arXiv subjects

Tsutomu Kobayashi

Publications and source records attributed to Tsutomu Kobayashi.

At least 19 recordsLinked to original sources

arXiv2026

Bi-scalar-tensor theory: a spatially covariant gravity approach

We propose a novel method for constructing ghost-free multi-field higher-derivative scalar-tensor theories. The idea is to start from spatially covariant gravity and couple it to an additional scalar field. The resulting spatially covariant scalar field theory can be understood as a bi-scalar-tensor theory in the unitary gauge of one scalar. Within a broad class in which metric velocities enter through the extrinsic curvature and the additional scalar enters through temporal derivatives up to second order, we perform a Hamiltonian constraint analysis. We show that the theory generally propagates five physical degrees of freedom (DOFs), i.e., two tensor modes and three scalar modes. One of the scalar modes is the unwanted mode associated with the additional scalar. We then derive a degeneracy condition and an additional consistency condition. When both conditions hold, the unwanted mode is eliminated and the theory propagates four degrees of freedom. The resulting theories fall into two cases, depending on whether the preservation of the tertiary constraint closes without a new constraint or generates a quaternary constraint. We also study the two-field disformal transformation, derive its invertibility condition, and express it in the unitary gauge. Our construction provides a systematic approach to constructing bi- and multi-scalar-tensor theories with higher derivatives.

gr-qc↗

arXiv2026

Spinoptics in the presence of axion-like particles in curved spacetime

We study the propagation of high-frequency electromagnetic waves coupled to an axionic scalar field in curved spacetime. By applying the effective action approach, we go beyond the standard geometric optics limit and derive spinoptics equations for the axion--Maxwell theory that are valid for arbitrary curved spacetimes and arbitrary axion profiles. These equations allow us to analyze helicity-dependent corrections to photon trajectories arising from the photon's interactions with both the axion field and spacetime curvature. We present representative examples to demonstrate how light trajectories deviate from null geodesics due to spinoptics effects in the presence of an axion field.

gr-qc↗

arXiv2026

Unscreened multipole moments of the fifth force in the EFT of dark energy

It has been argued that degenerate higher-order scalar-tensor theories and the effective field theory (EFT) of dark energy are endowed with the Vainshtein mechanism, resulting in a screened fifth force in the exterior of a gravitational source. However, spherical symmetry has been assumed in most of the discussions so far. In this paper, we study whether the Vainshtein mechanism operates in the EFT of dark energy beyond spherical symmetry, focusing in particular on the role of the ``beyond Horndeski'' EFT parameters. Assuming that deviations from spherical symmetry are small, we compute multipole moments of the gravitational potential for a given nonspherical source. For a generic choice of the ``beyond Horndeski'' EFT parameters, it is shown that the multipole moments of the fifth force are not screened in the region where the monopole component is screened. Rather, the gravitational potential shows a characteristic oscillatory behavior in its multipole components. In the special case where the EFT parameters are tuned so that graviton decay into dark energy is practically absent, the behavior of the multipole moments is qualitatively different from that in the generic case. However, also in this case, the Vainshtein mechanism is not efficient enough to screen the fifth force around the source.

gr-qc↗

arXiv2026

Abundance of cosmic voids in EFT of dark energy

Cosmic voids in the large-scale structure are among the useful probes for testing gravity on cosmological scales. In this paper, we investigate the evolution of voids in the Horndeski theory using the effective field theory (EFT) of dark energy. Modeling the void formation with the dynamics of spherical mass shells, we study how modifications of gravity encoded into the EFT of dark energy change the linearly extrapolated critical density contrast that is relevant for the criterion for void formation, with particular focus on the time-dependent parameter characterizing the effect of kinetic braiding. It is found that the change in the critical density contrast is one order of magnitude smaller than the dimensionless EFT parameter because of a slight imbalance between two compensating effects. We then compute the void abundance using the Sheth--van de Weygaert void size function and demonstrate that it exhibits scale-dependent modifications. It is shown that the modifications to the void size function on small scales are almost entirely determined by the modified linear matter power spectrum, while the modifications on large scales are dominated by the contributions from the linear matter spectrum and the critical density contrast.

astro-ph.CO↗

arXiv2026

Healthy scalar-tensor theories with third-order derivatives: Generalized disformal Horndeski and beyond

We systematically construct ghost-free scalar-tensor theories whose Lagrangian includes up to third-order derivatives of the scalar field. Using a spatially covariant action written in terms of the ADM variables, we impose degeneracy and consistency conditions that ensure the propagation of only one scalar and two tensor degrees of freedom. The resultant theories extend the generalized disformal Horndeski and U-DHOST theories. We discuss the transformation properties of these theories under generalized disformal transformations.

gr-qc↗

arXiv2025

Ghost-free 2-form fields in cosmology: implications for gravitational parity violation

We explore the possibility of parity-violating, nonminimally coupled 2-form field theories that retain the same dynamical degrees of freedom as a massive 2-form and thus are ghost-free. Starting from the most general kinetic terms and dimension four couplings between the 2-form field and the curvature tensors, we find a two-parameter family of such theories. However, we also find that parity-violating terms involving the dual 2-form field can be absorbed into a field redefinition, leaving a theory with essentially the same structure as that obtained by Heisenberg and Trenkler (i.e., the parity-preserving coupling to the double dual Riemann tensor). After the field redefinition, the only place where parity-violating terms can appear is in the potential. We then consider a homogeneous and isotropic cosmological model with an isotropic configuration of a triplet of 2-form fields, and study tensor perturbations in this setup. There are three types of tensor perturbations, two of which are dynamical. We show that chiral gravitational waves can be generated in the presence of parity-violating terms in the potential.

gr-qc↗

arXiv2025

Spherical collapse in DHOST theories and EFT of dark energy

We study the nonlinear evolution of matter overdensities using the spherical collapse model in degenerate higher-order scalar-tensor (DHOST) theories beyond Horndeski, employing the effective field theory (EFT) of dark energy approach. We investigate the impact of the EFT parameters characterising DHOST theories on the formation of large-scale structure. We identify the parameter space in which the collapse of the spherical overdensity is prevented by the scalar field turning imaginary at some moment, which allows us to place constraints on the model parameters. We show how the collapse time and the critical density contrast depend on the EFT parameters. To assess the observational implications, we compute the halo mass function using the Press-Schechter formalism. We find that the number density of halos is suppressed compared to the $Λ$CDM model due to ``beyond Horndeski'' effects, upon imposing the stability of linear perturbations.

astro-ph.CO↗

arXiv2025

Gravitomagnetic tidal response of relativistic stars in partially screened scalar-tensor theories

In scalar-tensor theories beyond Horndeski, the Vainshtein screening mechanism is only partially effective inside astrophysical bodies. We investigate the potential to detect this partial breaking of Vainshtein screening through the tidal response of fluid bodies. We calculate the gravitomagnetic tidal Love numbers in a specific model of degenerate higher-order scalar-tensor gravity and analyze how deviations from general relativity depend on parameters governing the breaking of Vainshtein screening in the weak-gravity regime. For fixed parameter values, the relative deviations increase with higher multipoles and larger compactness. However, we demonstrate that these parameters alone are insufficient to fully characterize the tidal response of relativistic bodies in scalar-tensor theories beyond Horndeski.

gr-qc↗

arXiv2024

Slowly moving black holes in Lorentz-violating scalar-tensor gravity

A scalar field with a timelike gradient defines a preferred slicing. This occurs even in a non-cosmological setup in scalar-tensor theories such as khronometric theory. We study a black hole moving slowly relative to the preferred slicing defined by the scalar field. We consider a family of higher-order scalar-tensor theories that extend khronometric theory. The action is characterized by one constant parameter and one arbitrary function of the kinetic term of the scalar field. A slowly moving black hole is described by a dipole perturbation of a black hole at rest. We treat the metric and scalar-field perturbations consistently, derive a single master equation for the coupled system, and reconstruct the metric for a slowly moving black hole from the master variable. In this way, we revisit and generalize the previous studies. For generic theories in the family we consider, we find a solution that is regular outside the universal horizon and agnostic to the arbitrary function in the action.

gr-qc↗

arXiv2024

Chromo-natural inflation supported by enhanced friction from Horndeski gravity

We study the extension of the chromo-natural inflation model by incorporating nonminimal coupling between the axion field and gravity. Nonminimal coupling is introduced so that it enhances friction in the axion's equation of motion and thus supports slow-roll inflation. This enhanced friction effectively delays the activation of the gauge field, thereby preventing the overproduction of gravitational waves in the CMB scale. We extend previous results by describing the nonminimal coupling in a general and unifying way utilizing Horndeski gravity. This allows us to explore systematically and comprehensively possible enhanced friction models of chromo-natural inflation consistent with observations. We find a novel enhanced friction model that shows better agreement (within 1$σ$) with CMB measurements than the previous nonminimally coupled chromo-natural inflation model. The gravitational-wave spectrum starts to rise at some wavenumber due to retarded activation of the gauge field in the late stage of inflation. We show how one can identify the wavenumber at which this occurs based on the background evolution and present a universal analytic formula for the gravitational-wave spectrum that can be used for any enhanced friction model of chromo-natural inflation.

astro-ph.CO↗

arXiv2024

Weak-field regime of scalar-tensor theories with an instantaneous mode

Higher-order scalar-tensor theories having an instantaneous mode do not develop the Ostrogradsky instability even if a seemingly dangerous mode is present. Such theories satisfy only partially the degeneracy conditions that are usually imposed to remove the dangerous mode completely, and are dubbed as U-DHOST theories. We study weak gravitational fields sourced by nonrelativistic matter distributions in U-DHOST theories. In contrast to the case of totally degenerate theories where nonlinear derivative interactions are crucial for exhibiting the Vainshtein mechanism and its partial breaking, we show that in generic U-DHOST theories the linear analysis is sufficient for weak gravitational fields. We identify the subset of U-DHOST theories in which solar system tests are evaded and gravitational waves propagate at the speed of light. Such theories can however be tested with cosmological observations. We also point out that there is a particular case of U-DHOST theories where nonlinear derivative interactions play an important role as in totally degenerate theories. In that case, it is found, however, that the Vainshtein mechanism does not operate and gravitational forces are modified.

gr-qc↗

arXiv2024

PPN meets EFT of dark energy: Post-Newtonian approximation in higher-order scalar-tensor theories

We study the post-Newtonian limit of higher-order scalar-tensor theories that are degenerate in the unitary gauge. They can be conveniently described by the effective field theory (EFT) of dark energy. We determine all the parametrized post-Newtonian (PPN) parameters in terms of the EFT of dark energy parameters. Experimental bounds on the PPN parameters are then translated to constraints on the EFT parameters. We present a Lagrangian of a unitary degenerate higher-order scalar-tensor theory characterized by a single function of the kinetic term of the scalar field whose PPN parameters have the same values as in general relativity.

gr-qc↗

arXiv2024

Formal Modelling of Safety Architecture for Responsibility-Aware Autonomous Vehicle via Event-B Refinement

Ensuring the safety of autonomous vehicles (AVs) is the key requisite for their acceptance in society. This complexity is the core challenge in formally proving their safety conditions with AI-based black-box controllers and surrounding objects under various traffic scenarios. This paper describes our strategy and experience in modelling, deriving, and proving the safety conditions of AVs with the Event-B refinement mechanism to reduce complexity. Our case study targets the state-of-the-art model of goal-aware responsibility-sensitive safety to argue over interactions with surrounding vehicles. We also employ the Simplex architecture to involve advanced black-box AI controllers. Our experience has demonstrated that the refinement mechanism can be effectively used to gradually develop the complex system over scenario variations.

cs.SE↗

arXiv2023

Consistency of higher derivative couplings to matter fields in scalar-tensor gravity

Recently, a generalization of invertible disformal transformations containing higher-order derivatives of a scalar field has been proposed in the context of scalar-tensor theories of gravity. By applying this generalized disformal transformation to the Horndeski theory, one can obtain the so-called generalized disformal Horndeski theories which are more general healthy scalar-tensor theories than ever. However, it is unclear whether or not the generalized disformal Horndeski theories can be coupled consistently to matter fields because introducing a matter field could break the degeneracy conditions of higher-order scalar-tensor theories and hence yield the unwanted Ostrogradsky ghost. We investigate this issue and explore the conditions under which a minimal coupling to a matter field is consistent in the generalized disformal Horndeski theories without relying on any particular gauge such as the unitary gauge. We find that all the higher derivative terms in the generalized disformal transformation are prohibited to avoid the appearance of the Ostrogradsky ghost, leading to the conclusion that only the theories that are related to the Horndeski theory through a conventional disformal transformation remain ghost-free in the presence of minimally coupled matter fields.

gr-qc↗

arXiv2023

Black hole perturbations in spatially covariant gravity with just two tensorial degrees of freedom

We study linear perturbations around a static and spherically symmetric black hole solution in spatially covariant gravity with just two tensorial degrees of freedom. In this theory, gravity modification is characterized by a single time-dependent function that appears in the coefficient of $K^2$ in the action, where $K$ is the trace of the extrinsic curvature. The background black hole solution is given by the Schwarzschild solution foliated by the maximal slices and has a universal horizon at which the lapse function vanishes. We show that the quadratic action for the odd-parity perturbations is identical to that in general relativity upon performing an appropriate coordinate transformation. This in particular implies that the odd-parity perturbations propagate at the speed of light, with the inner boundary being the usual event horizon. We also derive the quadratic action for even-parity perturbations. In the even-parity sector, one of the two tensorial degrees of freedom is mixed with an instantaneous scalar mode, rendering the system distinct from that in general relativity. We find that monopole and dipole perturbations, which are composed solely of the instantaneous scalar mode, have no solutions regular both at the universal horizon and infinity (except for the trivial one corresponding to the constant shift of the mass parameter). We also consider stationary perturbations with higher multipoles. By carefully treating the locations of the inner boundary, we show that also in this case there are no solutions regular both at the inner boundary and infinity. Thus, the black hole solution we consider is shown to be perturbatively unique.

gr-qc↗

arXiv2023

First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies (An explanatory video is available at https://youtu.be/Zi36ooLPhss.)

We present, for the first time, an observational test of the consistency relation for the large-scale structure (LSS) of the Universe through a joint analysis of the anisotropic two- and three-point correlation functions (2PCF and 3PCF) of galaxies. We parameterise the breakdown of the LSS consistency relation in the squeezed limit by $E_{\rm s}$, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. $E_{\rm s}\neq1$ is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain $E_{\rm s}$ by obtaining information about the nonlinear velocity field from the quadrupole component of the 3PCF without taking the squeezed limit. Using the galaxy catalogues in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we obtain $E_{\rm s} = -0.92_{-3.26}^{+3.13}$, indicating that there is no violation of the LSS consistency relation in our analysis within the statistical errors. Our parameterisation is general enough that our constraint can be applied to a wide range of theories, such as multicomponent fluids, modified gravity theories, and their associated galaxy bias effects. Our analysis opens a new observational window to test the fundamental physics using the anisotropic higher-order correlation functions of galaxy clustering.

astro-ph.CO↗

arXiv2023

New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies

We report a new test of modified gravity theories using the large-scale structure of the Universe. This paper is the first attempt to (1) apply a joint analysis of the anisotropic components of galaxy two- and three-point correlation functions (2 and 3PCFs) to actual galaxy data and (2) constrain the nonlinear effects of degenerate higher-order scalar-tensor (DHOST) theories on cosmological scales. Applying this analysis to the Baryon Oscillation Spectroscopic Survey (BOSS) data release 12, we obtain the lower bounds of $-1.655 < ξ_{\rm t}$ and $-0.504 < ξ_{\rm s}$ at the $95\%$ confidence level on the parameters characterising the time evolution of the tidal and shift terms of the second-order velocity field. These constraints are consistent with GR predictions of $ξ_{\rm t}=15/1144$ and $ξ_{\rm s}=0$. Moreover, they represent a $35$-fold and $20$-fold improvement, respectively, over the joint analysis with only the isotropic 3PCF. We ensure the validity of our results by investigating various quantities, including theoretical models of the 3PCF, window function corrections, cumulative ${\rm S/N}$, Fisher matrices, and statistical scattering effects of mock simulation data. We also find statistically significant discrepancies between the BOSS data and the Patchy mocks for the 3PCF measurement. Finally, we package all of our 3PCF analysis codes under the name \textsc{HITOMI} and make them publicly available so that readers can reproduce all the results of this paper and easily apply them to ongoing future galaxy surveys.

astro-ph.CO↗

arXiv2023

How does SU($N$)-natural inflation isotropize the universe?

We study the homogeneous and anisotropic dynamics of pseudoscalar inflation coupled to an SU($N$) gauge field. To see how the initially anisotropic universe is isotropized in such an inflation model, we derive the equations to obtain axisymmetric SU($N$) gauge field configurations in Bianchi type-I geometry and discuss a method to identify their isotropic subsets which are the candidates of their late-time attractor. Each isotropic solution is characterized by the corresponding SU(2) subalgebra of the SU($N$) algebra. It is shown numerically that the isotropic universe is a universal late-time attractor in the case of the SU(3) gauge field. Interestingly, we find that a transition between the two distinct gauge-field configurations characterized by different SU(2) subalgebras can occur during inflation. We clarify the conditions for this to occur. This transition could leave an observable imprint on the CMB and the primordial gravitational wave background.

gr-qc↗