We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models, and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill-defined at the quantum level in the high energy/sub horizon regime (and create serious problems for finding a well behaved UV completion); (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without vev in a FRW geometry, and of a vector with vev plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.
Bimetric gravity theories allow for many different types of cosmological solutions, but not all of them are theoretically allowed. In this work we discuss the conditions to satisfy the Higuchi bound and to avoid gradient instabilities in the scalar sector at the linear level. We find that in expanding universes the ratio of the scale factors of the reference and observable metric has to increase at all times. This automatically implies a ghost-free helicity-2 and helicity-0 sector and enforces a phantom dark energy. Furthermore, the condition for the absence of gradient instabilities in the sc…
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) …
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 $f_1(ϕ,X)ρ_c (n_c)$ and $f_2 (n_c, ϕ,X) J_c^μ \partial_μϕ$, where $X=-\partial^μ ϕ\partial_μ ϕ/2$, $ρ_c$ and $n_c$ are the energy density and number density of CDM …
Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Being teleparallel gravity of lower order in dynamics, this turns out to be more general than metric Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide rang…
We consider cosmological models with a dynamical dark energy field, and study the presence of three types of commonly found instabilities, namely ghost (when fields have negative kinetic energy), gradient (negative momentum squared) and tachyon (negative mass squared). In particular, we study the linear scalar perturbations of theories with two interacting scalar fields as a proxy for a dark energy and matter fields, and explicitly show how canonical transformations relate these three types of instabilities with each other. We generically show that low-energy ghosts are equivalent to tachyonic…
Models of inflation with antisymmetric tensor studied in the past are plagued with ghost instability even in an unperturbed FRW background. We show that it is possible to avoid ghosts in an unperturbed FRW background by considering the most general kinetic term for antisymmetric tensor field. The kinetic part acquires a new gauge symmetry violating term whose effect on perturbed modes is to prevent the appearance of nondynamical modes, and thus avoid ghosts. For completeness, we perform a check for gradient instability and derive the conditions for perturbations to be free of gradient instabil…
A non-abelian $SU(2)$ gauge field with a non-minimal 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 non-minimal 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 Hubb…
The weak field limit of the nonminimally coupled Boltzmann equation is studied, and relations between the invariant Bardeen scalar potentials are derived. The Jean's criterion for instabilities is found through the modified dispersion relation. Special cases are scrutinised and considerations on the model parameters are discussed for Bok globules.
We investigate vector contributions to the Lagrangian of $Λ_3-$massive gravity in the decoupling limit, the less explored sector of this theory. The main purpose is to understand the stability of maximally symmetric %self-accelerating vacuum solutions. Around self-accelerating configurations, vector degrees of freedom become strongly coupled since their kinetic terms vanish, so their dynamics is controlled by higher order interactions. Even in the decoupling limit, the vector Lagrangian contains an infinite number of terms. We develop a systematic method to covariantly determine the vector Lag…
In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter…
A vector curvaton model with a Maxwell kinetic term and varying kinetic function and mass during inflation is studied. It is shown that, if light until the end of inflation, the vector field can generate statistical anisotropy in the curvature perturbation spectrum and bispectrum, with the latter being predominantly anisotropic. If by the end of inflation the vector field becomes heavy, then particle production is isotropic and the vector curvaton can alone generate the curvature perturbation. The model does not suffer from instabilities such as ghosts and is the only concrete model, to date, …
We revisit nonsingular cosmologies in which the limiting curvature hypothesis is realized. We study the cosmological perturbations of the theory and determine the general criteria for stability. For the simplest model, we find generic Ostrogradski instabilities unless the action contains the Weyl tensor squared with the appropriate coefficient. When considering two specific nonsingular cosmological scenarios(one inflationary and one genesis model), we find ghost and gradient instabilities throughout most of the cosmic evolution. Furthermore, we show that the theory is equivalent to a theory of…
In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings $G_3(X)$, where $X=-A_μA^μ/2$ with a vector field $A_μ$, do not provide any additional stability condition as in General Re…
We consider the mimetic tachyon model in the Lagrange multiplier approach. We study both the linear and non-linear perturbations and find the perturbation and non-gaussianity parameters in this setup. By adopting two types of the scale factor as the power-law ($a=a_{0}\,t^{n}$) and intermediate ($a=a_{0}\exp(bt^β)$) scale factors, we perform a numerical analysis on the model which is based on Planck2018 TT, TE, EE+lowE+lensing +BAO +BK14 and Planck2018 TTT, EEE, TTE and EET data sets. We show that the mimetic tachyon model with both the power-law and intermediate scale factors, in some ranges …
We study the viability conditions for the absence of ghost, gradient and tachyonic instabilities, in scalar-torsion $f(T,ϕ)$ gravity theories in the presence of a general barotropic perfect fluid. To describe the matter sector, we use the Sorkin-Schutz action and then calculate the second order action for scalar perturbations. For the study of ghost and gradient instabilities, we found that the gravity sector keeps decoupled from the matter sector and then applied the viability conditions for each one separately. Particularly, we verified that this theory is free from ghost and gradient instab…
Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. Specifically, these theories lie beyond the quadratic/cubic DHOST class. We explore cosmological perturbations to identify a subclass where gravitational waves propagate at the speed of light and clarify the conditions for the absence of ghost/gradient instabi…
We study the cosmology of bimetric theory with a composite matter coupling. We find two possible branches of background evolution. We investigate the question of stability of cosmological perturbations. For the tensor and vector perturbations, we derive conditions on the absence of ghost and gradient instabilities. For the scalar modes, we obtain conditions for avoiding ghost degrees. In the first branch, we find that one of the scalar modes becomes a ghost at the late stages of the evolution. Conversely, this problem can be avoided in the second branch. However, we also find that the constrai…
We study cosmological applications of extended vector-tensor theories, whose Lagrangians contain up to two derivatives with respect to metric and vector field. We derive background equations under the assumption of homogeneous and isotropic universe and study the nature of cosmological perturbations on top of the background. We found an example of healthy cosmological solutions in non-trivial degenerate theory of gravity for the first time, where those perturbations do not suffer from any instabilities, that is, ghost and gradient instabilities.
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M^2, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that …
Cosmological perturbations of FRW solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that sub horizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations.
Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms. However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the locality assumption is weakened and the propagator of the graviton is represented by an entire function of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological solution describing the $R^2$, or Starobinsky, inflation. We study graviton production after inflation in this model and show that it is negligible despite the presence of the higher …
We study whether it is possible to design a "classical" spatially flat bouncing cosmology or a static, spherically symmetric asymptotically flat Lorentzian wormhole in cubic Galileon theories interacting with an extra scalar field. We show that bouncing models are always plagued with gradient instabilities, while there are always ghosts in wormhole backgrounds.
This paper presents the first derivation of the quadratic action for curvature perturbations, $ζ$, within the framework of cuscuton gravity. We study the scalar cosmological perturbations sourced by a canonical single scalar field in the presence of cuscuton field. We identify $ζ$ as comoving curvature with respect to the source field and we show that it retains its conservation characteristic on super horizon scales. The result provides an explicit proof that cuscuton modification of gravity around Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also investigate the potent…
We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to c…
We study inflationary solution in an extension of mimetic gravity with the higher derivative interactions coupled to gravity. Because of the higher derivative interactions, the setup is free from the ghost and gradient instabilities while it hosts a number of novel properties. The dispersion relation of scalar perturbations develops quartic momentum correction similar to the setup of ghost inflation. Furthermore, the tilt of tensor perturbations can take either signs with a modified consistency relation between the tilt and the amplitude of tensor perturbations. Despite the presence of higher …
We consider the 3-form field, which has been considered as a candidate for realizing inflation, coupled to a scalar field which models the relativistic matter particles produced during the reheating epoch. We have investigated the stability conditions for this theory and found that introducing such a coupling does not lead to any ghosts or Laplacian instabilities. We have also investigated the reheating temperature and the production of particles due to parametric resonances. We have found that this process is more efficient in this theory compared to the result of the standard-scalar-field in…
Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most second order derivatives of scalar field non-minimally coupled to curvature terms. Here we perform (3+1) decomposition of Lagrangian to separate second order time derivative form the rest. This is useful to check the degeneracy hidden in the Lagrangian will help us to find conditions under which Ostrogradsky instability do not appear. In our case, we find no such…
We revisit and extend the `Effective field theory for massive gravitons' constructed by Arkani-Hamed, Georgi and Schwartz in the light of recent progress in constructing ghost-free theories with multiple interacting spin-2 fields. We show that there exist several dual ways of restoring gauge invariance in such multi-gravity theories, find a generalised Fierz-Pauli tuning condition relevant in this context and highlight subtleties in demixing tensor and scalar modes. The generic multi-gravity feature of scalar mixing and its consequences for higher order interactions are discussed. In particula…
Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Iden…
In Brans-Dicke theory a non-linear self interaction of a scalar field allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict the allowed region of model parameters from the demand for the avoidance of ghosts and…
We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to th…
Is Phantom Divide Crossing in General Relativity Completely Impossible? Shortcomings in canonical and minimally coupled scalar field and Possible Solutions in $k$-essence Models
High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；ICREA（加泰罗尼亚高级研究中心）；Institute of Space Sciences (IEEC-CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Khazar University（哈扎尔大学）
Theories with a non-minimal coupling between the space-time curvature and matter fields introduce an extra force due to the non-conservation of the matter energy momentum. In the present work the theoretical consistency of such couplings is studied using a scalar field Lagrangian to model the matter content. The conditions that the coupling does not introduce ghosts, classical instabilities or superluminal propagation of perturbations are derived. These consistency conditions are then employed to rule out or severely restrict the forms of the non-minimal coupling functions considered in the pr…
The recently suggested generalized unimodular gravity theory, which was originally put forward as a model of dark energy, can serve as a model of cosmological inflation driven by the effective perfect fluid -- the dark purely gravitational sector of the theory. Its excitations are scalar gravitons which can generate, in the domain free from ghost and gradient instabilities, the red tilted primordial power spectrum of CMB perturbations matching with observations. The reconstruction of the parametric dependence of the action of the theory in the early inflationary Universe is qualitatively sketc…
Based on the effective field theory (EFT) of nonsingular cosmologies, we build a stable model, without the ghost and gradient instabilities, of bounce inflation (inflation is preceded by a cosmological bounce). We perform a full simulation for the evolution of scalar perturbation, and find that the perturbation spectrum has a large-scale suppression (as expected), which is consistent with the power deficit of the cosmic microwave background (CMB) TT-spectrum at low multipoles, but unexpectedly, it also shows itself one marked lower valley, which actually provides a better fit to the dip at mul…
We consider the minimally coupled 3-form field which has been considered as a candidate to realize inflation. We have studied the conditions to avoid ghosts and Laplacian instabilities and found that some classes of potentials, e.g. the Mexican-hat one, will in general be unstable. We then propose other classes of potentials which are instead free from any instability, drive a long-enough slow-roll regime followed by an oscillatory epoch, and as a consequence, can provide successful inflation. Finally, we also provide stable potentials which lead to a small enough propagation speed for the sca…
The fundamental difficulty in constructing a viable classical bouncing model is to evade the no-go theorem that states that, simultaneously maintaining the observational bounds on the tensor-to-scalar ratio and the non-Gaussian scalar spectrum is not possible. Furthermore, constructing the bouncing phase leads to numerous instabilities such as gradient, ghost, and so on. Most importantly, the model fails to be an attractor, in general, meaning that the solution heavily depends on the initial conditions, resulting in anisotropic (BKL) instability in the system. In this paper, using conformal tr…
We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and te…
