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We consider the possibility of extra spinning particles during inflation, focussing on the spin-2 case. Our analysis relies on the well-known fully non-linear formulation of interacting spin-2 theories. We explore the parameter space of the corresponding inflationary Lagrangian and identify regions therein exhibiting signatures within reach of upcoming CMB probes. We provide a thorough study of the early and late-time dynamics ensuring that stability conditions are met throughout the cosmic evolution. We characterise in particular the gravitational wave spectrum and three-point function finding a local-type non-Gaussianity whose amplitude may be within the sensitivity range of both the LiteBIRD and CMB-S4 experiments., 30 pages, 6 figures; v2 -- references added, minor changes, accepted for publication in JCAP

We present a non-linear analysis of perturbations around cosmological solutions in Generalised Massive gravity. This Lorentz invariant theory is an extension of de Rham, Gabadadze, Tolley massive gravity that propagates $5$ degrees of freedom while allowing stable open FLRW cosmologies. For a minimal model that supports a self-accelerating background, we study the dynamics of non-linear perturbations. We find that the equation for the scalar graviton is distinct from the analogues in Horndeski and DHOST theories. We numerically solve the equation to find a new type of nonlinear solution for the scalar mode, and confirm the presence of a Vainshtein screening mechanism. We show that the PPN parameter approaches its GR value at solar system scales and satisfies the current bounds., Comment: 21 pages, 6 figures

We introduce a cosmological model in the framework of Generalised Massive Gravity. This theory is an extension of non-linear massive gravity with a broken translation symmetry in the St��ckelberg space. In a recent work, we showed the existence of cosmological solutions stable against linear perturbations. In the present paper, we build up on the previous result and study the evolution of the background solutions and the linear perturbations. At the background level, we find that the mass terms act like a fluid with time dependent equation of state $w < -1$ at late times. At linear order, we derive the Poisson's equation. We find that the scalar graviton mode invokes anisotropic stress, which brings a modification with respect to LCDM in the effective Newton's constant and the growth rate of matter perturbations. Moreover, we study the propagation of gravitational waves and find that the tensor modes acquire a time dependent mass., 18 pages, 9 figures

We propose new massive gravity theories with 5 dynamical degrees of freedom. We evade uniqueness theorems regarding the form of the kinetic and potential terms by adopting the "generalized massive gravity" framework, where a global translation invariance is broken. By exploiting the rotation symmetry in the field space, we determine two novel classes of theories. The first one is an extension of generalized massive gravity with a non-minimal coupling. On the other hand, the second theory produces a mass term that is different from de Rham, Gabadadze, Tolley construction and trivially has 5 degrees of freedom. Both theories allows for stable cosmological solutions without infinite strong coupling, which are free of ghost and gradient instabilities., v2 : accepted for publication in PRD

We present a thorough analysis of the cosmological perturbations in Generalised Massive Gravity. This is an extension of de Rham-Gabadadze-Tolley theory where the translation invariance in the St\"uckelberg field space is broken. This allows the mass parameters to be promoted to functions of the St\"uckelberg fields. We consider an exact cosmological background in this theory and study the stability of perturbations. We derive conditions to avoid ghost, gradient and tachyonic instability. The cosmology is an extension of the self-accelerating branch of the constant mass parameter theory, but now all five massive graviton polarisations propagate. For concreteness, we consider a minimal version of the theory where cosmology undergoes an accelerated expansion at late times and show that the perturbative stability is preserved for a range of parameters., Comment: 13 pages, 2 figures. V2: Typos corrected, sentences added. Accepted for publication in PRD

For field theories in curved spacetime, defining how matter gravitates is part of the theory building process. In this letter, we adopt Bekenstein's multiple geometries approach to allow part of the matter sector to follow the geodesics on a general pseudo-Riemannian geometry, constructed from a tensor and a $U(1)$ gauge field. This procedure allows us to generate a previously unknown corner of vector-tensor theories. In the Jordan frame, apparent high-derivative terms of the vector field are reduced by integrating out an auxiliary variable, at the cost of introducing new matter interactions. As a simple example, we consider a conformal relation between different geometries and demonstrate the presence of an auxiliary degree. We conclude with a discussion of applications, in particular for the early universe., 5 pages; v2 update to match the published version

Massive gravity theory introduced by de Rham, Gabadadze, Tolley (dRGT) is restricted by several uniqueness theorems that protect the form of the potential and kinetic terms, as well as the matter coupling. These restrictions arise from the requirement that the degrees of freedom match the expectation from Poincar\'e representations of a spin--2 field. Any modification beyond the dRGT form is known to invalidate a constraint that the theory enjoys and revive a dangerous sixth mode. One loophole is to exploit the effective nature of the theory by pushing the sixth mode beyond the strong coupling scale without completely removing it. In this paper, we search for modifications to dRGT action by coupling the matter sector to an arbitrary metric constructed out of the already existing degrees of freedom in the dRGT action. We formulate the conditions that such an extension should satisfy in order to prevent the sixth mode from contaminating the effective theory. Our approach provides a new perspective for the "composite coupling" which emerges as the unique extension up to four-point interactions., Comment: 19 pages; v2: new references added, accepted for publication in PRD

We present a novel cosmological solution in the framework of extended quasidilaton theory which underwent scrutiny recently. We only consider terms that do not generate the Boulware-Deser degree of freedom, hence the "ghost-free" quasidilaton theory, and show three new branches of cosmological evolution therein. One of the solutions passes the perturbative stability tests. This new solution exhibits a late time self-acceleration and all graviton polarizations acquire masses that converge to a constant in the asymptotic future. Moreover, all modes propagate at the speed of light. We propose that this solution can be used as a benchmark model for future phenomenological studies., Comment: 12 pages

The cuscuton is a scalar field with infinite speed of propagation. It was introduced in the context of cosmology but it has also been claimed to resemble Horava gravity in a certain limit. Here we revisit the cuscuton theory as a Lorentz-violating gravity theory. We clarify its relation with Horava gravity and Einstein-aether theory, analyze its causal structure, and consider its initial value formulation. Finally, we discuss to which extent the cuscuton theory can be used as a proxy for Horava gravity in the context of gravitational collapse and formation of universal horizons., 9 pages, revised version as published in PRD

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 constraint for the second branch prevents the doubly coupled matter fields from being the standard ingredients of cosmology. We thus conclude that a realistic and stable cosmological model requires additional minimally coupled matter fields., Comment: 22 pages

Horava gravity has been constructed so as to exhibit anisotropic scaling in the ultraviolet, as this renders the theory power-counting renormalizable. However, when coupled to matter, the theory has been shown to suffer from quadratic divergences. A way to cure these divergences is to add terms with both time and space derivatives. We consider this extended version of the theory in detail. We perform a perturbative analysis that includes all modes, determine the propagators and discuss how including mixed-derivative terms affects them. We also consider the Lifshitz scalar with mixed-derivative terms as a toy model for power counting arguments and discuss the influence of such terms on renormalizability., Comment: 9 pages

We consider a linear effective vielbein matter coupling without introducing the Boulware-Deser ghost in ghost-free massive gravity. This is achieved in the partially constrained vielbein formulation. We first introduce the formalism and prove the absence of ghost at all scales. As next we investigate the cosmological application of this coupling in this new formulation. We show that even if the background evolution accords with the metric formulation, the perturbations display important different features in the partially constrained vielbein formulation. We study the cosmological perturbations of the two branches of solutions separately. The tensor perturbations coincide with those in the metric formulation. Concerning the vector and scalar perturbations, the requirement of absence of ghost and gradient instabilities yields slightly different allowed parameter space., Journal of Cosmology and Astroparticle Physics, 2016 (1), ISSN:1475-7516

It has been argued that Horava gravity needs to be extended to include terms that mix spatial and time derivatives in order avoid unacceptable violations of Lorentz invariance in the matter sector. In an earlier paper we have shown that including such mixed derivative terms generically leads to 4th instead of 6th order dispersion relations and this could be (naively) interpreted as a threat to renormalizability. We have also argued that power-counting renormalizability is not actually compromised, but instead the simplest power-counting renormalizable model is not unitary. In this paper we consider the Lifshitz scalar as a toy theory and we generalize our analysis to include higher order operators. We show that models which are power-counting renormalizable and unitary do exist. Our results suggest the existence of a new class of theories that can be thought of as Horava gravity with mixed derivative terms., Comment: 5 pages, 1 figure. v3: Published version

We study cosmological perturbations in bimetric theory with two fluids each of which is coupled to one of the two metrics. Focusing on a healthy branch of background solutions, we clarify the stability of the cosmological perturbations. For this purpose, we extend the condition for the absence of the so-called Higuchi ghost, and show that the condition is guaranteed to be satisfied on the healthy branch. We also calculate the squared propagation speeds of perturbations and derive the conditions for the absence of the gradient instability. To avoid the gradient instability, we find that the model parameters are weakly constrained., Comment: 16 pp; v2: minor corrections/references added to match the published version

We explore the possibility for generalized electromagnetism on flat spacetime. For a single copy of $U(1)$ gauge theory, we show that the Galileon-type generalization of electromagnetism is forbidden. Given that the equations of motion for the vector field are gauge invariant and Lorentz invariant, follow from an action and contain no more than second derivative on $A_\mu$, the equations of motion are at most linear with respect to second derivative of $A_\mu$., Comment: 10 pages

Recently the first example of a unitary theory of Lorentz-invariant massive gravity allowing for stable self-accelerating de Sitter solutions was found, extending the quasidilaton theory. In this paper we further generalize this new action for the quasidilaton field by introducing general Lagrangian terms which are consistent with the quasidilaton symmetry while leading to second order equations of motion. We find that the structure of the theory, compared to the simplest stable example, does not change on introducing these new terms., 11 pages

We present a review of cosmological solutions in non-linear massive gravity, focusing on the stability of perturbations. Although homogeneous and isotropic solutions have been found, these are now known to suffer from either Higuchi ghost or a new non-linear ghost instability. We discuss two approaches to alleviate this issue. By relaxing the symmetry of the background by e.g. breaking isotropy in the hidden sector, it is possible to accommodate a stable cosmological solution. Alternatively, extending the theory to allow for new dynamical degrees of freedom can also remove the conditions which lead to the instability. As examples for this case, we study the stability of self-accelerating solutions in the quasi-dilatonic extension and generic cosmological solutions in the varying mass extension. While the quasi-dilaton case turns out to be unstable, the varying mass case allows stable regimes of parameters. Viable self-accelerating solutions in the varying mass theory yet remain to be found., Comment: 20 pages, prepared for CQG focus issue ; v2: Published version

We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions., Comment: 28 pages ; v2. Minor changes to match the published version

We discuss the detectability of gravitational waves with a time dependent mass contribution, by means of the stochastic gravitational wave observations. Such a mass term typically arises in the cosmological solutions of massive gravity theories. We conduct the analysis based on a general quadratic action, and thus the results apply universally to any massive gravity theories in which modification of general relativity appears primarily in the tensor modes. The primary manifestation of the modification in the gravitational wave spectrum is a sharp peak. The position and height of the peak carry information on the present value of the mass term, as well as the duration of the inflationary stage. We also discuss the detectability of such a gravitational wave signal using the future-planned gravitational wave observatories., Comment: 22 pages, 6 figures; v2: Comments added to Sec. III, modifications to Sec. V

We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the gravity sector, we find that the scalar and vector degrees have vanishing kinetic terms and nonzero mass terms. Depending on their nonlinear behavior, this indicates either nondynamical nature of these degrees or strong couplings. Assuming the former, we integrate out the 2 vector and 2 scalar degrees of freedom. We then find that in the scalar and vector sectors, gauge-invariant variables constructed from metric and matter perturbations have exactly the same quadratic action as in general relativity. The difference from general relativity arises only in the tensor sector, where the graviton mass modifies the dispersion relation of gravitational waves, with a time-dependent effective mass. This may lead to modification of stochastic gravitational wave spectrum., 32 pages, 1 figure; v2: minor update to match the published version

We present a fully nonlinear study of long wavelength cosmological perturbations within the framework of the projectable Horava-Lifshitz gravity, coupled to a single scalar field. Adopting the gradient expansion technique, we explicitly integrate the dynamical equations up to any order of the expansion, then restrict the integration constants by imposing the momentum constraint. While the gradient expansion relies on the long wavelength approximation, amplitudes of perturbations do not have to be small. When the $\lambda\to 1$ limit is taken, the obtained nonlinear solutions exhibit a continuous behavior at any order of the gradient expansion, recovering general relativity in the presence of a scalar field and the "dark matter as an integration constant". This is in sharp contrast to the results in the literature based on the "standard" (and naive) perturbative approach where in the same limit, the perturbative expansion of the action breaks down and the scalar graviton mode appears to be strongly coupled. We carry out a detailed analysis on the source of these apparent pathologies and determine that they originate from an improper application of the perturbative approximation in the momentum constraint. We also show that there is a new branch of solutions, valid in the regime where $|\lambda-1|$ is smaller than the order of perturbations. In the limit $\lambda\to1$, this new branch allows the theory to be continuously connected to general relativity (plus "dark matter")., Comment: 21 pages; v2. minor update to match the published version

We compute the phenomenological signatures of a model [Watanabe et al. Phys. Rev. Lett. 102, 191302 (2009)] of anisotropic inflation driven by a scalar and a vector field. The action for the vector is U(1) invariant, and the model is free of ghost instabilities. A suitable coupling of the scalar to the kinetic term of the vector allows for a slow roll evolution of the vector vacuum expectation value, and hence for a prolonged anisotropic expansion; this provides a counter example to the cosmic no hair conjecture. We compute the nonvanishing two point correlation functions between physical modes of the system, and express them in terms of power spectra with angular dependence. The anisotropy parameter ${g}_{*}$ for the scalar-scalar spectrum (defined as in the Ackerman et al. [Phys. Rev. D 75, 0835002 (2007)] parametrization) turns out to be negative in the simplest realization of the model, which, therefore, cannot account for the angular dependence emerged in some analyses of the Wilkinson Microwave Anisotropy Probe data. A ${g}_{*}$ of order $\ensuremath{-}0.1$ is achieved when the energy of the vector is about 6--7 orders of magnitude smaller than that of the scalar during inflation. For such values of the parameters, the scalar-tensor correlation (which is in principle a distinctive signature of anisotropic spaces) is smaller than the tensor-tensor correlation.

We study exact stationary and axisymmetric solutions describing charged rotating black holes localized on a 3-brane in the Randall-Sundrum braneworld. The charges of the black holes are considered to be of two types, the first being an induced tidal charge that appears as an imprint of nonlocal gravitational effects from the bulk space and the second is a usual electric charge arising due to a Maxwell field trapped on the brane. We assume a special ansatz for the metric on the brane taking it to be of the Kerr-Schild form and show that the Kerr-Newman solution of ordinary general relativity in which the electric charge is superceded by a tidal charge satisfies a closed system of the effective gravitational field equations on the brane. It turns out that the negative tidal charge may provide a mechanism for spinning up the black hole so that its rotation parameter exceeds its mass. This is not allowed in the framework of general relativity. We also find a new solution that represents a rotating black hole on the brane carrying both charges. We show that for a rapid enough rotation the combined influence of the rotational dynamics and the local bulk effects of the "squared" energy momentum tensor on the brane distort the horizon structure of the black hole in such a way that it can be thought of as composed of non-uniformly rotating null circles with growing radii from the equatorial plane to the poles. We finally study the geodesic motion of test particles in the equatorial plane of a rotating black hole with tidal charge. We show that the effects of negative tidal charge tend to increase the horizon radius, as well as the radii of the limiting photon orbit, the innermost bound and the innermost stable circular orbits for both direct and retrograde motions of the particles., RevTeX 4, 33 pages, 4 figures, new references added

In the context of a recently proposed nonlinear massive gravity with Lorentz-invariant mass terms, we investigate open Friedmann-Robertson-Walker (FRW) universes driven by arbitrary matter source. While the flat FRW solutions were recently shown to be absent, the proof does not extend to the open universes. We find three independent branches of solutions to the equations of motion for the St\"uckelberg scalars. One of the branches does not allow any nontrivial FRW cosmologies, as in the previous no-go result. On the other hand, both of the other two branches allow general open FRW universes governed by the Friedmann equation with the matter source, the standard curvature term and an effective cosmological constant $\Lambda_{\pm}=c_{\pm}m_g^2$. Here, $m_g$ is the graviton mass, +and - represent the two branches, and $c_{\pm}$ are constants determined by the two dimensionless parameters of the theory. Since an open FRW universe with a sufficiently small curvature constant can approximate a flat FRW universe but there is no exactly flat FRW solution, the theory exhibits a discontinuity at the flat FRW limit., Comment: 9 pages, V2 with minor revision, and to appear on JCAP