right (R) Rindler wedges in the Regge-Wheeler gauge. The solutions for all metric components are obtained in an analytic form in each region. We identify the master variables, which are equivalent to massless scalar fields, to describe the gravitational degrees of freedom for the odd parity and even parity modes under the transformation in the two-dimensional plane symmetric space. Then, the master variables are quantized, and we develop the quantum field theory of the gravitational waves in the F, P, L, and R regions. We demonstrate that the mode functions of the quantized gravitational waves in the left and right Rindler wedges are obtained by an analytic continuation of the left-moving and right-moving wave modes in Kasner spacetime. On the basis of these analyses, we discuss the Unruh effect of quantized gravitational waves for an observer in a uniformly accelerated motion in Minkowski spacetime.

gr-qc↗
arXiv2021

Gravitational Wave Physics and Astronomy in the nascent era

The detections of gravitational waves (GW) by LIGO/Virgo collaborations provide various possibilities to physics and astronomy. We are quite sure that GW observations will develop a lot both in precision and in number owing to the continuous works for the improvement of detectors, including the expectation to the newly joined detector, KAGRA, and the planned detector, LIGO-India. In this occasion, we review the fundamental outcomes and prospects of gravitational wave physics and astronomy. We survey the development focusing on representative sources of gravitational waves: binary black holes, binary neutron stars, and supernovae. We also summarize the role of gravitational wave observations as a probe of new physics.

gr-qc↗
arXiv2021

Perturbations and quasi-normal modes of black holes with time-dependent scalar hair in shift-symmetric scalar-tensor theories

We study odd parity perturbations of spherically symmetric black holes with time-dependent scalar hair in shift-symmetric higher-order scalar-tensor theories. The analysis is performed in a general way without assuming the degeneracy conditions. Nevertheless, we end up with second-order equations for a single master variable, similarly to cosmological tensor modes. We thus identify the general form of the quadratic Lagrangian for the odd parity perturbations, leading to a generalization of the Regge-Wheeler equation. We also investigate the structure of the effective metric for the master variable and refine the stability conditions. As an application of our generalized Regge-Wheeler equation, we compute the quasi-normal modes of a certain nontrivial black hole solution. Finally, our result is extended to include the matter energy-momentum tensor as a source term.

gr-qc↗
arXiv2020

Nanohertz gravitational waves from NEC violation in the early universe

We study nanohertz gravitational waves relevant to pulsar timing array experiments from quantum fluctuations in the early universe with null energy condition (NEC) violation. The NEC violation admits accelerated expansion with the scale factor $a\propto (-t)^{-p}$ ($p>0$), which gives the tensor spectral index $n_t=2/(p+1)>0$. To evade the constraint from Big Bang nucleosynthesis (BBN), we connect the NEC-violating phase to a subsequent short slow-roll inflationary phase which ends with standard reheating, and thereby reduce the high frequency part of the spectrum. An explicit model is constructed within the cubic Horndeski theory which allows for stable violation of the NEC. We present numerical examples of the background evolution having the different maximal Hubble parameters (which determine the peak amplitude of gravitational waves), the different inflationary Hubble parameters (which determine the amplitudes of high frequency gravitational waves), and different durations of the inflationary phase (which essentially determine the peak frequency of the spectrum). We display the spectra with $n_t=0.8$, $0.9$, and $0.95$ for $f\lesssim 1/{\rm yr}$, which are consistent with the recent NANOGrav result. We also check that they do not contradict the BBN constraint. We discuss how the nearly scale-invariant spectrum of curvature perturbations is produced in the NEC-violating phase.

gr-qc↗
arXiv2020

UV sensitive one-loop matter power spectrum in degenerate higher-order scalar-tensor theories

We study matter density perturbations up to third order and the one-loop matter power spectrum in degenerate higher-order scalar-tensor (DHOST) theories beyond Horndeski. We systematically solve gravitational field equations and fluid equations order by order, and find three novel shape functions characterizing the third-order solution in DHOST theories. A complete form of the one-loop matter power spectrum is then obtained using the resultant second- and third-order solutions. We confirm the previous result that the convergence condition of the loop integrals in the infrared limit becomes more stringent than that of the standard one in general relativity. We show that also in the ultraviolet limit the convergence condition becomes more stringent and the one-loop matter power spectrum is thus sensitive to the short-wavelength behavior of the linear power spectrum.

gr-qc↗
arXiv2020

Effective scalar-tensor description of regularized Lovelock gravity in four dimensions

We reformulate the recently proposed regularized version of Lovelock gravity in four dimensions as a scalar-tensor theory. By promoting the warp factor of the internal space to a scalar degree of freedom by means of Kaluza-Klein reduction, we show that regularized Lovelock gravity can be described effectively by a certain subclass of the Horndeski theory. Cosmological aspects of this particular scalar-tensor theory are studied. It is found that the background with a scalar charge is generically allowed. The consequences of this scalar charge are briefly discussed.

gr-qc↗
arXiv2020

Extended Cuscuton as Dark Energy

Late-time cosmology in the extended cuscuton theory is studied, in which gravity is modified while one still has no extra dynamical degrees of freedom other than two tensor modes. We present a simple example admitting analytic solutions for the cosmological background evolution that mimics $Λ$CDM cosmology. We argue that the extended cuscuton as dark energy can be constrained, like usual scalar-tensor theories, by the growth history of matter density perturbations and the time variation of Newton's constant.

gr-qc↗
arXiv2020

Primordial tensor non-Gaussianities from general single-field inflation with non-Bunch-Davies initial states

It has been found that the primordial non-Gaussianity of the curvature perturbation in the case of non-Bunch-Davies initial states can be enhanced compared with those in the case of the Bunch-Davies one due to the interactions among the perturbations on subhorizon scales. The purpose of the present paper is to investigate whether tensor non-Gaussianities can also be enhanced or not by the same mechanism. We consider general gravity theory in the presence of an inflaton, and evaluate the tensor auto-bispectrum and the cross-bispectrum involving one tensor and two scalar modes with the non-Bunch-Davies initial states for tensor modes. The crucial difference from the case of the scalar auto-bispectrum is that the tensor three-point function vanishes at the flattened momentum triangles. We point out that the cross-bispectrum can potentially be enhanced at non-trivial triangle shapes due to the non-Bunch-Davies initial states.

gr-qc↗