F. T. Brandt, J. Frenkel
It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.
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Gravitational instabilities of isothermal spheres are studied in the presence of a positive or negative cosmological constant, in the Newtonian limit. In gravity, the statistical ensembles are not equivalent. We perform the analysis both in the microcanonical and the canonical ensembles, for which the corresponding instabilities are known as `gravothermal catastrophe' and `isothermal collapse', respectively. In the microcanonical ensemble, no equilibria can be found for radii larger than a critical value, which is increasing with increasing cosmological constant. In contrast, in the canonical …
We review (anti)evaporation phenomena within the context of quantum gravity and extended theories of gravity. The (anti)evaporation effect is an instability of the black hole horizon discovered in many different scenarios: quantum dilaton-gravity, $f(R)$-gravity, $f(T)$-gravity, string inspired black holes and brane-world cosmology. Evaporating and antievaporating black holes seem to have completely different thermodynamical features compared to standard semiclassical black holes. The purpose of this review is to provide an introduction to conceptual and technical aspects of (anti)evaporation …
Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field redefinitions needed to reach an Einstein frame. As a consequence, they are very prone to present dynamical instabilities that could spoil any attempt to construct viable models within these frameworks. In these three lectures we introduce the most common types of instabilities that appear in field theory as well as some techniques to detect them, and suppl…
We investigate the observational consequences of scalar instabilities in bimetric theory, under the assumption that the Vainshtein mechanism restores general relativity within a certain distance from gravitational sources. We argue that early time instabilities have a negligible impact on observed structures. Assuming that the instabilities affect sub-horizon density fluctuations, we constrain the redshift, z_i, below which instabilities are ruled out. For the "minimal" beta_1-model, observational constraints are close to the theoretical expectations of z_i = 0.5, potentially allowing the mode…
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 propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on "seed" scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar …
We discuss the modified gravity which may produce the current cosmic aceleration of the universe and eliminates the need for dark energy. It is shown that such models where the action quickly grows with the decrease of the curvature define the FRW universe with the minimal curvature. It is required the infinite time to reach the minimal curvature during the universe evolution. It is demonstrated that quantum effects of conformal fields may strongly suppress the instabilities discovered in modified gravity. We also briefly speculate on the modification of gravity combined with the presence of t…
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…
We study the instabilities and related anti-evaporation of the extremal Reissner-Nordström (RN) black hole in $F(R)$ gravity. It is remarkable that the effective electric charge can be generated for some solutions of $F(R)$ gravity without electromagnetic field. The anti-evaporation effect occurs but it emerges only in the strong coupling limit of the effective gravitational coupling. The instabilities of RN black hole are also investigated when the electromagnetic sector is added to the action of $F(R)$ gravity. We show the anti-evaporation occurs in the Maxwell-$F(R)$ gravity with the arbitr…
We discuss the cosmological implications of nonlocal modifications of general relativity containing tensorial structures. Assuming the presence of standard radiation- and matter-dominated eras, we show that, except in very particular cases, the nonlocal terms contribute a rapidly growing energy density. These models therefore generically do not have a stable cosmological evolution.
We consider class of modified $f(R)$ gravities with the effective cosmological constant epoch at the early and late universe. Such models pass most of solar system tests as well they satisfy to cosmological bounds. Despite their very attractive properties, it is shown that one realistic class of such models may lead to significant Newton law corrections which become small at the future universe only. The model with acceptable Newton law regime shows the matter instability. This suggests that more complicated version of such theory (or extended parameters space) should be investigated.
We investigate the scalar and tensor perturbations in Horava gravity, with and without detailed balance, around a flat background. Once both types of perturbations are taken into account, it is revealed that the theory is plagued by ghost-like scalar instabilities in the range of parameters which would render it power-counting renormalizable, that cannot be overcome by simple tricks such as analytic continuation. Implementing a consistent flow between the UV and IR limits seems thus more challenging than initially presumed, regardless of whether the theory approaches General Relativity at low …
We consider Modified Gravity models involving inverse powers of fourth-order curvature invariants. Using these models' equivalence to the theory of a scalar field coupled to a linear combination of the invariants, we investigate the properties of the propagating modes. Even in the case for which the fourth derivative terms in the field equations vanish, we find that the second derivative terms can give rise to ghosts, instabilities, and superluminal propagation speeds. We establish the conditions which the theories must satisfy in order to avoid these problems in Friedmann backgrounds, and sho…
We investigate the future evolution of Nariai black hole which is extremal limit of Schwarzschild-de Sitter one in modified gravity. The perturbations equations around Nariai black hole are derived in static and cosmological patches for general $F(R)$-gravity. The analytical and numerical study of several realistic $F(R)$-models shows the occurence of rich variety of scenarios: instabilities, celebrated Hawking evaporation and anti-evaporation of black hole. The realization of specific scenario depends on the model under consideration. It is remarkable that the presence of such primordial blac…
The higher dimensional instabilities of AdS in holographic semiclassical gravity
本文在AdS/CFT框架下研究一般二次引力理论的半经典问题，构造了4维和5维带量子毛的全局及双曲AdS黑洞解，发现双曲黑洞解存在动力学不稳定性，并通过自由能计算揭示了5维Gauss-Bonnet理论中带毛解的热力学不稳定性。
We show that the instabilities of higher derivative gravity models with quadratic curvature invariant $αR^2+βR_{μν}R^{μν}$ can be removed by judicious addition of constraints at the quadratic level of metric fluctuations around Minkowski/de Sitter background. With a suitable parameter choice, we find that the instabilities of helicity-0, 1, 2 modes can be removed while reducing the dimensionality of the original phase space. To retain the renormalization properties of higher derivative gravity, Lorentz symmetry in the constrained theory is explicitly broken.
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…
It is well known that linearized gravity in spacetimes with compact Cauchy surfaces and continuous symmetries suffers from linearization instabilities: solutions to classical linearized gravity in such a spacetime must satisfy so-called linearization stability conditions (or constraints) for them to extend to solutions in the full non-linear theory. Moncrief investigated implications of these conditions in linearized quantum gravity in such background spacetimes and found that the quantum linearization stability constraints lead to the requirement that all physical states must be invariant und…
We continue the exploration of the consistency of a modified-gravity theory that generalizes General Relativity by including a dynamical torsion in addition to the dynamical metric. The six-parameter theory we consider was found to be consistent around arbitrary torsionless Einstein backgrounds, in spite of its containing a (notoriously delicate) massive spin-2 excitation. At zero bare cosmological constant, this theory was found to admit a self-accelerating solution whose exponential expansion is sustained by a non-zero torsion background. The scalar-type perturbations of the latter torsionfu…
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…
It is widely accepted that moduli in the mass range 10eV - $10^4$GeV which start to oscillate with an amplitude of the order of the Planck scale either jeopardize successful predictions of nucleosynthesis or overclose the Universe. It is shown that the moduli problem can be relaxed by making use of parametric resonance. A new non-perturbative decay channel for moduli oscillations is discussed. This channel becomes effective when the oscillating field results in a net negative mass term for the decay products. This scenario allows for the decay of the moduli much before nucleosynthesis and, the…
A detailed numerical stability analysis of the static, spherically symmetric globally regular solutions of the Einstein-Yang-Mills equations with a positive cosmological constant, Lambda, is carried out. It is found that the number of unstable modes in the even parity sector is n for solutions with n=1,2 nodes as Lambda varies. The solution with n=3 nodes exhibits a rather surprising behaviour in that the number of its unstable modes jumps from 3 to 1 as Lambda crosses (from below) a critical value. In particular the topologically 3-sphere type solution with n=3 nodes has only a single unstabl…
We study the evolution of cosmological perturbations in f(G) gravity, where the Lagrangian is the sum of a Ricci scalar R and an arbitrary function f in terms of a Gauss-Bonnet term G. We derive the equations for perturbations assuming matter to be described by a perfect fluid with a constant equation of state w. We show that density perturbations in perfect fluids exhibit negative instabilities during both the radiation and the matter domination, irrespective of the form of f(G). This growth of perturbations gets stronger on smaller scales, which is difficult to be compatible with the observe…
The close limit approximation of binary black hole is a powerful method to study gravitational-wave emission from highly non-linear geometries. In this work, we use it as a tool to model black hole spacetimes in theories of gravity with a new fundamental scalar degree of freedom. As an example, we consider Einstein-scalar-Gauss-Bonnet gravity, which admits as solution the Schwarzschild geometry as well as black holes with scalar hair. Accordingly, we find scalar perturbations growing unbounded around binary systems. This "dynamical scalarization" process is easier to trigger (i.e. occurs at lo…
Products of large-N conformal field theories coupled by multi-trace interactions in diverse dimensions are used to define quantum multi-gravity (multi-string theory) on a union of (asymptotically) AdS spaces. One-loop effects generate a small O(1/N) mass for some of the gravitons. The boundary gauge theory and the AdS/CFT correspondence are used as guiding principles to study and draw conclusions on some of the well known problems of massive gravity - classical instabilities and strong coupling effects. We find examples of stable multi-graviton theories where the usual strong coupling effects …
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.
Attractive gravity probe surface with positive cosmological constant
本文在正宇宙学常数四维时空中引入与宇宙学视界相关的新几何对象，证明面积不等式，并研究吸引性引力探针面作为吸引性引力存在性指标。
We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques. The novel feature is the inclusion of higher-derivative terms in the scalar propagator. Such terms give rise to Ostrogradski ghosts which signal an instability of the system and are therefore dangerous for the consistency of the theory. Since it is expected that such terms are generated dynamically by the renormalization group flow they provide a potential threat when constructing a theory of quantum gravity based on Asymptotic Safety. Our work then establishes the fol…
Modified Newtonian dynamics (MOND) can be obtained by modifying the entropic formulation of gravity, this is achieved by considering the quantum statistical nature of the degrees of freedom on the holographic screen. Through this frame work, we find some constraints on a cosmological extension for MOND, with no additional auxiliary fields. The connections between MOND to conformal gravity and Rindler force gravity are examined. These two alternative gravity theories are subsequently considered as possible cosmological extensions of MOND.
Recently a new extended nonlinear massive gravity model has been proposed which includes the $F(R)$ modifications to dRGT model.We follow the $F(R)$ nonlinear massive gravity and study its implications on cosmological evolutions. We derive the critical points of the cosmic system and study the corresponding kinetics by performing the phase-plane analysis.
The hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. We discuss static, spherically symmetric vacuum solutions of HMPG with the aid of its scalar-tensor representation. This scalar-tensor theory coincides with general relativity with a conformally coupled scalar field (which can be canonical or phantom), therefore the known solutions of this theory are re-interpreted in terms of HMPG. In particular, in the case of zero scalar field potential $V (ϕ)$, such that both Ri…
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated with the breaking of supersymmetry. Chapter 5 contains new unpublished material on various instabilities of the weakly curved non-supersymmetric $AdS_4$ backgrounds of M-theory.
Anisotropic exponential cosmological solutions for a space of arbitrary dimension filled with ordinary matter in the 4th and 5th orders of Lovelock gravity are obtained. Also we have supposed a generalization of such solutions on an arbitrary order. All the solutions are represented as a set of conditions on Hubble parameters.
In this paper we present an alternative cosmological extension of the three-dimensional extended Newtonian Chern-Simons gravity by switching on the torsion. The theory is obtained as a non-relativistic limit of an enhancement and $U(1)$-enlargement of the so-called teleparallel algebra and can be seen as the teleparallel analogue of the Newtonian gravity theory. The infinite-dimensional extension of our result is also explored through the Lie algebra expansion method. An infinite-dimensional torsional Galilean gravity model is presented which in the vanishing cosmological constant limit reprod…
We study the condition for the consistency of the Gödel metric with the dynamical Chern-Simons modified gravity. It turns out to be that this compatibility can be achieved only if the cosmological constant is variable in the space.
We derive dynamical equations to describe a single 3-brane containing fluid matter and a scalar field coupling to the dilaton and the gravitational field in a five dimensional bulk. First, we show that a scalar field or an arbitrary fluid on the brane cannot evolve to cancel the cosmological constant in the bulk. Then we show that the Randall-Sundrum model is unstable under small deviations from the fine-tuning between the brane tension and the bulk cosmological constant and even under homogeneous gravitational perturbations. Implications for brane world cosmologies are discussed.
We discuss the emergence of black hole shadow and photon-sphere in the context of $f(R)$ gravity. It is shown that the shadow is exponentially sensitive to linear instabilities of metric coming from some $f(R)$ solutions. Thus, the instabilities of photon circular trajectories, delimiting the black hole photon-sphere, are double exponentialized. Specifically we individuate two Lyapunov exponents, rather than only one, related to two different sources of chaos in geodesic orbits as a sort of butterfly effect. Such a result violates the black hole chaos bound proposed by Maldacena, Shenker and S…
Defining a new r-matrix compatible with the scalar product at the basis of the Chern-Simons action for a particle coupled to (2+1) Lorentzian gravity with cosmological constant, I show how deformed symmetries of $κ$-de Sitter and, in the vanishing cosmological limit, of $κ$-Poincaré kind, arise naturally as quantum-deformation of three dimensional gravity. I obtain moreover the non-commutative spacetime associated to these kinds of symmetries.
We investigate Bianchi I cosmological model in the theory of a dilatonM field coupled to gravity through a Gauss-Bonnet term. Two type ofM cosmological singularity are distinguished. The former is analogous toM the Einstein gravity singularity, the latter (which does not appear inM classical General Relativity) occurs when the main determinant of theM system of field equations vanishes. An analogy between the latterM cosmological singularity and the singularity inside a black hole withM a dilatonic hair is discussed. Initial conditions, leading to theseM two types of cosmological singularity a…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can provide a way of addressing the issue: we consider the case of two-dimensional quantum dilaton gravity non-minimally coupled to a U(1) gauge field, in the presence of an arbitrary number of massless scalar matter fields, intended also as an effective description of highly symmetrical higher-dimensional models. We are able to quantize the system non-perturbatively…
The behavior of fundamental fields in strong gravity or nontrivial environments is important for our understanding of nature. This problem has interesting applications in the context of dark matter, of dark energy physics or of quantum field theory. The dynamics of fundamental fields has been studied mainly in static or stationary backgrounds, whereas most of our Universe is dynamic. In this paper we investigate "blueshift" and parametric instabilities of scalar fields in dynamical backgrounds, which can be triggered (for instance) by oscillating stars in scalar-tensor theories of gravity. We …
A finite and unitary nonlocal formulation of quantum gravity is applied to the cosmological constant problem. The entire functions in momentum space at the graviton-standard model particle loop vertices generate an exponential suppression of the vacuum density and the cosmological constant to produce agreement with their observational bounds.
In this contribution, classes of shear-free cosmological dust models with irrotational fluid flows will be investigated in the context of scalar-tensor theories of gravity. In particular, the integrability conditions describing a consistent evolution of the linearised field equations of quasi-Newtonian universes are presented. We also derive the covariant density and velocity propagation equations of such models and analyse the corresponding solutions to these perturbation equations.
In the dimensionally reduced model of the 2+1 dimensional cosmological massive gravity, we obtain the central charges of the two types of the black hole based on the entropy function method. One is for the BTZ black hole and the other one is actually for the warped AdS$_3$ black hole.
We use the non-Gaussian fixed points (NGFPs) appearing in the renormalization group flow of gravity and gravity-matter systems to construct models of NGFP-driven inflation via a renormalization group improvement scheme. The cosmological predictions of these models depend sensitively on the characteristic properties of the NGFPs, including their position and stability coefficients, which in turn are determined by the field content of the underlying matter sector. We demonstrate that the NGFPs appearing in gravity-matter systems where the matter content is close to the one of the standard model …
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…
We investigate some aspects of anomaly cancellation realized by the subtraction of an anomaly pole, stressing on some of its properties in superspace. In a local formulation these subtractions can be described in terms of a physical scalar, an axion and related ghosts. They appear to be necessary for the unitarization of the theory in the ultraviolet, but they may generate an infrared instability of the corresponding effective action, signalled by ghost condensation. In particular the subtraction of the superanomaly multiplet by a pole in superspace is of dubious significance, due to the diffe…
It is well known that the Klein Gordon (KG) equation $\Box Φ+ m^2Φ=0$ has tachyonic unstable modes on large scales ($k^2<\vert m \vert^2$) for $m^2<m_{cr}^2=0$ in a flat Minkowski spacetime with maximum growth rate $Ω_{F}(m)= \vert m \vert$ achieved at $k=0$. We investigate these instabilities in a Reissner-Nordström-deSitter (RN-dS) background spacetime with mass $M$, charge $Q$, cosmological constant $Λ>0$ and multiple horizons. By solving the KG equation in the range between the event and cosmological horizons, using tortoise coordinates $r_*$, we identify the bound states of the emerging S…
In self-tuning brane-world models with extra dimensions, large contributions to the cosmological constant are absorbed into the curvature of extra dimensions and consistent with flat 4d geometry. In models with conventional Lagrangians fine-tuning is needed nevertheless to ensure a finite effective Planck mass. Here, we consider a class of models with non conventional Lagrangian in which known problems can be avoided. Unfortunately these models are found to suffer from tachyonic instabilities. An attempt to cure these instabilities leads to the prediction of a positive cosmological constant, w…
We address issues on the origin of gravity and the cosmological constant problem based on a recent understanding about the correspondence between noncommutative field theory and gravity. We suggest that the cosmological constant problem can be resolved in a natural way if gravity emerges from a gauge theory in noncommutative spacetime. Especially, we elucidate why the emergent gravity implies that vacuum energy does not gravitate but only fluctuations around the vacuum generate gravity. That is, a flat spacetime emerges from uniform condensation of energy, previously identified with the cosmol…
This brief contribution is devoted to phenomenological consequences of deviations from Lorentz invariance in gravity and dark matter. We will discuss main effects on cosmological observables and current constraints derived from astrophysical and cosmological data.
We demonstrate that finite time singularities of Type IV can be consistently incorporated in the Universe's cosmological evolution, either appearing in the inflationary era, or in the late-time regime. While using only one scalar field instabilities can in principle occur at the time of the phantom-divide crossing, when two fields are involved we are able to avoid such instabilities. Additionally, the two-field scalar-tensor theories prove to be able to offer a plethora of possible viable cosmological scenarios, at which various types of cosmological singularities can be realized. Amongst othe…
We investigate some cosmological models arising from a non-minimal coupling of a fermionic field to gravity in the geometrical setting of Einstein-Cartan-Sciama-Kibble gravity. The role played by the non-minimal coupling together with torsion in facing problems such as cosmological singularity, inflation and dark energy is discussed.
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…
It is expected that the Gregory-Laflamme (GL) instability in the black string in gravity is related to the Rayleigh-Plateau instability in fluid mechanics. Especially, the orders of the phase transitions associated with these instabilities depend on the number of the transverse space dimensions, and they are of first and second order below and above the critical dimension. Through the gauge-gravity correspondence, the GL instability is conjectured to be thermodynamically related to the Hagedorn instability in large-N gauge theories, and it leads to a prediction that the order of the confinemen…
The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory has a cosmological solution unifying early-time inflation with late-time acceleration.
We argue that the Einstein gravity theory can be reformulated in almost Kahler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distributions is analyzed. There are considered some conditions when the fundamental geometric and physical objects are determined/ modified by nonholonomic deformations in general relativity or by contributions from Ricci flow theory and/or quantum gravity. We prove that in such NGT, for…
Counterflow and coflow instabilities in miscible binary superfluids
研究二元超流体中反向流和共流不稳定性，推导不稳定性起始判据，揭示临界速度与相互作用强度的关系。
We consider some cosmological aspects of nonlocal modified gravity with $Λ$ term, where nonlocality is of the type $R \mathcal{F}(\Box) R$. Using ansatz of the form $\Box R = r R +s,$ we find a few a(t) nonsingular bounce cosmological solutions for all three values of spatial curvature parameter k. We also discuss this modified gravity model from F(R) theory point of view.
Bimetric theory describes gravitational interactions in the presence of an extra spin-2 field. Previous work has suggested that its cosmological solutions are generically plagued by instabilities. We show that by taking the Planck mass for the second metric, $M_f$, to be small, these instabilities can be pushed back to unobservably early times. In this limit, the theory approaches general relativity with an effective cosmological constant which is, remarkably, determined by the spin-2 interaction scale. This provides a late-time expansion history which is extremely close to $Λ$CDM, but with a …
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