arXiv subjects

Hayato Motohashi

Publications and source records attributed to Hayato Motohashi.

At least 55 records · Page 3Linked to original sources

arXiv2022

Black hole perturbations in higher-order scalar-tensor theories: initial value problem and dynamical stability

We propose a physically sensible formulation of initial value problem for black hole perturbations in higher-order scalar-tensor theories. As a first application, we study monopole perturbations around stealth Schwarzschild solutions in a shift- and reflection-symmetric subclass of degenerate higher-order scalar-tensor (DHOST) theories. In particular, we investigate the time evolution of the monopole perturbations by solving a two-dimensional wave equation and analyze the Vishveshwara's classical scattering experiment, i.e., the time evolution of a Gaussian wave packet. As a result, we confirm that stealth Schwarzschild solutions in the DHOST theory are dynamically stable against the monopole perturbations with the wavelength comparable or shorter than the size of the black hole horizon. We also find that the damped oscillations at the late time do not show up unlike the ringdown phase in the standard case of general relativity. Moreover, we investigate the characteristic curves of the monopole perturbations as well as a static spherically symmetric solution with monopole hair.

gr-qc↗

arXiv2022

Inflation with $0 \leq c_{\rm s} \leq 1$

We investigate a novel single field inflationary scenario which allows a transition between a slow-roll k-inflation with $c_{\rm s}$ of order unity and a ghost inflation with $ c_{\rm s} \simeq 0$, where $ c_{\rm s}$ is the sound speed for the curvature perturbations. We unify the two phases smoothly by appropriately taking into account a higher derivative scordatura term, which is always there from the effective field theory point of view but which becomes important only in the $c_{\rm s} \simeq 0$ regime. The model achieves the whole range of $0 \leq c_{\rm s} \leq 1$ avoiding strong coupling and gradient instability, and allows us to access the $c_{\rm s} \simeq 0$ regime in a self-consistent manner. We also discuss implications to the formation of primordial black holes.

hep-th↗

arXiv2022

Invertible disformal transformations with higher derivatives

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These conditions allow us to systematically construct the inverse transformation in a fully covariant manner. Applying the invertible generalized disformal transformation to known ghost-free scalar-tensor theories, we obtain a novel class of ghost-free scalar-tensor theories, whose action contains the third- or higher-order derivatives of the scalar field as well as nontrivial higher-order derivative couplings to the curvature tensor.

gr-qc↗

arXiv2021

Exact solution for wave scattering from black holes: Formulation

We establish an exact formulation for wave scattering of a massless field with spin and charge by a Kerr-Newman-de Sitter black hole. Our formulation is based on the exact solution of the Teukolsky equation in terms of the local Heun function, and does not require any approximation. It serves as simple exact formulae with arbitrary high precision, which realize fast calculation without restrictions on model parameters. We highlight several applications including quasinormal modes, cross section, reflection/absorption rate, and Green function.

gr-qc↗

arXiv2021

Black hole perturbations in DHOST theories: Master variables, gradient instability, and strong coupling

We study linear perturbations about static and spherically symmetric black hole solutions with stealth scalar hair in degenerate higher-order scalar-tensor (DHOST) theories. We clarify master variables and derive the quadratic Lagrangian for both odd- and even-parity perturbations. It is shown that the even modes are in general plagued by gradient instabilities, or otherwise the perturbations would be strongly coupled. Several possible ways out are also discussed.

gr-qc↗

arXiv2021

Stealth dark energy in scordatura DHOST theory

A stealth de Sitter solution in scalar-tensor theories has an exact de Sitter background metric and a nontrivial scalar field profile. Recently, in the context of Degenerate Higher-Order Scalar-Tensor (DHOST) theories it was shown that stealth de Sitter solutions suffer from either infinite strong coupling or gradient instability for scalar field perturbations. The sound speed squared is either vanishing or negative. In the first case, the strong coupling scale is zero and thus lower than the energy scale of any physical phenomena. From the viewpoint of effective field theory, this issue is naturally resolved by introducing a controlled detuning of the degeneracy condition dubbed scordatura, recovering a version of ghost condensation. In this paper we construct a viable dark energy model in the scordatura DHOST theory based on a stealth cosmological solution, in which the metric is the same as in the standard $Λ$CDM model and the scalar field profile is linearly time-dependent. We show that the scordatura mechanism resolves the strong coupling and gradient instability. Further, we find that the scordatura is also necessary to make the quasi-static limit well-defined, which implies that the subhorizon observables are inevitably affected by the scordatura. We derive the effective gravitational coupling and the correction to the friction term for the subhorizon evolution of the linear dark matter energy density contrast as well as the Weyl potential and the gravitational slip parameter. In the absence of the scordatura, the quasi-static approximation would break down at all scales around stealth cosmological solutions even if the issue of the infinite strong coupling is unjustly disregarded. Therefore previous estimations of the subhorizon evolution of matter density contrast in modified gravity in the literature need to be revisited by taking into account the scordatura effect.

gr-qc↗

arXiv2020

On Rotating Black Holes in DHOST Theories

Using the disformal solution-generating method, we construct new axisymmetric solutions in Degenerate Higher Order Scalar Tensor (DHOST) theories. The method consists in first considering a "seed" known solution in DHOST theories and then performing a disformal transformation of the metric to obtain a new solution. In vacuum, the two solutions are equivalent but they become physically inequivalent when one considers coupling to matter. In that way, we "disform" the stealth Kerr black hole solution and we obtain a first analytic rotating non-stealth solution in DHOST theories, while the associated scalar field is time-dependent with a constant kinetic density. The new solution is characterized by three parameters: the mass, the spin and the disformal parameter which encodes the deviation with respect to the Kerr geometry. We explore some geometrical properties of the novel disformed Kerr geometry which is no more Ricci flat, has the same singularity as the Kerr metric, admits an ergoregion, and is asymptotically flat. Moreover, the hidden symmetry of the Kerr solution is broken, providing an example of a non-circular geometry in a higher order theory of gravity. We also discuss geodesic motions and compute its (disformed) null directions which are interesting tools to understand the causal structure of the geometry. In addition, to illustrate again the potentiality of the disformal solution-generating method, we present another axisymmetric solution for DHOST theories obtained from a disformal transformation of the generalized Kerr solution of Einstein-Scalar gravity.

gr-qc↗

arXiv2020

Quantum Ostrogradsky theorem

The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly depends on the canonical momenta. Recently, the original theorem has been generalized to nondegeneracy with respect to non-highest-order derivatives. These theorems have been playing a central role in construction of sensible higher-derivative theories. We explore quantization of such nondegenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.

hep-th↗

arXiv2020

Ghost from constraints: a generalization of Ostrogradsky theorem

Ostrogradsky theorem states that Hamiltonian is unbounded when Euler-Lagrange equations are higher than second-order differential equations under the nondegeneracy assumption. Since higher-order nondegenerate Lagrangian can be always recast into an equivalent system with at most first-order derivatives by introducing auxiliary variables and constraints, it is conceivable that the link between ghost and higher derivatives may be reinterpreted as a link between ghost and constraints and/or auxiliary variables. We find that the latter point of view actually provides more general perspective than the former, by exploring the un/boundedness of the Hamiltonian for general theories containing auxiliary variables, for which Euler-Lagrange equations can be essentially second order or lower than that. For Lagrangians including auxiliary variables nonlinearly, we derive the degeneracy condition to evade the Ostrogradsky ghost that can apply even if auxiliary variables can be solved only locally. For theories with constraints with Lagrange multipliers, we establish criteria for inclusion of nonholonomic (velocity-dependent) constraints leading to the absence of local minimum of Hamiltonian. Our criteria include the Ostrogradsky theorem as a special case, and can detect not only ghost associated with higher-order derivatives, but also ghost coming from lower-order derivatives in system with constraints. We discuss how to evade such a ghost. We also provide various specific examples to highlight application and limitation of our general arguments.

hep-th↗

arXiv2020

Primordial Black Holes as Dark Matter through Higgs Criticality

We study the dynamics of a spectator Higgs field which stochastically evolves during inflation onto near-critical trajectories on the edge of a runaway instability. We show that its fluctuations do not produce primordial black holes (PBHs) in sufficient abundance to be the dark matter, nor do they produce significant second-order gravitational waves. First we show that the Higgs produces larger fluctuations on CMB scales than on PBH scales, itself a no-go for a viable PBH scenario. Then we track the superhorizon perturbations nonlinearly through reheating using the delta N formalism to show that they are not converted to large curvature fluctuations. Our conclusions hold regardless of any fine-tuning of the Higgs field for both the Standard Model Higgs and for Higgs potentials modified to prevent unbounded runaway.

astro-ph.CO↗

arXiv2020

General Relativity solutions with stealth scalar hair in quadratic higher-order scalar-tensor theories

We explore General Relativity solutions with stealth scalar hair in general quadratic higher-order scalar-tensor theories. Adopting the assumption that the scalar field has a constant kinetic term, we derive in a fully covariant manner a set of conditions under which the Euler-Lagrange equations allow General Relativity solutions as exact solutions in the presence of a general matter component minimally coupled to gravity. The scalar field possesses a nontrivial profile, which can be obtained by integrating the condition of constant kinetic term for each metric solution. We demonstrate the construction of the scalar field profile for several cases including the Kerr-Newman-de Sitter spacetime as a general black hole solution characterized by mass, charge, and angular momentum in the presence of a cosmological constant. We also show that asymptotically anti-de Sitter spacetimes cannot support nontrivial scalar hair.

gr-qc↗

arXiv2020

Effective field theory of degenerate higher-order inflation

We extend the effective field theory of inflation to a general Lagrangian constructed from Arnowitt-Deser-Misner variables that encompasses the most general interactions with up to second derivatives of the scalar field whose background breaks temporal diffeomorphism invariance. Degeneracy conditions, corresponding to 8 distinct types -- only one of which corresponds to known degenerate higher-order scalar-tensor models -- provide necessary conditions for eliminating the Ostrogradsky ghost in a covariant theory at the level of the quadratic action in unitary gauge. Novel implications of the degenerate higher-order system for the Cauchy problem are illustrated with the phase space portrait of an explicit inflationary example: not all field configurations lead to physical solutions for the metric even for positive potentials; solutions are unique for a given configuration only up to a branch choice; solutions on one branch can apparently end at nonsingular points of the metric and their continuation on alternate branches lead to nonsingular bouncing solutions; unitary gauge perturbations can go unstable even when degenerate terms in the Lagrangian are infinitesimal. The attractor solution leads to an inflationary scenario where slow-roll parameters vary and running of the tilt can be large even with no explicit features in the potential far from the end of inflation, requiring the optimized slow-roll approach for predicting observables.

hep-th↗

arXiv2020

Constant roll and primordial black holes

The constant-roll inflation with small positive value of the constant-roll parameter $β\equiv \frac{\ddotϕ}{H\dotϕ}={\rm const.}$ has been known to produce a slightly red-tilted curvature power spectrum compatible with the current observational constraints. In this work, we shed light on the constant-roll inflation with negative $β$ and investigate how a stage of constant-roll inflation may realize the growth in the primordial curvature power spectrum necessary to produce a peaked spectrum of primordial black hole abundance. We first review the behavior of constant-roll models in the range of parameters $-\frac32<β<0$, which allows for a constant-roll attractor stage generating a blue-tilted curvature power spectrum without superhorizon growth. As a concrete realization, we consider a potential with two slow-roll stages, separated by the constant-roll stage, in a way that satisfies the current constraints on the power spectrum and the primordial black hole abundance. The model can produce primordial black holes as all dark matter, LIGO-Virgo events, or OGLE microlensing events. Due to the range of different scalar tilts allowed by the constant-roll potential, this construction is particularly robust and testable by future observations.

gr-qc↗

arXiv2020

Constant-roll inflation in scalar-tensor gravity

We generalize the notion of constant-roll inflation earlier introduced in General Relativity (GR) and $f(R)$ gravity to inflationary models in more general scalar-tensor gravity. A number of novel exact analytic solutions for a FLRW spatially flat cosmological background is found for this case. All forms of the scalar field potential and its coupling to gravity producing the exact de Sitter solution, while the scalar field is varying, are presented. In the particular cases of induced gravity and GR with a non-minimally coupled scalar field, all constant-roll inflationary solutions are found. In the former case they represent power-law inflation, while in the latter case the solution is novel and more complicated. Comparison of scalar perturbations generated during such inflation in induced gravity with observational data shows that the constant-roll parameter should be small, similar to constant-roll inflation in GR and $f(R)$ gravity. Then the solution reduces to the standard slow-roll one with small corrections.

gr-qc↗

arXiv2020

Weakly-coupled stealth solution in scordatura degenerate theory

In scalar-tensor theories we revisit the issue of strong coupling of perturbations around stealth solutions, i.e.\ backgrounds with the same forms of the metric as in General Relativity but with non-trivial configurations of the scalar field. The simplest among them is a stealth Minkowski (or de Sitter) solution with a constant, timelike derivative of the scalar field, i.e.\ ghost condensation. In the decoupling limit the effective field theory (EFT) describing perturbations around the stealth Minkowski (or de Sitter) solution shows the universal dispersion relation of the form $ω^2 = αk^4/M^2$, where $M$ is a mass scale characterizing the background scalar field and $α$ is a dimensionless constant. Provided that $α$ is positive and of order unity, a simple scaling argument shows that the EFT is weakly coupled all the way up to $M$. On the other hand, if the structure of the underlining theory forces the perturbations to follow second-order equations of motion then $α=0$ and the dispersion relation loses dependence on the spatial momentum. This not only explains the origin of the strong coupling problem that was recently pointed out in a class of degenerate theories but also provides a hint for a possible solution of the problem. We then argue that a controlled detuning of the degeneracy condition, which we call scordatura, renders the perturbations weakly coupled without changing the properties of the stealth solutions of degenerate theories at astrophysical scales.

gr-qc↗

arXiv2019

Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations

We study static spherically symmetric black hole solutions with a linearly time-dependent scalar field and discuss their linear stability in the shift- and reflection-symmetric subclass of quadratic degenerate higher-order scalar-tensor (DHOST) theories. We present the explicit forms of the reduced system of background field equations for a generic theory within this subclass. Using the reduced equations of motion, we show that in several cases the solution is forced to be of the Schwarzschild or Schwarzschild-(anti-)de Sitter form. We consider odd-parity perturbations around general static spherically symmetric black hole solutions, and derive the concise criteria for the black holes to be stable. Our analysis also covers the case with a static or constant profile of the scalar field.

gr-qc↗

arXiv2019

Exact black hole solutions in shift-symmetric quadratic degenerate higher-order scalar-tensor theories

We find various exact black hole solutions in the shift-symmetric subclass of the quadratic degenerate higher-order scalar-tensor (DHOST) theories with linearly time dependent scalar field whose kinetic term is constant. The exact solutions are the Schwarzschild and Schwarzschild-(anti-)de Sitter solutions, and the Schwarzschild-type solution with a deficit solid angle, which are accompanied by nontrivial scalar field regular at the black hole event horizon. We derive the conditions for the coupling functions in the DHOST Lagrangian that allow the exact solutions, clarify their compatibility with the degeneracy conditions, and provide general form of coupling functions as well as simple models that satisfy the conditions.

gr-qc↗

arXiv2019

Primordial Black Holes and Local Non-Gaussianity in Canonical Inflation

Primordial black holes (PBHs) cannot be produced abundantly enough to be the dark matter in canonical single-field inflation under slow roll. This conclusion is robust to local non-Gaussian correlations between long- and short-wavelength curvature modes, which we show have no effect in slow roll on local primordial black hole abundances. For the prototypical model which evades this no go, ultra-slow roll (USR), these squeezed non-Gaussian correlations have at most an order unity effect on the variance of PBH-producing curvature fluctuations for models that would otherwise fail to form sufficient PBHs. Moreover, the transition out of USR, which is necessary for a successful model, suppresses even this small enhancement unless it causes a large increase in the inflaton kinetic energy in a fraction of an e-fold, which we call a large and fast transition. Along the way we apply the in-in formalism, the delta N formalism, and gauge transformations to compute non-Gaussianities and illuminate different aspects of the physical origin of these results. Local non-Gaussianity in the squeezed limit does not weaken the Gaussian conclusion that PBHs as dark matter in canonical single-field inflation require a complicated and fine-tuned potential shape with an epoch where slow roll is transiently violated.

astro-ph.CO↗