arXiv subjects

Shinji Tsujikawa

Publications and source records attributed to Shinji Tsujikawa.

At least 55 records · Page 3Linked to original sources

arXiv2023

Constraining Horndeski theory with gravitational waves from coalescing binaries

In the broad subclass of Horndeski theories with a luminal speed of gravitational waves, we derive gravitational waveforms emitted from a compact binary by considering the wave propagation on a spatially flat cosmological background. A scalar field nonminimally coupled to gravity gives rise to hairy neutron star (NS) solutions with a nonvanishing scalar charge, whereas black holes (BHs) do not have scalar hairs in such theories. A binary system containing at least one hairy neutron star modifies the gravitational waveforms in comparison to those of the BH-BH binary. Using the tensor gravitational waveforms, we forecast the constraints on a parameter characterizing the difference of scalar charges of NS-BH or NS-NS binaries for Advanced LIGO and Einstein Telescope. We illustrate how these constraints depend on redshift and signal-to-noise ratio, and on different possible priors. We show that in any case it is possible to constrain the scalar charge precisely, so that some scalarized NS solutions known in the literature can be excluded.

astro-ph.CO↗

arXiv2023

Stability of Schwarzshild black holes in quadratic gravity with Weyl curvature domination

We study the linear stability of static and spherically symmetric (SSS) black holes (BHs) in the presence of a Weyl-squared curvature besides an Einstein-Hilbert term in the action. In this theory, there is always an exact Schwarzschild BH irrespective of the Weyl coupling constant $α$, with the appearance of a non-Schwarzschild solution for a particular range of the coupling of order $|α| \approx r_h^2$ (where $r_h$ is the horizon radius). On the SSS background, we show that the propagating degrees of freedom (DOFs) are three in the odd-parity sector and four in the even-parity sector. Since the number of total seven DOFs coincides with those on the Minkowski and isotropic cosmological backgrounds, the Weyl gravity does not pose a strong coupling problem associated with the vanishing kinetic term of dynamical perturbations. The odd-parity perturbations possess at least one ghost mode, but the propagation speeds of all three dynamical modes are luminal. In the even-parity sector, our analysis, based on the WKB approximation, shows that, besides the appearance of at least one ghost mode, the Schwarzschild solution is prone to both radial and angular Laplacian instabilities of several dynamical perturbations for the Weyl coupling in the range $|α| \gg r_h^2$. For large radial and angular momentum modes, the time scales of such instabilities are much shorter than the horizon distance $r_h$ divided by the speed of light. In the coupling regime $|α|\lesssim r_h^2$, the WKB approximation does not hold any longer, and a different analysis should be performed if one wants to state the stability of both the Schwarzschild and non-Schwarzschild BH solutions in this range of model parameters.

gr-qc↗

arXiv2023

Excluding static and spherically symmetric black holes in Einsteinian cubic gravity with unsuppressed higher-order curvature terms

Einsteinian cubic gravity is a higher-order gravitational theory in which the linearized field equations of motion match Einstein's equations on a maximally symmetric background. This theory allows the existence of a static and spherically symmetric black hole solution where the temporal and radial metric components are equivalent to each other ($f=h$), with a modified Schwarzschild geometry induced by cubic curvature terms. We study the linear stability of the static and spherically symmetric vacuum solutions against odd-parity perturbations without dealing with Einsteinian cubic gravity as an effective field theory where the cubic curvature terms are always suppressed relative to the Ricci scalar. Unlike General Relativity containing one dynamical perturbation, Einsteinian cubic gravity has three propagating degrees of freedom in the odd-parity sector. We show that at least one of those dynamical perturbations always behaves as a ghost mode. We also find that one dynamical degree of freedom has a negative sound speed squared $-1/2$ for the propagation of high angular momentum modes. Thus, the static and spherically symmetric hairy black hole solutions realized by unsuppressed cubic curvature terms relative to the Ricci scalar are excluded by ghost and Laplacian instabilities.

gr-qc↗

arXiv2023

Black holes in a new gravitational theory with trace anomalies

In a new gravitational theory with the trace anomaly recently proposed by Gabadadze, we study the existence of hairy black hole solutions on a static and spherically symmetric background. In this theory, the effective 4-dimensional action contains a kinetic term of the conformal scalar field related to a new scale $bar{M}$ much below the Planck mass. This property can overcome a strong coupling problem known to be present in general relativity supplemented by the trace anomaly as well as in 4-dimensional Einstein-Gauss-Bonnet gravity. We find a new hairy black hole solution arising from the Gauss-Bonnet trace anomaly, which satisfies regular boundary conditions of the conformal scalar and metric on the horizon. Unlike unstable exact black hole solutions with a divergent derivative of the scalar on the horizon derived for some related theories in the literature, we show that our hairy black hole solution can be consistent with all the linear stability conditions of odd- and even-parity perturbations.

gr-qc↗

arXiv2023

Coupled vector Gauss-Bonnet theories and hairy black holes

We study vector-tensor theories in which a 4-dimensional vector field $A_μ$ is coupled to a vector quantity ${\cal J}^μ$, which is expressed in terms of $A_μ$ and a metric tensor $g_{μν}$. The divergence of ${\cal J}^μ$ is equivalent to a Gauss-Bonnet (GB) term. We show that an interacting Lagrangian of the form $f(X)A_μ{\cal J}^μ$, where $f$ is an arbitrary function of $X=-(1/2)A_μA^μ$, belongs to a scheme of beyond generalized Proca theories. For $f(X)=α={\rm constant}$, this interacting Lagrangian reduces to a particular class of generalized Proca theories. We apply the latter coupling to a static and spherically symmetric vacuum configuration by incorporating the Einstein-Hilbert term, Maxwell scalar, and vector mass term $ηX$ ($η$ is a constant). Under an expansion of the small coupling constant $α$ with $η\neq 0$, we derive hairy black hole solutions endowed with nonvanishing temporal and radial vector field profiles. The asymptotic properties of solutions around the horizon and at spatial infinity are different from those of hairy black holes present in scalar-GB theories. We also show that black hole solutions without the vector mass term, i.e., $η=0$, are prone to ghost instability of odd-parity perturbations.

gr-qc↗

arXiv2023

Black hole perturbations in Maxwell-Horndeski theories

We study the linear stability of black holes in Maxwell-Horndeski theories where a $U(1)$ gauge-invariant vector field is coupled to a scalar field with the Lagrangian of full Horndeski theories. The perturbations on a static and spherically symmetric background can be decomposed into odd- and even-parity modes under the expansion of spherical harmonics with multipoles $l$. For $l \geq 2$, the odd-parity sector contains two propagating degrees of freedom associated with the gravitational and vector field perturbations. In the even-parity sector, there are three dynamical perturbations arising from the scalar field besides the gravitational and vector field perturbations. For these five propagating degrees of freedom, we derive conditions for the absence of ghost/Laplacian stabilities along the radial and angular directions. We also discuss the stability of black holes for $l=0$ and $l=1$, in which case no additional conditions are imposed to those obtained for $l \geq 2$. We apply our general results to Einstein-Maxwell-dilaton-Gauss-Bonnet theory and Einstein-Born-Infeld-dilaton gravity and show that hairy black hole solutions present in these theories can be consistent with all the linear stability conditions. In regularized four-dimensional Einstein-Gauss-Bonnet gravity with a Maxwell field, however, exact charged black hole solutions known in the literature are prone to instabilities of even-parity perturbations besides a strong coupling problem with a vanishing kinetic term of the radion mode.

gr-qc↗

arXiv2023

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field $ϕ$ nonminimally coupled to the Ricci scalar $R$ of the form $F(ϕ)R$. The scalar field has a self-interacting potential and sits at its vacuum expectation value $ϕ_v$ far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value $ϕ_c$ close to $0$. This allows the existence of scalarized NS solutions connecting $ϕ_v$ with $ϕ_c$ whose difference is significant, whereas the field is located in the vicinity of $ϕ=ϕ_v$ for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field $ϕ$ finally approaches the asymptotic value $ϕ_v$ without spoiling a successful cosmological evolution. After $ϕ$ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

gr-qc↗

arXiv2023

Primordial black holes from Higgs inflation with a Gauss-Bonnet coupling

Primordial black holes (PBHs) can be the source for all or a part of today's dark matter density. Inflation provides a mechanism for generating the seeds of PBHs in the presence of a temporal period where the velocity of an inflaton field $ϕ$ rapidly decreases toward 0. We compute the primordial power spectra of curvature perturbations generated during Gauss-Bonnet (GB) corrected Higgs inflation in which the inflaton field has not only a nonminimal coupling to gravity but also a GB coupling. For a scalar-GB coupling exhibiting a rapid change during inflation, we show that curvature perturbations are sufficiently enhanced by the appearance of an effective potential $V_{\rm eff}(ϕ)$ containing the structures of plateau-type, bump-type, and their intermediate type. We find that there are parameter spaces in which PBHs can constitute all dark matter for these three types of $V_{\rm eff}(ϕ)$. In particular, models with bump- and intermediate-types give rise to the primordial scalar and tensor power spectra consistent with the recent Planck data on scales relevant to the observations of cosmic microwave background. This property is attributed to the fact that the number of e-foldings $ΔN_c$ acquired around the bump region of $V_{\rm eff}(ϕ)$ can be as small as a few, in contrast to the plateau-type where $ΔN_c$ typically exceeds the order of 10.

astro-ph.CO↗

arXiv2023

Cosmology in theories with spontaneous scalarization of neutron stars

In a model of spontaneous scalarization of neutron stars proposed by Damour and Esposite-Farese, a general relativistic branch becomes unstable to trigger tachyonic growth of a scalar field $ϕ$ toward a scalarized branch. Applying this scenario to cosmology, there is fatal tachyonic instability of $ϕ$ during inflation and matter dominance being incompatible with solar-system constraints on today's field value $ϕ_0$. In the presence of a four-point coupling $g^2 ϕ^2 χ^2/2$ between $ϕ$ and an inflaton field $χ$, it was argued by Anson et al. that a positive mass squared heavier than the square of a Hubble expansion rate leads to the exponential suppression of $ϕ$ during inflation and that $ϕ_0$ can remain small even with the growth of $ϕ$ after the radiation-dominated epoch. For several inflaton potentials approximated as $V(χ)=m^2 χ^2/2$ about the potential minimum, we study the dynamics of $ϕ$ during reheating as well as other cosmological epochs in detail. For certain ranges of the coupling $g$, the homogeneous field $ϕ$ can be amplified by parametric resonance during a coherent oscillation of the inflaton. Incorporating the backreaction of created particles under a Hartree approximation, the maximum values of $ϕ$ reached during preheating are significantly smaller than those obtained without the backreaction. We also find that the minimum values of $g$ consistent with solar system bounds on $ϕ$ at the end of reheating are of order $10^{-5}$ and hence there is a wide range of acceptable values of $g$. Thus, the scenario proposed by Anson et al. naturally leads to the viable cosmological evolution of $ϕ$ consistent with local gravity constraints, without modifying the property of scalarized neutron stars.

gr-qc↗

arXiv2023

Cosmological stability in $f(ϕ,{\cal G})$ gravity

In gravitational theories where a canonical scalar field $ϕ$ with a potential $V(ϕ)$ is coupled to a Gauss-Bonnet (GB) term ${\cal G}$ with the Lagrangian $f(ϕ,{\cal G})$, we study the cosmological stability of tensor and scalar perturbations in the presence of a perfect fluid. We show that, in decelerating cosmological epochs with a positive tensor propagation speed squared, the existence of nonlinear functions of ${\cal G}$ in $f$ always induces Laplacian instability of a dynamical scalar perturbation associated with the GB term. This is also the case for $f({\cal G})$ gravity, where the presence of nonlinear GB functions $f({\cal G})$ is not allowed during the radiation- and matter-dominated epochs. A linearly coupled GB term with $ϕ$ of the form $ξ(ϕ){\cal G}$ can be consistent with all the stability conditions, provided that the scalar-GB coupling is subdominant to the background cosmological dynamics.

gr-qc↗

arXiv2023

Inspiral gravitational waveforms from compact binary systems in Horndeski gravity

In a subclass of Horndeski theories with the speed of gravity equivalent to that of light, we study gravitational radiation emitted during the inspiral phase of compact binary systems. We compute the waveform of scalar perturbations under a post-Newtonian expansion of energy-momentum tensors of point-like particles that depend on a scalar field. This scalar mode not only gives rise to breathing and longitudinal polarizations of gravitational waves, but it is also responsible for scalar gravitational radiation in addition to energy loss associated with transverse and traceless tensor polarizations. We calculate the Fourier-transformed gravitational waveform of two tensor polarizations under a stationary phase approximation and show that the resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE) formalism. The ppE parameters are directly related to a scalar charge in the Einstein frame, whose existence is crucial to allow the deviation from General Relativity (GR). We apply our general framework to several concrete theories and show that a new theory of spontaneous scalarization with a higher-order scalar kinetic term leaves interesting deviations from GR that can be probed by the observations of gravitational waves emitted from neutron star-black hole binaries. If the scalar mass exceeds the order of typical orbital frequencies $ω\simeq 10^{-13}$~eV, which is the case for a recently proposed scalarized neutron star with a self-interacting potential, the gravitational waveform practically reduces to that in GR.

gr-qc↗

arXiv2022

Probing Modified Gravity with Integrated Sachs-Wolfe CMB and Galaxy Cross-correlations

We use the cross-correlation power spectrum of the integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) temperature anisotropy and galaxy fluctuations to probe the physics of late-time cosmic acceleration. For this purpose, we focus on three models of dark energy that belong to a sub-class of Horndeski theories with the speed of gravity equivalent to that of light: Galileon Ghost Condensate (GGC), Generalized Cubic Covariant Galileon (GCCG), and K-mouflage. In the GGC and GCCG models, the existence of cubic-order scalar self-interactions allows a possibility for realizing negative ISW-galaxy cross-correlations, while the K-mouflage model predicts a positive correlation similar to the $Λ$-cold-dark-matter (LCDM) model. In our analysis, we fix the parameters of each model to their best-fit values derived from a baseline likelihood analysis with observational data from CMB, baryon acoustic oscillations, and supernovae type Ia. Then we fit those best-fit models to the ISW-galaxy cross-correlation power spectrum extracted from a collection of photometric redshift surveys. We find that both GGC and GCCG best-fit models degrade the fit to the ISW-galaxy cross-correlation data compared to LCDM best-fit model. This is attributed to the fact that, for their best-fit values constrained from the baseline likelihood, the cubic-order scalar self-interaction gives rise to suppressed ISW tails relative to $Λ$CDM. The K-mouflage best-fit model is largely degenerate with the LCDM best-fit model and has a positively correlated ISW-galaxy power close to that of LCDM.

astro-ph.CO↗

arXiv2022

Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models

In full Horndeski theories, we show that the static and spherically symmetric black hole (BH) solutions with a static scalar field~$ϕ$ whose kinetic term~$X$ is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically Minkowski hairy BH solutions with a vanishing $X$ on the horizon free from ghost/Laplacian instabilities. We show that models with regular coupling functions of $ϕ$ and $X$ result in no-hair Schwarzschild BHs in general. On the other hand, the presence of a coupling between the scalar field and the Gauss-Bonnet (GB) term $R_{\rm GB}^2$, even with the coexistence of other regular coupling functions, leads to the realization of asymptotically Minkowski hairy BH solutions without ghost/Laplacian instabilities. Finally, we find that hairy BH solutions in power-law $F(R_{\rm GB}^2)$ gravity are plagued by ghost instabilities. These results imply that the GB coupling of the form $ξ(ϕ)R_{\rm GB}^2$ plays a prominent role for the existence of asymptotically Minkowski hairy BH solutions free from ghost/Laplacian instabilities.

gr-qc↗

arXiv2022

Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity

In regularized 4-dimensional Einstein-Gauss-Bonnet (EGB) gravity derived from a Kaluza-Klein reduction of higher-dimensional EGB theory, we study the existence and stability of black hole (BH) solutions on a static and spherically symmetric background. We show that asymptotically-flat hairy BH solutions realized for a spatially-flat maximally symmetric internal space are unstable against linear perturbations for any rescaled GB coupling constant. This instability is present for the angular propagation of even-parity perturbations both in the vicinity of an event horizon and at spatial infinity. There is also a strong coupling problem associated with the kinetic term of even-parity perturbations vanishing everywhere.

gr-qc↗

arXiv2022

Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings

In Horndeski theories containing a scalar coupling with the Gauss-Bonnet (GB) curvature invariant $R_{\rm GB}^2$, we study the existence and linear stability of neutron star (NS) solutions on a static and spherically symmetric background. For a scalar-GB coupling of the form $αξ(ϕ) R_{\rm GB}^2$, where $ξ$ is a function of the scalar field $ϕ$, the existence of linearly stable stars with a nontrivial scalar profile without instabilities puts an upper bound on the strength of the dimensionless coupling constant $|α|$. To realize maximum masses of NSs for a linear (or dilatonic) GB coupling $α_{\rm GB}ϕR_{\rm GB}^2$ with typical nuclear equations of state, we obtain the theoretical upper limit $\sqrt{|α_{\rm GB}|}<0.7~{\rm km}$. This is tighter than those obtained by the observations of gravitational waves emitted from binaries containing NSs. We also incorporate cubic-order scalar derivative interactions, quartic derivative couplings with nonminimal couplings to a Ricci scalar besides the scalar-GB coupling and show that NS solutions with a nontrivial scalar profile satisfying all the linear stability conditions are present for certain ranges of the coupling constants. In regularized 4-dimensional Einstein-GB gravity obtained from a Kaluza-Klein reduction with an appropriate rescaling of the GB coupling constant, we find that NSs in this theory suffer from a strong coupling problem as well as Laplacian instability of even-parity perturbations. We also study NS solutions with a nontrivial scalar profile in power-law $F(R_{\rm GB}^2)$ models, and show that they are pathological in the interior of stars and plagued by ghost instability together with the asymptotic strong coupling problem in the exterior of stars.

gr-qc↗

arXiv2022

Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field

We study linear perturbations about static and spherically symmetric black holes with a time-independent background scalar field in shift-symmetric Horndeski theories, whose Lagrangian is characterized by coupling functions depending only on the kinetic term of the scalar field $X$. We clarify conditions for the absence of ghosts and Laplacian instabilities along the radial and angular directions in both odd- and even-parity perturbations. For reflection-symmetric theories described by a k-essence Lagrangian and a nonminimal derivative coupling with the Ricci scalar, we show that black holes endowed with nontrivial scalar hair are unstable around the horizon in general. This includes nonasymptotically flat black holes known to exist when the nonminimal derivative coupling to the Ricci scalar is a linear function of $X$. We also investigate several black hole solutions in nonreflection-symmetric theories. For cubic Galileons with the Einstein-Hilbert term, there exists a nonasymptotically flat hairy black hole with no ghosts/Laplacian instabilities. Also, for the scalar field linearly coupled to the Gauss-Bonnet term, asymptotically flat black hole solutions constructed perturbatively with respect to a small coupling are free of ghosts/Laplacian instabilities.

gr-qc↗

arXiv2022

Relativistic star perturbations in Horndeski theories with a gauge-ready formulation

We present a general framework for studying the relativistic star perturbations on a static and spherically symmetric background in full Horndeski theories. We take a perfect fluid into account as a form of the Schutz-Sorkin action. Our formulation is sufficiently versatile in that the second-order actions of perturbations in odd- and even-parity sectors are derived without choosing particular gauge conditions, so they can be used for any convenient gauges at hand. The odd-parity sector contains one dynamical gravitational degree of freedom coupled to a time-independent four velocity of the fluid. In the even-parity sector there are three dynamical perturbations associated with gravity, scalar field, and matter sectors, whose equations of motion are decoupled from other nondynamical perturbations. For high radial and angular momentum modes, we obtain the propagation speeds of all dynamical perturbations and show that the perfect fluid in the even-parity sector has a standard sound speed affected by neither gravity nor the scalar field. Our general stability conditions and perturbation equations of motion can be directly applied to the stabilities of neutron stars and black holes as well as the calculations of their quasi-normal frequencies.

gr-qc↗

arXiv2021

Odd-parity stability of black holes in Einstein-Aether gravity

In Einstein-Aether theory, we study the stability of black holes against odd-parity perturbations on a spherically symmetric and static background. For odd-parity modes, there are two dynamical degrees of freedom arising from the tensor gravitational sector and Aether vector field. We derive general conditions under which neither ghosts nor Laplacian instabilities are present for these dynamical fields. We apply these results to concrete black hole solutions known in the literature and show that some of those solutions can be excluded by the violation of stability conditions. The exact Schwarzschild solution present for $c_{13} = c_{14} = 0$, where $c_i$'s are the four coupling constants of the theory with $c_{ij}=c_i + c_j$, is prone to Laplacian instabilities along the angular direction throughout the horizon exterior. However, we find that the odd-parity instability of high radial and angular momentum modes is absent for black hole solutions with $c_{13} = c_4 = 0$ and $c_1 \geq 0$.

gr-qc↗