We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in $\left(d+1\right)$-dimensional de Sitter space. Gauge invariance of observables with external (partially)-massless spinning fields translates into Ward-Takahashi identities on the boundary. Using the Mellin-Barnes representation for boundary correlators in momentum space, we give a systematic study of Ward-Takahashi identities for tree-level 3- and 4-point processes involving a single external (partially-)massless field of arbitrary integer spin-$J$. 3-point Ward-Takahashi identities constrain the mass of the scalar fields to which a (partially-)massless spin-$J$ field can couple. 4-point Ward-Takahashi identities then constrain the corresponding cubic couplings. For massless spinning fields, we show that Weinberg's flat space results carry over to $\left(d+1\right)$-dimensional de Sitter space: For spins $J=1,2$ gauge-invariance implies charge-conservation and the equivalence principle while, assuming locality, higher-spins $J>2$ cannot couple consistently to scalar matter. This result also applies to anti-de Sitter space. For partially-massless fields, restricting for simplicity to those of depth-2, we show that there is no consistent coupling to scalar matter in local theories. Along the way we give a detailed account of how contact amplitudes with and without derivatives are represented in the Mellin-Barnes representation. Various new explicit expressions for 3- and 4-point functions involving (partially-)massless fields and conformally coupled scalars in dS$_4$ are given.
Casimir effect for massless minimally coupled scalar field is studied. An explicit answer for de Sitter spacetime is obtained and analized. Cosmological implications of the result are discussed.
We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrödinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with mu…
Over the last ten years interest in the physics of de Sitter spacetime has been growing very fast. Besides the supposed existence of a "de sitterian period" in inflation theories, the observational evidence of an acceleration of the universe expansion (interpreted as a positive cosmological constant or a "dark energy" or some form of "quintessence") has triggered a lot of attention in the physics community. A specific de sitterian field called "massless minimally coupled field" (mmc) plays a fundamental role in inflation models and in the construction of the de sitterian gravitational field. A…
We study the response of a classical massless minimally coupled scalar to a static point scalar charge on de Sitter. By considering explicit solutions of the problem we conclude that -- even though the dynamics formally admits dilatation (scaling) symmetry -- the physical scalar field profile necessarily breaks the symmetry. This is an instance of symmetry breaking in classical physics due to large infrared effects. The gravitational backreaction, on the other hand, does respect dilatation symmetry, making this an example of symmetry non-inheritance phenomenon.
The issue of de Sitter invariance for a massless minimally coupled scalar field is revisited. Formally, it is possible to construct a de Sitter invariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observer's space-time path grows linearly with the observer's…
Perturbative gravity in global de Sitter space is subject to so-called linearization stability constraints: If they are to couple consistently to the gravitational field, quantum states must be invariant under the de Sitter isometries. While standard Fock spaces contain no de Sitter-invariant states apart from (possibly) the vacuum, a full Hilbert space of de Sitter-invariant quantum states can be constructed via group averaging techiniques. We re-examine the simple toy model of de Sitter group averaging given by the free 1+1 scalar field, expanding on an earlier analysis by Higuchi. Our purpo…
We examine the behavior of correlation functions for a massless scalar field in de Sitter space with a quartic interaction. We find that two-loop corrections are relevant, and that the resummation of these corrections generates a complicated structure whereby high momentum modes stay massless while low momentum modes develop a dynamical mass.
We use a simplified formalism to re-compute the single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on de Sitter background which was originally made by Boran, Kahya and Park [1-3]. Our result resolves the problem with the flat space correspondence limit that was pointed out by Fröb [4]. We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.
We show explicitly that all partially and strictly massless fields with spins s<=3 in (A)dS have null propagation. Assuming that this property holds also for s>3, we derive the mass-cosmological constant tunings required to yield all higher spin partially massless theories. As s increases, the unitarily allowed region for massive spins is squeezed around Λ=0, so that an infinite tower of massive particles forces vanishing Λ. We also speculate on the relevance of this result to string theory and supergravity in (A)dS backgrounds.
We analyze infrared divergences arising in calculations involving light and massless fields in de Sitter space. We show that these arise from an incorrect treatment of the constant mode of the field, and show that a correct quantization leads to a well-defined and calculable perturbation expansion. We illustrate this by computing the first nontrivial loop correction in a theory of a massless scalar field with a quartic interaction.
The quantum field theory is expanding in de Sitter space-time. The ambient space formalism let us to develop the quantum field theory in a careful mathematical framework. Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found. In this paper, the equations of the conjugate spinor for massless spin-$\frac{3}{2}$ gravitational field is obtained by Euler-Lagrange equation. Finally, these equations can be written in terms of the operator of the Casimir group de Sitter.
We consider the perturbative treatment of the minimally coupled, massless, self-interacting scalar field in Euclidean de Sitter space. Generalizing work of Rajaraman, we obtain the dynamical mass m^2 \propto sqrt{lambda} H^2 of the scalar for non-vanishing Lagrangian masses and the first perturbative quantum correction in the massless case. We develop the rules of a systematic perturbative expansion, which treats the zero-mode non-perturbatively, and goes in powers of sqrt{lambda}. The infrared divergences are self-regulated by the zero-mode dynamics. Thus, in Euclidean de Sitter space the int…
Motivated by the endeavors of Li Xiang and You-Gen Shen on naked singularities, we investigate the validity of the cosmic censorship conjecture in the context of generalized uncertainty principle. In particular, upon considering both linear and quadratic terms of momentum in the uncertainty principle, we first compute the entropy of a massless charged black hole in de Sitter spacetime at a given modified temperature. Then, we compute the corresponding modified cosmological radius and express the black hole electric charge in terms of this modified cosmological radius and, thus, in terms of the…
There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under an internal Yang-Mills like extension of the partially massless symmetry. We give two arguments that such a partially massless Yang-Mills theory does not exist. The first is that there is no Yang-Mills like non-abelian deformation of the partially massless symmetry, and the second is that cubic vertices with the appropriate structure constants …
Since horizon formation in global anti-de Sitter spacetime is dual to thermalization of a conformal field theory on a compact space, whether generic initial data is stable or unstable against gravitational collapse is of great interest. We argue that all the known stable initial data for massless scalars are dominated by single scalar eigenmodes, specifically providing strong numerical evidence consistent with the interpretation that initial data with equal energies in two modes collapse on time scales of order the inverse square of the amplitude. We further scan the parameter space for massiv…
We prove that, under the standard conformal scaling, a massless field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. This result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum.
Free massless fermionic fields of arbitrary spins $s>0$ corresponding to totally (anti)symmetric tensor-spinor representations of the $SO(d-1)$ compact subgroup and in $d$-dimensional anti-de Sitter space are investigated. We propose the free equations of motion, subsidiary conditions and corresponding gauge transformations for such fields. The equations obtained are used to derive the lowest energy values for the above-mentioned representations. A new representation for equations of motion and gauge transformations in terms of generators of anti-de Sitter group $SO(d-1,2)$ is found. It is dem…
We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Our models mimic Dirac-Born-Infeld theory but it is unclear whether they are Lagrangian.
We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\sqrtλ$ and in $1/N$. The results reduce to those known in the leading infrared approximati…
We have investigated the emerging conformal field theory behavior on the interior interface of the region near the cosmological event horizon on an example of massless Dirac fermions. Indeed, we have constructed and verified the emerging de Sitter/CFT correspondence for the near cosmological event horizon region. It is in this near horizon region where the infinitely thin shell of matter with the stiffest equation of state (Zeldovich's matter) is placed in the model for a thermodynamically stable `would be black hole' which is sometimes called a gravastar or a dark energy star. We put forward …
In d=4 de Sitter space, novel conformally invariant photon-like theories consistently couple to charged matter. We show that these higher spin, maximal depth, partially massless systems enjoy a Maxwellian, "electric-magnetic" duality.
Arbitrary spin free massless bosonic fields propagating in even $d$ - dimensional anti-de Sitter spacetime are investigated. Free wave equations of motion, subsidiary conditions and the corresponding gauge transformations for such fields are proposed. The lowest eigenvalues of the energy operator for the massless fields and the gauge parameter fields are derived. The results are formulated in $SO(d-1,2)$ covariant form as well as in terms of intrinsic coordinates. An inter-relation of two definitions of masslessness based on gauge invariance and conformal invariance is discussed.
We find and classify the ${\cal N}=1$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying the non-unitary representations of the $d=3$ superconformal algebra of the boundary. The simplest super-multiplet which contains a partially massless spin-2 particle also contains a massless photon, a massless spin-$3/2$ particle and a massive spin-$3/2$ particle. The gauge parameters form a Wess-Zumino super-multiplet which contains the gauge parameters of the photon, the partially massless graviton, and the massless spin-$3/2$ particle. We find the AdS$_4$ action a…
We construct higher spin quasinormal modes algebraically in $D$-dimensional de Sitter spacetime using the ambient space formalism. The quasinormal modes fall into two nonunitary lowest-weight representations of $\mathfrak{so}(1, D)$. From a local QFT point of view, the lowest-weight quasinormal modes of massless higher spin fields are produced by gauge-invariant boundary conserved currents and boundary higher-spin Weyl tensors inserted at the southern pole of the past boundary. We also show that the quasinormal spectrum of a massless/massive spin-$s$ field is precisely encoded in the Harish-Ch…
We investigate the possibility of extending the "partially massless" symmetry of a spin-2 field in de Sitter to nonlinear order. To do so, we impose a closure condition on the symmetry transformations. This requirement imposes strong constraints on the form of the nonlinear symmetry while making only minimal assumptions about the form of the nonlinear partially massless action. We find a unique nonlinear extension of the free partially massless symmetry. However, we show that no consistent Lagrangian that contains at most two derivatives of the fields can realize this symmetry.
Higgs mechanism to massive higher-spin gauge fields is an outstanding open problem. We investigate this issue in the context of Kaluza-Klein compactification. Starting from a free massless higher-spin field in $(d+2)$-dimensional anti-de Sitter space and compactifying over a finite angular wedge, we obtain an infinite tower of heavy, light and massless higher-spin fields in $(d+1)$-dimensional anti-de Sitter space. All massive higher-spin fields are described gauge invariantly in terms of Stüeckelberg fields. The spectrum depends on the boundary conditions imposed at both ends of the wedges. W…
Partially massless theory in three dimensions is revisited and its relationship with the self-dual massive gravity is considered. The only mode of the partially massless theory is shown explicitly through an action for a scalar field on (A)dS background. This fact can be generalized to higher dimensions. This degree of freedom is altered when a triadic Chern-Simons is introduced, giving rise to the self-dual massive gravity on (A)dS background. We present another physical system with partially massless symmetry and its connection with topologically massive gravity is discussed.
We consider the massless scalar field on the four-dimensional sphere $S^4$. Its classical action $S={1\over 2}\int_{S^4} dV (\nabla ϕ)^2$ is degenerate under the global invariance $ϕ\to ϕ+ \hbox{constant}$. We then quantize the massless scalar field as a gauge theory by constructing a BRST-invariant quantum action. The corresponding gauge-breaking term is a non-local one of the form $S^{\rm GB}={1\over {2αV}}\bigl(\int_{S^4} dV ϕ\bigr)^2$ where $α$ is a gauge parameter and $V$ is the volume of $S^4$. It allows us to correctly treat the zero mode problem. The quantum theory is invariant under S…
Free massless higher-superspin superfields on the N=1, D=4 anti-de Sitter superspace are introduced. The linearized gauge transformations are postulated. Two families of dually equivalent gauge-invariant action functionals are constructed for massless half-integer-superspin s+1/2 (s >= 2) and integer-superspin s (s >= 1) superfields. For s=1, one of the formulations for half-integer superspin multiplets reduces to linearized minimal N=1 supergravity with a cosmological term, while the other is the lifting to the anti-de Sitter superspace of linearized non-minimal n=-1 supergravity.
We employ gauge-gravity duality to study the backreaction effect of 4-dimensional large-$N$ quantum field theories on constant-curvature backgrounds, and in particular de Sitter space-time. The field theories considered are holographic QFTs, dual to RG flows between UV and IR CFTs. We compute the holographic QFT contribution to the gravitational effective action for 4d Einstein manifold backgrounds. We find that for a given value of the cosmological constant $λ$, there generically exist two backreacted constant-curvature solutions, as long as $λ< λ_{\textrm{max}} \sim M_p^2 / N^2$, otherwise n…
We present a new hybrid Cauchy-characteristic evolution method that is particularly suited for the study of gravitational collapse in spherically-symmetric asymptotically (global) Anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows us to track the scalar field through the different bounces off the AdS boundary while the characteristic method can bring us very close to the point of formation of an apparent horizon. Here, we describe all the details of the method, including the transition between the two evolution schemes and the details of the numerical implementation for the case of m…
In cosmological backgrounds, there can be 'partially massless' higher spin fields which have fewer degrees of freedom than their massive partners. The equations for the partially massless spin-2 fields are usually taken to be the linearized Einstein equations augmented with a 'tuned' Pauli-Fierz mass. Here, we add more powers of curvatures and show that for the string-generated Einstein-Gauss-Bonnet model, partially massless spin-2 fields have real mass in AdS, in contrast to the Einstein level result. We discuss the implication of this for the AdS/CFT applications and briefly study the C^4-co…
In this paper time machines are constructed from anti-de Sitter space. One is constructed by identifying points related via boost transformations in the covering space of anti-de Sitter space and it is shown that this Misner-like anti-de Sitter space is just the Lorentzian section of the complex space constructed by Li, Xu, and Liu in 1993. The others are constructed by gluing an anti-de Sitter space to a de Sitter space, which could describe an anti-de Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua for a massless conformally coupled scalar field are found for …
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. The solution has a curva…
We present analytic solutions to the Teukolsky equation for massless perturbations of any spin in the 4-dimensional de Sitter background. The angular part of the equation fixes the separation constant to a discrete set and its solution is given by hypergeometric polynomials. For the radial part, we derive analytic power series solution which is regular at the poles and determine a transcendental function whose zeros give the characteristic values of the wave frequency. We study the existence of explicit polynomial solutions to the radial equation and obtain two classes of singular closed-form …
We propose that maximal depth, partially massless, higher spin excitations can mediate charged matter interactions in a de Sitter universe. The proposal is motivated by similarities between these theories and their traditional Maxwell counterpart: their propagation is lightlike and corresponds to the same Laplacian eigenmodes as the de Sitter photon; they are conformal in four dimensions; their gauge invariance has a single scalar parameter and actions can be expressed as squares of single derivative curvature tensors. We examine this proposal in detail for its simplest spin 2 example. We find…
We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results se…
We analyze the first-order formulation of the ghost-free bigravity model in three-dimensions known as zwei-dreibein gravity. For a special choice of parameters, it was argued to have an additional gauge symmetry and give rise to a partially massless theory. We provide a thorough canonical analysis and identify that whether the theory becomes partially massless depends on the form of the stability condition of the secondary constraint responsible for the absence of the ghost. Generically, it is found to be an equation for a Lagrange multiplier implying that partially massless zwei-dreibein grav…
We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that sp…
A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a way that the resulting, generalized action reduces to the original action in a limit that de Sitter radius goes to infinity. We analyze the Hamiltonian formulation in accordance with Dirac's prescription for constrained Hamiltonian systems and carry out its subsequent canonical quantization in coordinate representation following DeWitt. As the result, we deriv…
We describe the dimensional reduction of massive and partially massless spin-2 fields on general Einstein direct product manifolds. As with massless fields, the higher-dimensional gauge symmetry of the partially massless field displays itself upon dimensional reduction as a tower of Stückelberg symmetries for the massive modes of the tower. Unlike the massless case, the zero mode of the gauge symmetry does not display itself as a lower-dimensional non-Stuckelberg gauge symmetry enforcing partial masslessness on the zero mode. Partial masslessness is destroyed by the dimensional reduction and t…
We derive the decoupling limit of Massive Gravity on de Sitter in an arbitrary number of space-time dimensions d. By embedding d-dimensional de Sitter into d+1-dimensional Minkowski, we extract the physical helicity-1 and helicity-0 polarizations of the graviton. The resulting decoupling theory is similar to that obtained around Minkowski. We take great care at exploring the partially massless limit and define the unique fully non-linear candidate theory that is free of the helicity-0 mode in the decoupling limit, and which therefore propagates only four degrees of freedom in four dimensions. …
We investigate the evolution of a scalar field propagating in Reissner--Nordström Anti--de Sitter spacetime. Due to the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object--picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is faster for larger charges. However, after the black hole charge reaches a critical value, we get the opposite behavior for the imaginary frequencies of the quasinormal modes. Some possible explanations …
Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes -- particularly around black holes -- we show how, for certain classes of geometries, one might obtain its retarded or advanced minimally coupled massless scalar Green's function by using the corresponding Green's functions in the higher dimensional Minkowski spacetime where it is embedded. Analogous statements hold for certain classes of curved Riemannian spaces, with positive definite metrics, which may be embedded in higher dimensional Euclidean spaces. The general formula is applied…
Massive higher spin fields on de Sitter space exhibit enhanced gauge symmetries at special values of the mass. These fields are known as "partially massless." We study the structure of the charges and Gauss laws which characterize sources for the partially massless spin-2. Despite having a simple scalar gauge symmetry, there is a rich structure of gauge charges. The charges come in electric and magnetic varieties, each taking values in the fundamental representation of the de Sitter group. We find two invariant electric-like charges and two invariant magnetic-like charges and we find the point…
Starting with a manifestly conformal ($O(d,2)$ invariant) mechanics model in $d$ space and 2 time dimensions, we derive the action for a massless spinning particle in $d$-dimensional anti-de Sitter space. The action obtained possesses both gauge $N$-extended worldline supersymmetry and local $O(N)$ invarince. Thus we improve the old statement by Howe et al. that the spinning particle model with extended worldline supersymmetry admits only flat space-time background for $N > 2$ (spin greater one). The original $(d+2)$-dimensional model is characterized by rather unusual property that the corres…
We consider the quantization of the massless minimally coupled scalar field in de Sitter spacetime. The no-boundary Euclidean prescription naturally picks out the de Sitter invariant vacuum state of Kirsten and Garriga. We extend Strominger's dS/CFT correspondence to this case which allows us to interpret the massless field in terms of a Euclidean CFT. The extension is non-trivial and requires careful treatment of the zero mode. Since the graviton is massless, this work may also be considered a step towards a theory of gravity in de Sitter space.
Quasinormal modes and greybody factors of magnetically charged de Sitter black holes probed by massless external fields in Einstein Euler Heisenberg gravity
Xihang University（西航大学）；National Joint Engineering Research Center for Special Pump System Technology, Xihang University（西航大学特种泵系统技术国家联合工程研究中心）；Yangzhou University（扬州大学）；Jiangxi Normal University（江西师范大学）
It was recently shown that Strong Cosmic Censorship might be violated for near-extremally-charged black holes in 4-dimensional de Sitter space under scalar perturbations. Here, we extend the study of neutral massless scalar perturbations in higher dimensions and discuss the dimensional influence on the validity of Strong Cosmic Censorship hypothesis. By giving an elaborate description of neutral massless scalar perturbations of Reissner-Nordström-de Sitter black holes in $d=4,5$ and $6$ dimensions we conclude that Strong Cosmic Censorship is violated near extremality.
We study the constraint structure of Fierz -Pauli action in both flat and curved space in the framework of Hamiltonian formalism. We observe an abrupt change in the constraint algebra and the characteristics of the constraints when the mass term is turned off. As is well-known, for de Sitter background with a special tuning of the mass, we will have a gauge symmetry and one degree of freedom less. We will show how this abrupt change in the behavior of the system is reflected on the properties of the constraint algebra. We also obtain the generating functional of gauge transformations both for …
We show that consistent nonlinear Partially Massless models cannot be obtained starting from "f-g" massive gravity, with "f" the embedding de Sitter space. The obstruction, which is also the source of f-g acausality, is the very same fifth constraint that removes the notorious sixth ghost excitation. Here, however, it blocks extension of the mass to cosmological background tuned gauge invariance that took away the helicity zero mode at linear level. Separately, our methods allow us to almost complete the class of acausal f-g models.
