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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 c13=c14=0, where ci's are the four coupling constants of the theory with cij=ci+cj, 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 c13=c4=0 and c1≥0. [ABSTRACT FROM AUTHOR]

We provide a general framework for studying the dark energy cosmology in which a scalar field ϕ is nonminimally and kinetically coupled to cold dark matter (CDM). The scalar-graviton sector is described by the action of Horndeski theories with the speed of gravitational waves equivalent to that of light, whereas CDM is treated as a perfect fluid given by a Schutz-Sorkin action. We consider two interacting Lagrangians of the forms f1(ϕ,X)ρc(nc) and f2(nc,ϕ,X)Jcμ∂μϕ, where X=-∂μϕ∂μϕ/2, ρc and nc are the energy density and number density of CDM respectively, and Jμc is a vector field related to the CDM four velocity. We derive the scalar perturbation equations of motion without choosing any special gauges and identify conditions for the absence of ghosts and Laplacian instabilities on scales deep inside the sound horizon. Applying a quasistatic approximation in a gauge-invariant manner, we also obtain the effective gravitational couplings felt by CDM and baryons for the modes relevant to the linear growth of large-scale structures. In particular, the nc dependence in the coupling f2 gives rise to an interesting possibility for realizing the gravitational coupling with CDM weaker than the Newton gravitational constant G. [ABSTRACT FROM AUTHOR]

The Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories up to quartic order are the general scheme of scalar-tensor theories allowing the possibility for realizing the tensor propagation speed ct equivalent to 1 on the isotropic cosmological background. We propose a dark energy model in which the late-time cosmic acceleration occurs by a simple k-essence Lagrangian analogous to the ghost condensate with cubic and quartic Galileons in the framework of GLPV theories. We show that a wide variety of the variation of the dark energy equation of state wDE including the entry to the region wDE<-1 can be realized without violating conditions for the absence of ghosts and Laplacian instabilities. The approach to the tracker equation of state wDE=-2 during the matter era, which is disfavored by observational data, can be avoided by the existence of a quadratic k-essence Lagrangian X2. We study the evolution of nonrelativistic matter perturbations for the model c2t=1 and show that the two quantities μ and Σ, which are related to the Newtonian and weak lensing gravitational potentials respectively, are practically equivalent to each other, such that μ≃Σ>1. For the case in which the deviation of wDE from -1 is significant at a later cosmological epoch, the values of μ and Σ tend to be larger at low redshifts. We also find that our dark energy model can be consistent with the bounds on the deviation parameter αH from Horndeski theories arising from the modification of gravitational law inside massive objects. [ABSTRACT FROM AUTHOR]

We show that the universal «-attractor models of inflation can be realized by including an auxiliary vector field Ah for the Starobinsky model with the Lagrangian f(R) = R + R²/(6M²). If the same procedure is applied to general modified f(R) theories in which the Ricci scalar R is replaced by R + AμAμ + βVμAμ with constant β, we obtain the Brans-Dicke theory with a scalar potential and the Brans- Dicke parameter ωBD = β²/4. We also place observational constraints on inflationary models based on auxiliary vector modified f(R) theories from the latest Planck measurements of the cosmic microwave background anisotropies in both temperature and polarization. In the modified Starobinsky model, we find that the parameter β is constrained to be β < 25 (68% confidence level) from the bounds of the scalar spectral index and the tensor-to-scalar ratio. [ABSTRACT FROM AUTHOR]

We consider perturbations of a static and spherically symmetric background endowed with a metric tensor and a scalar field in the framework of the effective field theory of modified gravity. We employ the previously developed 2 + 1 + 1 canonical formalism of a double Arnowitt-Deser-Misner (ADM) decomposition of space-time, which singles out both time and radial directions. Our building block is a general gravitational action that depends on scalar quantities constructed from the 2 + 1 + 1 canonical variables and the lapse. Variation of the action up to first order in perturbations gives rise to three independent background equations of motion, as expected from spherical symmetry. The dynamical equations of linear perturbations follow from the second-order Lagrangian after a suitable gauge fixing. We derive conditions for the avoidance of ghosts and Laplacian instabilities for the odd-type perturbations. We show that our results not only incorporate those derived in the most general scalar-tensor theories with second-order equations of motion (the Horndeski theories) but they can be applied to more generic theories beyond Horndeski. [ABSTRACT FROM AUTHOR]

The general k-essence Lagrangian for the existence of cosmological scaling solutions is derived in the presence of multiple scalar fields coupled to a barotropic perfect fluid. In addition to the scaling fixed point associated with the dynamics during the radiation and matter eras, we also obtain a scalar-field dominated solution relevant to dark energy and discuss the stability of them in the two-field setup. We apply our general results to a model of two canonical fields with coupled exponential potentials arising in string theory. Depending on model parameters and initial conditions, we show that the scaling matter-dominated epochs followed by an attractor with cosmic acceleration can be realized with/without the couplings to scalar fields. The different types of scaling solutions can be distinguished from each other by the evolution of the dark energy equation of state from high redshifts to today. [ABSTRACT FROM AUTHOR]

The recent Planck data of cosmic microwave background temperature anisotropies support the Starobinsky theory in which the quadratic Ricci scalar drives cosmic inflation. We build up a multidimensional quantum consisted ultraviolet completion of the model in a phenomenological "bottom-up approach." We present the maximal class of theories compatible with unitarity and (super-)renormalizability or finiteness which reduces to the Starobinsky theory in the low-energy limit. The outcome is a maximal extension of the Krasnikov-Tomboulis-Modesto theory including an extra scalar degree of freedom besides the graviton field. The original theory was afterwards independently discovered by Biswas-Gerwick-Koivisto-Mazumdar starting from first principles. We explicitly show power counting super-renormalizability or finiteness (in odd dimensions) and unitarity (no ghosts) of the theory. Any further extension of the theory is nonunitary, confirming the existence of at most one single extra degree of freedom, the scalaron. A mechanism to achieve the Starobinsky theory in string (field) theory is also investigated at the end of the paper. [ABSTRACT FROM AUTHOR]

We study a coupled dark energy scenario in which a massive vector field Aμ with broken U(1) gauge symmetry interacts with the four-velocity uμc of cold dark matter (CDM) through the scalar product Z=-uμcAμ. This new coupling corresponds to the momentum transfer, so that the background vector and CDM continuity equations do not have explicit interacting terms analogous to the energy exchange. Hence the observational preference of uncoupled generalized Proca theories over the ΛCDM model can be still maintained at the background level. Meanwhile, the same coupling strongly affects the evolution of cosmological perturbations. While the effective sound speed of CDM vanishes, the propagation speed and no-ghost condition of a longitudinal scalar of Aμ and the CDM no-ghost condition are subject to nontrivial modifications by the Z dependence in the Lagrangian. We propose a concrete dark energy model and show that the gravitational interaction on scales relevant to the linear growth of large-scale structures can be smaller than the Newton constant at low redshifts. This leads to the suppression of growth rates of both CDM and total matter density perturbations, so our model allows an interesting possibility for reducing the tension of matter density contrast σ8 between high- and low-redshift measurements. [ABSTRACT FROM AUTHOR]

In a class of generalized Proca theories, we study the existence of neutron star solutions with a nonvanishing temporal component of the vector field Aμ approaching 0 toward spatial infinity, as they may be the endpoints of tachyonic instabilities of neutron star solutions in general relativity with Aμ=0. Such a phenomenon is called spontaneous vectorization, which is analogous to spontaneous scalarization in scalar-tensor theories with nonminimal couplings to the curvature or matter. For the nonminimal coupling βXR, where β is a coupling constant and X=-AμAμ/2, we show that there exist both 0-node and 1-node vector-field solutions, irrespective of the choice of the equations of state of nuclear matter. The 0-node solution, which is present only for β=-Ϭ(0.1), may be induced by some nonlinear effects such as the selected choice of initial conditions. The 1-node solution exists for β=-O(1), which suddenly emerges above a critical central density of star and approaches the general relativistic branch with the increasing central density. We compute the mass M and radius rs of neutron stars for some realistic equations of state and show that the M-rs relations of 0-node and 1-node solutions exhibit a notable difference from those of scalarized solutions in scalar-tensor theories. Finally, we discuss the possible endpoints of tachyonic instabilities. [ABSTRACT FROM AUTHOR]

In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lemaître-Robertson-Walker background by taking into account a matter perfect fluid. We derive the second-order action of scalar perturbations and resulting linear perturbation equations of motion without fixing any gauge conditions. Depending on physical problems at hand, most convenient gauges can be chosen to study the development of inhomogeneities in the presence of scalar and vector fields coupled to gravity. This versatile framework, which encompasses Horndeski and generalized Proca theories as special cases, is applicable to a wide variety of cosmological phenomena including nonsingular cosmology, inflation, and dark energy. By deriving conditions for the absence of ghost and Laplacian instabilities in several different gauges, we show that, unlike Horndeski theories, it is possible to evade no-go arguments for the absence of stable nonsingular bouncing/genesis solutions in both generalized Proca and SVT theories. We also apply our framework to the case in which scalar and vector fields are responsible for dark energy and find that the separation of observables relevant to the evolution of matter perturbations into tensor, vector, and scalar sectors is transparent in the unitary gauge. Unlike the flat gauge chosen in the literature, this result is convenient to confront SVT theories with observations associated with the cosmic growth history. [ABSTRACT FROM AUTHOR]

We study the cosmology on the Friedmann-Lemaître-Robertson-Walker background in scalar-vector-tensor theories with a broken U(1) gauge symmetry. For parity-invariant interactions arising in scalar-vector-tensor theories with second-order equations of motion, we derive conditions for the absence of ghosts and Laplacian instabilities associated with tensor, vector, and scalar perturbations at linear order. This general result is applied to the computation of the primordial tensor power spectrum generated during inflation as well as to the speed of gravity relevant to the late-time cosmic acceleration. We also construct a concrete inflationary model in which a temporal vector component A0 contributes to the dynamics of cosmic acceleration besides a scalar field ϕ through their kinetic mixings. In this model, we show that all the stability conditions of perturbations can be consistently satisfied during inflation and subsequent reheating. [ABSTRACT FROM AUTHOR]

In scalar-vector-tensor theories with U(1) gauge invariance, it was recently shown that there exists a new type of hairy black hole (BH) solutions induced by a cubic-order scalar-vector interaction. In this paper, we derive conditions for the absence of ghosts and Laplacian instabilities against odd-parity perturbations on a static and spherically symmetric background for most general U(1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion. We apply those conditions to hairy BH solutions arising from the cubic-order coupling and show that the odd-parity stability in the gravity sector is always ensured outside the event horizon with the speed of gravity equivalent to that of light. We also study the case in which quartic-order interactions are present in addition to the cubic coupling and obtain conditions under which black holes are stable against odd-parity perturbations. [ABSTRACT FROM AUTHOR]

We study relativistic star solutions in second-order generalized Proca theories characterized by a U(1)-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence is dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity. [ABSTRACT FROM AUTHOR]

In a model of the late-time cosmic acceleration within the framework of generalized Proca theories, there exists a de Sitter attractor preceded by the dark energy equation of state wDE = -1-s, where s is a positive constant. We run the Markov-chain-Monte Carlo code to confront the model with the observational data of the cosmic microwave background (CMB), baryon acoustic oscillations, supernovae type Ia, and local measurements of the Hubble expansion rate for the background cosmological solutions and obtain the bound s = 0.254-0.097+0.118 at 95% confidence level (C.L.). Existence of the additional parameter s to those in the-cold-dark-matter (Λ CDM) model allows to reduce tensions of the Hubble constant H0 between the CMB and the low-redshift measurements. Including the cosmic growth data of redshift-space distortions in the galaxy power spectrum and taking into account no-ghost and stability conditions of cosmological perturbations, we find that the bound on s is shifted to s = 0.16-0.08+0.08 (95% C.L.) and hence the model with s > 0 is still favored over the Λ CDM model. Apart from the quantities s,H0 and the today's matter density parameter Ωm0, the constraints on other model parameters associated with perturbations are less stringent, reflecting the fact that there are different sets of parameters that give rise to a similar cosmic expansion and growth history. [ABSTRACT FROM AUTHOR]

We place observational constraints on two models within a class of scenarios featuring an elastic interaction between dark energy and dark matter that only produces momentum exchange up to first order in cosmological perturbations. The first one corresponds to a perfect-fluid model of the dark components with an explicit interacting Lagrangian, where dark energy acts as a dark radiation at early times and behaves as a cosmological constant at late times. The second one is a dynamical dark energy model with a dark radiation component, where the momentum exchange covariantly modifies the conservation equations in the dark sector. Using cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and supernovae type Ia (SnIa) data, we show that the Hubble tension can be alleviated due to the additional radiation, while the s8 tension present in the Λ-cold-dark-matter model can be eased by the weaker galaxy clustering that occurs in these interacting models. Furthermore, we show that, while CMB+BAO+SnIa data put only upper bounds on the coupling strength, adding low-redshift data in the form of a constraint on the parameter S8 strongly favors nonvanishing values of the interaction parameters. Our findings are in line with other results in the literature that could signal a universal trend of the momentum exchange among the dark sector. [ABSTRACT FROM AUTHOR]

We investigate the possibility that axionlike particles (ALPs) with various potentials account for the isotropic birefringence recently reported by analyzing the Planck 2018 polarization data. For the quadratic and cosine potentials, we obtain lower bounds on the mass, coupling constant to photon g, abundance and equation of state of the ALP to produce the observed birefringence. Especially when the ALP is responsible for dark energy, it is possible to probe the tiny deviation of dark energy equation of state from-1 through the cosmic birefringence. We also explore ALPs working as early dark energy (EDE), which alleviates the Hubble tension problem. Since the other parameters are limited by the EDE requirements, we narrow down the ALP-photon coupling to 10-19 GeV-1g10-16 GeV-1 for the decay constant f=Mpl. Therefore, the Hubble tension and the isotropic birefringence imply that g is typically the order of f-1, which is a nontrivial coincidence. [ABSTRACT FROM AUTHOR]

We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form F(ϕ)R, where F depends on a scalar field ϕ and R is the Ricci scalar. On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action. The odd-parity perturbation for the multipoles l≥2 is ghost-free under the condition F(ϕ)>0, with the speed of gravity equivalent to that of light. For even-parity perturbations with l≥2, there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors. For l=0, 1, the dynamical degrees of freedom reduce to two modes. We derive no-ghost conditions and the propagation speeds of these perturbations and apply them to concrete theories of hairy relativistic stars with F(ϕ)>0. As long as the perfect fluid satisfies a weak energy condition with a positive propagation speed squared c²m, there are neither ghost nor Laplacian instabilities for theories of spontaneous scalarization and Brans-Dicke (BD) theories with a BD parameter ωBD>-3/2 (including f(R) gravity). In these theories, provided 0

We place observational constraints on the Galileon ghost condensate model, a dark energy proposal in cubic-order Horndeski theories consistent with the gravitational-wave event GW170817. The model extends the covariant Galileon by taking an additional higher-order field derivative X² into account. This allows for the dark energy equation of state wDE to access the region -2

We study observational constraints on a specific dark energy model in the framework of Gleyzes-Langlois-Piazza-Vernizzi theories, which extends the Galileon ghost condensate (GGC) to the domain of beyond Horndeski theories. In this model, we show that the Planck cosmic microwave background (CMB) data, combined with datasets of baryon acoustic oscillations, supernovae type Ia, and redshift-space distortions, give the tight upper bound |α(0)H|≤Ϭ(10-6) on today's beyond-Horndeski (BH) parameter αH. This is mostly attributed to the shift of CMB acoustic peaks induced by the early-time changes of cosmological background and perturbations arising from the dominance of αH in the dark energy density. In comparison to the Λ cold dark matter (ΛCDM) model, our BH model suppresses the large-scale integrated-Sachs-Wolfe tail of CMB temperature anisotropies due to the existence of cubic Galileons, and it modifies the small-scale CMB power spectrum because of the different background evolution. We find that the BH model considered fits the data better than ΛCDM according to the χ² statistics, yet the deviance information criterion (DIC) slightly favors the latter. Given the fact that our BH model with αH=0 (i.e., the GGC model) is favored over ΛCDM even by the DIC, there are no particular signatures for the departure from Horndeski theories in current observations. [ABSTRACT FROM AUTHOR]

The gravitational-wave event GW170817, together with the electromagnetic counterpart, shows that the speed of tensor perturbations cT on the cosmological background is very close to that of light c for the redshift z<0.009. In generalized Proca theories, the Lagrangians compatible with the condition cT=c are constrained to be derivative interactions up to cubic order, besides those corresponding to intrinsic vector modes. We place observational constraints on a dark energy model in cubic-order generalized Proca theories with intrinsic vector modes by running the Markov chain Monte Carlo (MCMC) code. We use the cross-correlation data of the integrated Sachs-Wolfe (ISW) signal and galaxy distributions in addition to the data sets of cosmic microwave background, baryon acoustic oscillations, type Ia supernovae, local measurements of the Hubble expansion rate, and redshift-space distortions. We show that, unlike cubic-order scalar-tensor theories, the existence of intrinsic vector modes allows the possibility for evading the ISW-galaxy anticorrelation incompatible with the current observational data. As a result, we find that the dark energy model in cubic-order generalized Proca theories exhibits a better fit to the data than the cosmological constant, even by including the ISW-galaxy correlation data in the MCMC analysis. [ABSTRACT FROM AUTHOR]

In cubic-order Horndeski theories where a scalar field ϕ is coupled to nonrelativistic matter with a field-dependent coupling Q(ϕ), we derive the most general Lagrangian having scaling solutions on the isotropic and homogenous cosmological background. For constant Q including the case of vanishing coupling, the corresponding Lagrangian reduces to the form L=Xg2(Y)-g3(Y)□ϕ, where X=-∂μϕ∂μϕ/2 and g2, g3 are arbitrary functions of Y=Xeλϕ with constant λ. We obtain the fixed points of the scaling Lagrangian for constant Q and show that the ϕ-matter-dominated epoch (ϕMDE) is present for the cubic coupling g3(Y) containing inverse power-law functions of Y. The stability analysis around the fixed points indicates that the ϕMDE can be followed by a stable critical point responsible for the cosmic acceleration. We propose a concrete dark energy model allowing for such a cosmological sequence and show that the ghost and Laplacian instabilities can be avoided even in the presence of the cubic coupling. [ABSTRACT FROM AUTHOR]

We propose a viable dark energy scenario in the presence of cubic Horndeski interactions and a standard scalar-field kinetic term with two exponential potentials. We show the existence of new scaling solutions along which the cubic coupling G3 provides an important contribution to the field density that scales in the same way as the background fluid density. The solutions finally exit to the epoch of cosmic acceleration driven by a scalar-field dominated fixed point arising from the second exponential potential. We clarify the viable parameter space in which all the theoretically consistent conditions including those for the absence of ghost and Laplacian instabilities are satisfied on scaling and scalar-field dominated critical points. In comparison to quintessence with the same scalar potential, we find that the cubic coupling gives rise to some novel features: (i) the allowed model parameter space is wider in that a steeper potential can drive the cosmic acceleration; (ii) the dark energy equation of state wϕ today can be closer to -1 relative to quintessence; (iii) even if the density associated with the cubic coupling dominates over the standard field density in the scaling era, the former contribution tends to be suppressed at low redshifts. We also compute quantities associated with the growth of matter perturbations and weak lensing potentials under the quasi-static approximation in the subhorizon limit and show that the cubic coupling leads to the modified evolution of perturbations which can be distinguished from quintessence. [ABSTRACT FROM AUTHOR]

We study the evolution of gravitational waves (GWs) during and after inflation as well as the resulting observational consequences in a Lorentz-violating massive gravity theory with one scalar (inflaton) and two tensor degrees of freedom. We consider two explicit examples of the tensor mass mg that depends either on the inflaton field ϕ or on its time derivative ˙ϕ, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinsky's R² inflation model with a ϕ-dependent mg, and the second is a low energy-scale inflation model with a ˙ϕ-dependent mg. We compute the energy density spectrum ΩGW(k) today of the GW background. In the Starobinsky's model, we show that the GWs can be amplified up to the detectable ranges of both cosmic microwave background and DECi-hertz Interferometer Gravitational wave Observatory, but the bound from the big bang nucleosynthesis is quite tight to limit the growth. In low-scale inflation with a fast transition to the reheating stage driven by the potential V(ϕ)=M²ϕ²/2 around ϕ≈Mpl (where Mpl is the reduced Planck mass), we find that the peak position of ΩGW(k) induced by the parametric resonance can reach the sensitivity region of advanced LIGO for the Hubble parameter of order 1 GeV at the end of inflation. Thus, our massive gravity scenario offers exciting possibilities for probing the physics of primordial GWs at various different frequencies. [ABSTRACT FROM AUTHOR]

A non-Abelian SU(2) gauge field with a nonminimal Horndeski coupling to gravity gives rise to a de Sitter solution followed by a graceful exit to a radiation-dominated epoch. In this Horndeski-Yang-Mills (HYM) theory we derive the second-order action for tensor perturbations on the homogeneous and isotropic quasi-de Sitter background. We find that the presence of the Horndeski nonminimal coupling to the gauge field inevitably introduces ghost instabilities in the tensor sector during inflation. Moreover, we also find Laplacian instabilities for the tensor perturbations deep inside the Hubble radius during inflation. Thus, we conclude that the HYM theory does not provide a consistent inflationary framework due to the presence of ghosts and Laplacian instabilities. [ABSTRACT FROM AUTHOR]

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate fσ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the ΛCDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry. [ABSTRACT FROM AUTHOR]