arXiv subjects

Shinji Mukohyama

Publications and source records attributed to Shinji Mukohyama.

At least 37 records · Page 2Linked to original sources

arXiv2025

Effective Field Theory of Perturbations on Arbitrary Black Hole Backgrounds with Spacelike Scalar Profile

We develop the effective field theory (EFT) of perturbations in the context of scalar-tensor theories with a spacelike scalar profile on arbitrary black hole backgrounds. Our construction of the EFT is based on the fact that in the unitary gauge, where the scalar field is chosen as one of the spatial coordinates, the background scalar field spontaneously breaks the diffeomorphism invariance along the direction of its gradient. The residual symmetry on a timelike hypersurface of constant scalar field is referred to as the $(2+1)$d diffeomorphism invariance. We then derive a set of consistency relations, imposed on the EFT parameters, by requiring that the EFT action in the unitary gauge be invariant under the $(2+1)$d diffeomorphisms. For concreteness, we apply the EFT to study the background dynamics of a class of non-static and spherically symmetric solutions, focusing in particular on a black hole solution with a time-varying mass. We emphasize that our EFT framework is broadly applicable to any black hole background as long as the scalar field remains spacelike throughout the spacetime region of interest. This formulation provides a model-independent approach for testing scalar-tensor theories as gravity beyond general relativity in the strong-gravity regime.

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arXiv2025

Constraining Cubic Curvature Corrections to General Relativity with Quasi-Periodic Oscillations

We investigate observational constraints on cubic curvature corrections to general relativity by analyzing quasi-periodic oscillations (QPOs) in accreting black hole systems. In particular, we study Kerr black hole solution corrected by cubic curvature terms parameterized by $β_5$ and $β_6$. While $β_6$ corresponds to a field-redefinition invariant structure, the $β_5$ term can in principle be removed via a field redefinition. Nonetheless, since we work in the frame where the accreting matter minimally couples to the metric, $β_5$ is in general present. Utilizing the corrected metric, we compute the QPO frequencies within the relativistic precession framework. Using observational data from GRO J1655$-$40 and a Bayesian analysis, we constrain the coupling parameters to $-12.31<\frac{β_5}{(5 M_\odot)^4}<24.15$ and $-1.99<\frac{β_6}{(5 M_\odot)^4}<0.30$ at 2-$σ$. These bounds improve upon existing constraints from big-bang nucleosynthesis and the speed of gravitational waves.

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arXiv2025

Linear Higher-Order Maxwell-Einstein-Scalar Theories

In the context of the Higher-Order Maxwell-Einstein-Scalar (HOMES) theories, which are invariant under spacetime diffeomorphisms and $U(1)$ gauge symmetry, we study two broad subclasses: the first is up to linear in $R_{μναβ}$, $\nabla_μ\nabla_νϕ$, $\nabla_ρ{F}_{μν}$ and up to quadratic in the vector field strength tensor $F_{μν}$; the second is up to linear in $\nabla_μ\nabla_νϕ$, contains no second derivatives of vector field and metric, but allows for arbitrary functions/powers of $F_{μν}$. Under these assumptions, we systematically derive the most general form of the action that leads to second-order (or lower) equations of motion. We prove that, among 41 possible terms in the first subclass, only four independent higher-derivative terms are allowed: the kinetic gravity braiding term $G_3(ϕ,X)\Boxϕ$ in the scalar sector with $X = -\nabla_μϕ\nabla^μϕ/ 2$; the Horndeski non-minimal coupling term $w_0(ϕ)R_{βδαγ}\tilde{F}^{αβ} \tilde{F}^{γδ}$ in the vector field sector, where $\tilde{F}^{μν}$ is the Hodge dual of $F_{μν}$; and two interaction terms between the scalar and vector field sectors: $[w_1(ϕ,X) g_{ρσ} + w_2(ϕ,X) \nabla_ρϕ\nabla_σϕ] \nabla_β\nabla_αϕ\, \tilde{F}^{αρ} \tilde{F}^{βσ}$. For the second subclass, which admits 11 possible terms, three of these four, excluding the Horndeski non-minimal coupling term proportional to $w_0(ϕ)$, are allowed. These independent terms serve as the building blocks of each subclass of HOMES. Remarkably, there is no higher-derivative parity-violating term in either subclass. Finally, we propose a new generalization of higher-derivative interaction terms for the case of a charged complex scalar field.

hep-th↗

arXiv2025

Emergent Lorentzian dispersion relations from a Euclidean scalar-tensor theory

Can one be fooled into thinking that space and time are fundamentally described by a Lorentzian manifold? In this article, we describe a scenario in which a theory constructed on a (Euclidean signature) Riemannian manifold can lead to degrees of freedom with Lorentzian dispersion relations, due to a nontrivial configuration of a scalar field. In particular, we perform a perturbative analysis of a renormalizable shift-symmetric scalar-tensor theory and find that it can, in principle, admit a massless tensor degree of freedom with a Lorentzian dispersion relation. While the remaining degrees of freedom in the gravity sector will, in general, satisfy Euclidean dispersion relations, we argue that they can be brought under control by elliptic equations with an appropriate choice of boundary conditions.

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arXiv2025

HBT Interferometry and Quantum Nature of Primordial Gravitational Waves in Hořava-Lifshitz Gravity

Hořava-Lifshitz gravity (to be precise, its projectable version) is recognized as a renormalizable, unitary, and asymptotically free quantum field theory of gravity. Notably, one of its cosmological predictions is that it can produce scale-invariant primordial density fluctuations and primordial gravitational waves without relying on inflation. In this paper, we investigate the quantum nature of the primordial gravitational waves generated in Hořava-Lifshitz gravity. It has been suggested that, for some inflationary models, the non-classicality of primordial gravitational waves in the squeezed coherent quantum state can be detected using the Hanbury Brown - Twiss (HBT) interferometry. We show that in Hořava-Lifshitz gravity, scale-invariant primordial gravitational waves can be generated during both the radiation-dominated and matter-dominated eras of the Universe. Moreover, the frequency range of their quantum signatures is shown to extend beyond that of inflationary models.

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arXiv2025

Spherical black hole perturbations in EFT of scalar-tensor gravity with timelike scalar profile

We study linear even-parity perturbations of static and spherically symmetric black holes with a timelike scalar profile by use of the effective field theory (EFT) approach. For illustrative purposes, we consider a simple subclass of the EFT that accommodates ghost condensate, namely the k-essence model along with the so-called scordatura term, and focus on the spherical (monopole) perturbations about an approximately stealth Schwarzschild solution. The scordatura effect is introduced to avoid the strong coupling problem that typically happens in the scalar sector around stealth solutions with a timelike scalar profile. We argue that the scalar perturbation is decoupled from the metric perturbations at the leading order in the scordatura effect under a particular gauge choice. We stress that this is an important step in understanding the dynamics of even-parity perturbations, paving the way towards deriving a set of master equations -- the generalized Zerilli and the scalar-field equations -- for generic multipoles.

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arXiv2025

Anisotropic quantum universe in Hořava-Lifshitz gravity

We quantize a Bianchi IX universe in Hořava-Lifshitz theory. For analytical tractability, we consider the small anisotropy limit of the Bianchi IX, that is, a perturbative anisotropic deformation of a closed, homogeneous and isotropic universe. In the case of the projectable theory we further set the ``dark matter as integration constant'' to zero by assuming that the space consists of only one connected piece. In that limit and under the assumption, we first study the semi-classical WKB solutions to the Wheeler-DeWitt equation. We find the wave function of the universe, up to an overall normalization, and estimate the semi-classical tunneling probability for the emergence of an expanding universe. We establish a dictionary of correspondence between the WKB wave functions in General Relativity and Hořava-Lifshitz theory in the large-scale factor (or IR) limit. For a small universe (UV limit), on the other hand, due to contributions from higher-dimensional operators, the anisotropies decouple from the scale factor, a behavior significantly different from General Relativity, and analytic solutions to the Wheeler-DeWitt equation beyond the WKB approximation can be found. The wave function of the scale factor satisfies the DeWitt criterion, whereas the wave functions of anisotropies resemble those of quantum harmonic oscillators. The quantum prediction for the initial condition of anisotropies is obtained in terms of the coupling parameters of Hořava-Lifshitz theory. We find a bound on the coupling parameters from the normalizability of the wave functions of anisotropies. Further, we calculate the expectation values for squared anisotropic shear and squared anisotropies in both the large universe and small universe limits.

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arXiv2025

Boulware Vacuum vs. Regularity: Thoughts on Anomaly-Induced Effective Action

We examine the vacuum state and its corresponding renormalized stress-energy tensor (RSET) in static horizonless regular spacetime in both two and four dimensions. Using the local field formulation of the anomaly-induced effective action, we show that the regularities of the spacetime and the RSET dictate the appropriate vacuum state. Furthermore, through a case study under the horizonless Bardeen-type spacetime, we demonstrate that the preferred vacuum state is not the Boulware vacuum, but a nontrivial one with a different RSET profile.

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arXiv2025

Ghostly interactions in (1+1) dimensional classical field theory

We investigate the classical stability of two coupled scalar fields with opposite-sign kinetic terms evolving in 1+1 dimensional Minkowski spacetime. In the first part, we characterise unquenched ghostly interactions and present numerical solutions that support the following statements. First, the classical instability is not instantaneous and can even be benign, i.e., free of finite-time singularities. Second, while the classical instability can cascade towards higher frequency excitations, it is not driven by high frequency modes: At fixed amplitude, high-frequency modes are more stable than low-frequency modes. In the second part, we demonstrate that the classical instability can be quenched by mass terms. In particular, we exemplify that heavy high-frequency ghost fields seem to not violate the decoupling theorem and can be integrated out classically. In the third part, we demonstrate how self-interactions can quench the instability, for instance, by postponing its onset to parametrically large times. Extrapolating numerical results at large but finite evolution time to infinite evolution time, we demonstrate that classical fluctuations around trivial and nontrivial field-theory vacua are increasingly long-lived with (i) smaller initial amplitude of fluctuations, (ii) higher initial frequency of fluctuations, (iii) larger masses of the fields, or (iv) weaker interaction coupling. Moreover, our numerical simulations for field-theoretical generalisations of some globally-stable ghostly mechanical models do not feature any instability.

hep-th↗

arXiv2025

Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory

The low-energy limit of string theory contains additional gravitational degrees of freedom, a skew-symmetric tensor $B$-field and a scalar dilaton, that are not present in general relativity. Together with the metric, these three fields are naturally embedded in the $\mathbf{O}(D,D)$-symmetric framework of double field theory. The $\mathbf{O}(D,D)$ symmetry uniquely prescribes the interactions between the extended gravitational sector and other matter, leading to novel features beyond conventional string cosmology. In this work we present the equations of motion for linear perturbations around $\mathbf{O}(D,D)$ string cosmological backgrounds in $D=4$ under a scalar-vector-tensor decomposition. We obtain analytic solutions in the superhorizon limit for scalar perturbations around various homogeneous and isotropic background solutions, including some candidate models for bouncing cosmologies. The generalized energy-momentum tensor includes source terms for the $B$-field and dilaton, and we show how the resulting generalized conservation laws modify the conditions for conservation of curvature perturbations.

hep-th↗

arXiv2025

Gravitational wave cosmology in Einstein-scalar-Gauss-Bonnet gravity

In the framework of Einstein-scalar-Gauss-Bonnet (EsGB) gravity, we systematically study gravitational waves (GWs), first produced by remote compact astrophysical sources and then propagating through the flat homogeneous and isotropic Universe at cosmic distances before arriving at detectors. Assuming that the speed $c_T$ of the spin-2 graviton is the same as that of photons, we find explicitly the stability conditions of the theory and then obtain the severest observational constraint found so far. In particular, all these conditions and constraints are satisfied, provided that $0 \leq α\dot{f}(ϕ_0) \lesssim 8.97 \times 10^{-24}$ (km), where $α{f}(ϕ)$ denotes the coupling strength between the scalar field $ϕ$ and the Gauss-Bonnet term, an over-dot represents the derivative with respect to the cosmic time, and $ϕ_0$ is the present value of $ϕ$. The trajectories for both spin-2 and spin-0 gravitons and the amplitudes of GWs along the trajectories are explicitly obtained. The amplitude of a spin-2 GW is practically indistinguishable from that of GR, while the spin-0 GWs remain almost constant during radiation- and matter-dominated epochs, and in the dark energy-dominated epoch it is proportional to the physical distance between the source and the observer. A careful analysis shows that the latter is due to the assumption $c_T = 1$. When $c_T \not= 1$ to the extent that is consistent with the stability conditions and observational constraints, the above behavior disappears.

gr-qc↗

arXiv2025

Violations of energy conservation in Horava-Lifshitz gravity: a new ingredient in the dark matter puzzle

We investigate the interplay between Horava-Lifshitz (HL) gravity and more general theories where the local Hamiltonian constraint is lost, for example due to the time variability of the Lagrangian (e.g. via its parameters) where time is defined on a foliation according to a prescription mimicking Lambda and 4-volume time in unimodualr gravity. In one direction we subject the multitude of parameters in HL to this variability game, mimicking RG flow in a cosmological setting. In the opposite direction, we examine the evolution on the left-over Hamiltonian should the HL algebra of constraints be still applicable, rather than the algebra of General Relativity being restored. Within the projectable theory, the non-vanishing Hamiltonian can be reinterpreted as a pressureless fluid, resulting in essentially the same phenomenologies at macroscopic scales as in the standard cold dark matter paradigm. At high energies and short distances, however, unlike in theories with similar variability based on GR, violations of stress-energy tensor conservation persist, and these are computed here for the full class of projectable HL models. The phenomenological implications are examined: remarkably the driven solution resulting from these energy conservation violations is shown to be the attractor of the system during a free-fall collapse as far as the backreaction is negligible. When the backreaction is taken into account, the driven solution is expected to play an important role towards our understanding of microscopic caustic avoidance, which is one of the most significant issues in many alternatives to particle dark matter scenarios.

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arXiv2025

Bridging Dark Energy and Black Holes with EFT: Frame Transformation and Gravitational Wave Speed

Typically, constraints on parameters of the effective field theory (EFT) of dark energy have been obtained in the Jordan frame, where matter fields are minimally coupled to gravity. To connect these constraints with those of the EFT of black hole perturbations with a timelike scalar profile, it is necessary to perform a frame transformation on the EFT in general. In this paper, we study the conformal/disformal transformation of EFT parameters on an arbitrary background. Furthermore, we explore the effect of an EFT operator $M_6(r) \barσ^μ_ν δK^ν_α δK^α_μ$, which is elusive to the LIGO/Virgo bound on gravitational-wave speed, on the dynamics of odd-parity black hole perturbations. Intriguingly, a deviation from luminal propagation shows up only in the vicinity of the black hole, and the speeds of perturbations in the radial and angular directions are different in general due to the traceless part $\barσ^μ_ν$ of the background extrinsic curvature. This study establishes an important link between cosmological constraints and those obtained in the black hole regime.

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arXiv2024

Spin wave optics for gravitational waves lensed by a Kerr black hole

Gravitational waves exhibit the unique signature of their spin-2 nature in processes of wave scattering, due to the interaction between spin and a background spacetime. Since the spin effect is more pronounced for longer wavelengths and gravitational waves sourced by binaries have a long wavelength, it may become an important effect in addition to the wave effect. We study the propagation of gravitational waves lensed by a Kerr black hole by numerically solving the Teukolsky equation with a source term of the equal-mass circular binary, taking into account both spin effect and wave effect. We find helicity-dependent small-period oscillation in the power spectrum of the amplification factor in the forward direction and the oscillation is enhanced as spin of a prograde Kerr black hole increases.

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arXiv2024

Tidal Love Numbers from EFT of Black Hole Perturbations with Timelike Scalar Profile

We study static tidal Love numbers (TLNs) of a static and spherically symmetric black hole for odd-parity metric perturbations. We describe black hole perturbations using the effective field theory (EFT), formulated on an arbitrary background with a timelike scalar profile in the context of scalar-tensor theories. In particular, we obtain a static solution for the generalized Regge-Wheeler equation order by order in a modified-gravity parameter and extract the TLNs uniquely by analytic continuation of the multipole index $\ell$ to non-integer values. For a stealth Schwarzschild black hole, the TLNs are vanishing as in the case of Schwarzschild solution in general relativity. We also study the case of Hayward black hole as an example of non-stealth background, where we find that the TLNs are non-zero (or there is a logarithmic running). This result suggests that our EFT allows for non-vanishing TLNs and can in principle leave a detectable imprint on gravitational waves from inspiralling binary systems, which opens a new window for testing gravity in the strong-field regime.

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arXiv2024

Revisiting linear stability of black hole odd-parity perturbations in Einstein-Aether gravity

In Einstein-Aether gravity, we revisit the issue of linear stabilities of black holes against odd-parity perturbations on a static and spherically symmetric background. In this theory, superluminal propagation is allowed and there is a preferred timelike direction along the unit Aether vector field. If we choose the usual spherically symmetric background coordinates with respect to the Killing time $t$ and the areal radius $r$, it may not be appropriate for unambiguously determining the black hole stability because the constant $t$ hypersurfaces are not necessarily always spacelike. Unlike past related works of black hole perturbations, we choose an Aether-orthogonal frame in which the timelike Aether field is orthogonal to spacelike hypersurfaces over the whole background spacetime. In the short wavelength limit, we show that no-ghost conditions as well as radial and angular propagation speeds coincide with those of vector and tensor perturbations on the Minkowski background. Thus, the odd-parity linear stability of black holes for large radial and angular momentum modes is solely determined by constant coefficients of the Aether derivative couplings.

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arXiv2024

Bispectrum from inflation/bouncing Universe in VCDM

We discuss the non-linear interactions within the VCDM model, a type II minimally modified gravity model with the same number of degrees of freedom as in General Relativity but not connected to the latter by field redefinitions. During an inflationary phase in the early universe, if the VCDM potential does not modify the slow-roll behavior of the inflaton field, we recover, up to the leading order, the standard results for the bispectrum in slow-roll inflation. On the other hand, if the VCDM potential becomes dominant, the interactions can strongly deviate and even violate the Maldacena's consistency relation for the local non-Gaussianities. Furthermore, we apply the formalism to the recently introduced bouncing model in VCDM, and show that the bispectrum still respects current observational constraints. Future measurements on non-Gaussianities of the local type should provide the test ground for the model's validity.

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arXiv2024

Even-parity black hole perturbations in Minimal Theory of Bigravity

We study even-parity black hole perturbations in Minimal Theory of Bigravity (MTBG). We consider the Schwarzschild solution written in the spatially-flat coordinates in the self-accelerating branch as the background solution. We clarify the gauge transformations for the $\ell=0$, $1$, and $\geq2$ modes with $\ell$ being the angular multipole moments under the joint foliation-preserving diffeomorphism transformation. Requiring that the asymptotic regions in the physical and fiducial sectors share the same Minkowski vacua, the solution to the $\ell=0$ perturbations can be absorbed by a redefinition of the Schwarzschild background. In order to analyze the $\ell=1$ and $\geq 2$ modes, for simplicity we focus on the effectively massless case, where the constant parameter measuring the ratio of the proper times between the two sectors is set to unity and the effective mass terms in the equations of motion vanish. We also find that as a particular solution all the $\ell=1$ perturbations vanish by imposing their regularity at spatial infinity. For each of the $\ell\geq 2$ modes, in the effectively massless case, we highlight the existence of the expected two propagating modes and four instantaneous modes.

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