We study linearized massive gravity on the de Sitter background. With a small-enough graviton mass this may have had relevance to inflation, or the present-day cosmic acceleration. Higuchi has shown that this theory has a ghost as long as the dS curvature exceeds the graviton mass, 2H^2 > m^2; this would entail rapid instabilities. In this work we extend the model and observe that the helicity-0 mode which is a ghost, can be turned into a positive energy state via kinetic mixing with the conformal mode. The latter gets restricted here by the requirement that the Bianchi identities be satisfied. This eliminates the ghost from the linearized theory. However, the spectrum still contains scalar tachyonic instabilities with the time scale ~1/H. This would have been problematic for the early univesre, however, may be acceptable for the present-day accelerated expansion as the tachyon instability would take the age of the universe to develop.
We compute the Pauli-Jordan, Hadamard and Feynman propagators for the massive metrical perturbations on de Sitter space. They are expressed both in terms of mode sums and in invariant forms.
Two different systems of the generalized coherent states for the de Sitter group are constructed. These systems have the physical sense of particles and antiparticles over de Sitter space and obeys the Klein-Gordon equation. Using these systems the de Sitter-invariant propagators for massive spin~0 and~1/2 fields over de Sitter space are constructed.
We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter spaces. We find that there are supersymmetric de Sitter solutions in supergravity theories including maximally supersymmetric ones in 10- and 11-dimensional supergravities. Moreover, warped flux Minkowski backgrounds can admit Killing spinors which are not Killing on the Minkowski subspace and therefore cannot be put in a factorized form.
In this paper, by taking de Sitter space-time as a thermodynamic system, we study the equivalent thermodynamic quantities of de Sitter black hole in massive gravity, and furthermore obtain the equivalent thermodynamic quantities of the space-time. Our results show that the entropy of this type of space-time takes the same form as that in Reissner-Nordstrom-de Sitter space-time, which lays a solid foundation for deeply understanding the universal thermodynamic characteristics of de Sitter space-time in the future. Moreover, our analysis indicates that the equivalent thermodynamic quantities and…
We show that a massive scalar field on a 2-dimensional Anti-De Sitter space can be mapped by means of a time-dependent canonical transformation into a massless free field theory when the mass square of the field is equal to minus the curvature of the background metric. We also provide the (hidden) conformal symmetry of the massive scalar field.
We show that there exists a supersymmetric de Sitter background for the D=6, N=2, F(4) supergravity preserving the compact R-symmetry and gauging with respect to the conventional Anti de Sitter version of the theory. We construct the gauged matter coupled F(4) de Sitter supergravity explicitly and show that it contains ghosts in the vector sector.
We reformulate free equations of motion for massive spin 0 and spin 1/2 matter fields in 2+1 dimensional anti-de Sitter space in the form of some covariant constantness conditions. The infinite-dimensional representation of the anti-de Sitter algebra underlying this formulation is shown to admit a natural realization in terms of the algebra of deformed oscillators with a deformation parameter related to the parameter of mass.
We use the superspace formulation of (massive) IIA supergravity to obtain the explicit form of the dilatino terms, and we find that the quartic-dilatino term is positive. The theory admits a ten-dimensional de Sitter solution, obtained by assuming a nonvanishing quartic-dilatino condensate which generates a positive cosmological constant. Moreover, in the presence of dilatino condensates, the theory admits formal four-dimensional de Sitter solutions of the form $dS_4\times M_6$, where $M_6$ is a six-dimensional Kähler-Einstein manifold of positive scalar curvature.
We review some facts about AdS2xS2 branes in AdS3xS3 with a Neveu-Schwarz background, and consider the case of Ramond-Ramond backgrounds. We compute the spectrum of quadratic fluctuations in the low-energy approximation and discuss the open-string geometry.
We study the problem of obtaining de Sitter and inflationary vacua from dimensional reduction of double field theory (DFT) on nongeometric string backgrounds. In this context, we consider a new class of effective potentials that admit Minkowski and de Sitter minima. We then construct a simple model of chaotic inflation arising from T-fold backgrounds and we discuss the possibility of trans-Planckian field range from nongeometric monodromies as well as the conditions required to get slow roll.
We prove that the mathematical framework for the de Sitter top system is the de Sitter fiber bundle. In this context, the concept of soldering associated with a fiber bundle plays a central role. We comment on the possibility that our formalism may be of particular interest in different contexts including MacDowell-Mansouri theory, two time physics and oriented matroid theory.
We study particle decay in de Sitter space-time as given by first order perturbation theory in an interacting quantum field theory. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur there. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with lower mass are even stranger: The masses of their decay products must obey quantification rules, and their lifetime is zero.
The theory of a massive spin-2 state on the de Sitter space -- with the mass squared equal to one sixth of the curvature -- is special for two reasons: (i) it exhibits an enhanced local symmetry; (ii) it emerges as a part of the model that gives rise to the self-accelerated Universe. The known problems of this theory are: either it cannot be coupled to a non-conformal conserved stress-tensor because of the enhanced symmetry, or it propagates a ghost-like state when the symmetry is constrained by the Lagrange multiplier method. Here we propose a solution to these problems in the linearized appr…
We investigated the evolution of a scalar field propagating in small Schwarzschild Anti-de Sitter black holes. The imaginary part of the quasinormal frequency decreases with the horizon size and the real part of the quasinormal frequency keeps nearly as a constant. The object-picture clarified the question on the quasinormal modes for small Anti-de Sitter black holes. Dependence of quasinormal modes on spacetime dimensions and the multipole index for small Anti-de Sitter black holes have also been illustrated.
Three-dimensional warped anti-de Sitter space in topologically massive gravity with a negative cosmological constant has been proposed to be holographically dual to a two-dimensional conformal field theory. We extend this proposal to both positive and vanishing values of the cosmological constant where stretched warped anti-de Sitter space is found to be a solution. For positive cosmological constant, another class of warped solutions is obtained by a spacelike (timelike) line fibration over Lorentzian (Euclidean) two-dimensional de Sitter space. These solutions exhibit a cosmological horizon …
In this paper we present a covariant quantization of the ``massive'' spin-2 field on de Sitter (dS) space. By ``massive'' we mean a field which carries a specific principal series representation of the dS group. The work is in the direct continuation of previous ones concerning the scalar, the spinor and the vector cases. The quantization procedure, independent of the choice of the coordinate system, is based on the Wightman-Garding axiomatic and on analyticity requirements for the two-point function in the complexified pseudo-Riemanian manifold. Such a construction is necessary in view of pre…
We analyze the evolution of a homogenous and pressureless ball of dust (or "star") in ghost-free massive gravity on de Sitter spacetime. We find that gravitational collapse does not take place for all parameters of the massive gravity theory. For parameters where it does occur, we find the expression for the location of the apparent horizon where it crosses the surface of the star, indicating the location of the apparent horizon of the vacuum solution at that moment. We determine the Ricci curvature at the boundary of the star and extract the finite correction to the curvature of the apparent …
With the help of the general theory of the Heun equation, this paper completes previous work by the authors and other groups on the explicit representation of the massive gravitino propagator in four-dimensional de Sitter space. As a result of our original contribution, all weight functions which multiply the geometric invariants in the gravitino propagator are expressed through Heun functions, and the resulting plots are displayed and discussed after resorting to a suitable truncation in the series expansion of the Heun function. It turns out that there exist two ranges of values of the indep…
Interacting massive fields with m > d H/2 in d+1 dimensional de Sitter space are fundamentally unstable. Scalar fields in this mass range can decay to themselves. This process (which is kinematically forbidden in Minkowski space) can lead to an important change to the propagator and the physics of these fields. We compute this decay rate by doing a 1-loop computation for a massive scalar field with a cubic interaction. We resum the 1-loop result by consistently solving the Schwinger-Dyson equations. We also perform an explicit resummation of all chain graphs in the case of the retarded propaga…
It is shown that a static $(1+3)$ anti-de Sitter metric defines, in a natural way, a relativistic harmonic oscillator in Minkowski space. The quantum theory can be solved exactly and leads to wave functions having a significantly different behaviour with respect to the non-relativistic ones. The energy spectrum coincides, up to the ground state energy, with that of the non-relativistic oscillator.
To describe a massive particle with fixed, but arbitrary, spin on $d=4$ anti-de Sitter space $M^4$, we propose the point-particle model with configuration space ${\cal M}^6 = M^{4}\times S^{2}$, where the sphere $S^2$ corresponds to the spin degrees of freedom. The model possesses two gauge symmetries expressing strong conservation of the phase-space counterparts of the second- and fourth-order Casimir operators for $so(3,2)$. We prove that the requirement of energy to have a global positive minimum $E_o$ over the configuration space is equivalent to the relation $E_o > s$, $s$ being the parti…
Besides black holes, the phase space of three-dimensional massive gravity about Warped-Anti de Sitter (WAdS) space contains solutions that decay exponentially in time. They describe evanescent graviton configurations that, while governed by a wave equation with non-vanishing effective mass, do not carry net gravitational energy. Explicit examples of such solutions have been found in the case of Topologically Massive Gravity; here, we generalize them to a much more general ghost-free massive deformation, with the difference being that the decay rate gets corrected due to the presence of higher-…
We continue a previous study about the infrared loop effects in the $D$-dimensional de Sitter space for a real scalar $ϕ^4$ theory from the complementary series whose bare mass belongs to the interval $\frac{\sqrt{3}}{4}\, \left(D-1\right) < m \leq \frac{D-1}{2}$, in units of the Hubble scale. The lower bound comes from the appearance of discrete states in the mass spectrum of the theory when that bound is violated, causing large IR loop effects in the vertices. We derive an equation which allows to perform a self--consistent resummation of the leading IR contributions from all loops to the tw…
We classify all warped product de-Sitter backgrounds in heterotic supergravity, up to two loops. We find that warped $dS_n$ backgrounds, with $n\ge 3$, are $\mathbb{R}^{1,n}\times M_{9-n}$, where $M_{9-n}$ is a $(9-n)$-dimensional Riemannian manifold. Moreover, we establish that warped $dS_2$ backgrounds are $AdS_3\times M_7$, where $M_7$ is a 7-dimensional Riemannian manifold.
Instantons and their quantisation in pure Yang-Mills theory formulated in the background of de Sitter spacetime represented by spatially-closed ($k = 1$) Friedmann-Robertson-Walker metric are discussed. As for the classical treatment of the instanton physics, first, explicit instanton solutions are found and next, quantities like Pontryagin index and the semiclassical approximation to the inter-vacua tunnelling amplitude are evaluated. The Atiyah-Patodi-Singer index theorem is checked as well by constructing explicitly the normalizable fermion zero modes in this de Sitter spacetime instanton b…
We study the possible types of the nucleation of vacuum bubbles. We classify vacuum bubbles in de Sitter background and present some numerical solutions. The thin-wall approximation is employed to obtain the nucleation rate and the radius of vacuum bubbles. With careful analysis we confirm that Parke's formula is also applicable to the large true vacuum bubbles. The nucleation of the false vacuum bubble in de Sitter background is also evaluated. The tunneling process in the potential with degenerate vacua is analyzed as the limiting cases of the large true vacuum bubble and false vacuum bubble…
The Casimir stress on a spherical shell in de Sitter signature changing background for massless scalar field satisfying Dirichlet boundary conditions on the shell is calculated. The Casimir stress is calculated for inside and outside of the shell with different backgrounds corresponding to different metric signatures and cosmological constants. An important contribution appears due to signature change which leads to a transient rapid expansion of the bubbles in this background.
A general form of quasi-de Sitter(dS) modes in a dynamical background is used to study the creation of particle during the inflation. Actually, by considering the general form of inflaton field equation as a function of the Hankel function index and by using the Planck 2015 constraint on spectral index, we obtain the possible new constraints for the values of coupling constant in the era with quasi-dS space-time. Then, we explicitly calculate the general form of expectation value of the created particles in terms of the Hankel function index and the conformal time. As an important result, we s…
The Romans type IIA theory is the only known example of 10-dimensional maximal supergravity where (tensor) fields are explicitly massive. We provide an example of a non-relativistic anti-de Sitter $NRadS_4\times S^6$ background as a solution in massive type IIA. A compactification of which on $S^6$ gives immediately the prototype NRadS background in D=4 which is proposed to be dual to `cold atoms' or unitary fermions on a wire.
We discuss peculiarities of quantum fields in de Sitter space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Non-conformal quantum field theories in de Sitter space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-de-Sitter space: in de Sitter space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance…
We propose a new form of dimensional reduction that constrains dilatation instead of a component of momentum. It corresponds to replacing toroidal compactification in a Cartesian coordinate with that in the logarithm of the radius. Massive theories in de Sitter or anti de Sitter space are thus produced from massless (scale invariant) theories in one higher space or time dimension. As an example, we derive free massive actions for arbitrary representations of the (anti) de Sitter group in arbitrary dimensions. (Previous general results were restricted to symmetric tensors.) We also discuss gene…
It is well known that de Sitter(dS) black holes generally have a black hole horizon and a cosmological horizon, both of which have Hawking radiation. But the radiation temperature of the two horizons is generally different, so dS black holes do not meet the requirements of thermal equilibrium stability, which brings certain difficulties to the study of the thermodynamic characteristics of black holes. In this paper, dS black hole is regarded as a thermodynamic system, and the effective thermodynamic quantities of the system are obtained. The influence of various state parameters on the effecti…
We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
Closed forms are derived for the effective actions for free, massive spinless fields in anti-de Sitter spacetimes in arbitrary dimensions. The results have simple expressions in terms of elementary functions (for odd dimensions) or multiple Gamma functions (for even dimensions). We use these to argue against the quantum validity of a recently-proposed duality relating such theories with differing masses and cosmological constants.
By considering Hadamard vacuum states, we first construct the two-point functions associated with Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes. Then, from the general formalism developed in [A. Belokogne and A. Folacci, Phys. Rev. D \textbf{93}, 044063 (2016)], we obtain an exact analytical expression for the vacuum expectation value of the renormalized stress-energy tensor of the massive vector field propagating in these maximally symmetric spacetimes.
We study New Massive Gravity on de Sitter background and discuss several interrelated properties: The appearance of an enhanced symmetry point at linearized level where the theory becomes partially massless; its absence at full nonlinear level, and its relation with the existence of static black hole solutions and their hair parameter.
We obtain a general class of time-dependent, asymptotically de Sitter backgrounds which solve the first order bosonic equations that extremize the action for supergravity with gauged non-compact $R$-symmetry. These backgrounds correspond only to neutral fields with the correct sign of kinetic energy. Within N=2 five-dimensional supergravity with vector-superfields we provide examples of multi-centered charged black holes in asymptotic de Sitter space, whose spatial part is given by a time-dependent hyper-Kähler space. Reducing these backgrounds to four dimensions yields asymptotically de Sitte…
In the thesis, results presented in various papers involving the author are reviewed. First, general results about consistent deformations at first order (i.e. cubic) using the antifield formalism in Minkowski spacetime are gathered. Secondly, a correspondance between the consistent nonabelian cubic vertices in (Anti)de Sitter and those in Minkowski spacetime is establish. The Minkowski nonabelian cubic solutions for the triplets of spin 2-2-3, 3-3-3 (in particular the parity-breaking ones), 1-s-s and 2-s-s are then studied, the last of which providing the uniqueness of the 2-s-s Fradkin-Vasil…
We study the string propagation in the 2+1 black hole anti de Sitter background (2+1 BH-ADS). We find the first and second order fluctuations around the string center of mass and obtain the expression for the string mass. The string motion is stable, all fluctuations oscillate with real frequencies and are bounded, even at $r=0.$ We compare with the string motion in the ordinary black hole anti de Sitter spacetime, and in the black string background, where string instabilities develop and the fluctuations blow up at $r=0.$ We find the exact general solution for the circular string motion in al…
We find the propagator and calculate the tree level scattering amplitude between two covariantly conserved sources in an Anti-de Sitter background for the most general D-dimensional quadratic, four-derivative, gravity with a Pauli-Fierz mass. We also calculate the Newtonian potential for various limits of the theory in flat space. We show how the recently introduced three dimensional New Massive Gravity is uniquely singled out among higher derivative models as a (tree level) unitary model and that its Newtonian limit is equivalent to that of the usual massive gravity in flat space.
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…
In this paper we complete our construction of frame-like gauge invariant description for massive mixed symmetry tensor fields corresponding to arbitrary Young tableau with two rows started in [1]. We consider general massive theory in (A)dS spaces with arbitrary cosmological constant as well as all special limits which exist both in de Sitter and in anti-de Sitter spaces.
The Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black hole metrics appear as exact solutions in the recently formulated massive gravity of de Rham, Gabadadze and Tolley (dRGT), where the mass term sets the curvature scale. They occur within a two-parameter family of dGRT mass terms. They show no trace of a cloud of scalar graviton modes, and in the limit of vanishing graviton mass they go smoothly to the Schwarzschild and Reissner-Nordström metrics.
Stable non-supersymmetric Anti-de Sitter (AdS) vacua of string theory are widely believed not to exist. In this letter, we analytically compute the full bosonic Kaluza-Klein spectrum around the ${\rm G_2}$-invariant non-supersymmetric $\textrm{AdS}_4$ solution of massive IIA supergravity, and show that it is perturbatively stable. We also provide evidence that six other non-supersymmetric $\textrm{AdS}_4$ solutions of massive IIA supergravity are perturbatively stable. Since previous studies have indicated that these AdS vacua may also be non-perturbatively stable, our findings pose a challeng…
Split Representations and Bubble Resummation for Massive de Sitter Correlators
Max-Planck-Institut für Physik, Werner-Heisenberg-Institut（马克斯·普朗克物理研究所，维尔纳·海森堡研究所）；Max Planck-IAS-NTU Center for Particle Physics, Cosmology and Geometry（马克斯·普朗克粒子物理、宇宙学与几何中心）；Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München（阿诺德·索末菲理论物理中心，慕尼黑大学）
We study strongly coupled mass-deformed-CFT on a fixed de Sitter spacetime in three dimensions via holography. We elucidate the global causal structure of the four-dimensional spacetime dual to the de Sitter invariant vacuum state. The conformal boundaries of de Sitter appear as spacelike defects sourced by the mass deformation, which extend into the bulk as curvature singularities in AdS. We compute all one- and two-point functions of the deformed-CFT stress tensor and a scalar operator order-by-order in the mass deformation for a simple holographic model. These correlation functions admit a …
We derive covariant expressions for the one loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. …
Inspired by the studies of gravitational waves in anti-de Sitter universe, in general relativity, in this paper we investigate the possibility of similar solutions in IIB string theory on $AdS_3 x S^3 x R^4$. We give a general form for such solutions in this background and present several explicit examples, by directly solving the field equations, as well as the ones obtained by taking a scaling limit on D1-D5 brane systems in a pp-wave background. The form of the metric in our solutions corresponds to a gravitational wave in $AdS_3$. We show the supersymmetric nature of these solutions and di…
We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the two-point function is calculated up to two loops. Comparing our results with the Hartree-Fock approximation and with the stochastic approach shows that the former resums only the cactus type diagrams, whereas the latter contains the sunset diagram as well and produces the correct result. We also demonstrate that the long-wavelength expectation value of the commutator of two fields is equal to zero both for spacelike and timelike separated points.
We construct the graviton propagator on de Sitter background in exact de Donder gauge. We prove that it must break de Sitter invariance, just like the propagator of the massless, minimally coupled scalar. Our explicit solutions for its two scalar structure functions preserve spatial homogeneity and isotropy so that the propagator can be used within the larger context of inflationary cosmology, however, it is simple to alter the residual symmetry. Because our gauge condition is de Sitter invariant (although no solution for the propagator can be) renormalization should be simpler using this prop…
We study here the gravitational collapse of a matter cloud with a non-vanishing tangential pressure in the presence of a non-zero cosmological term. Conditions for bounce and singularity formation are derived for the model. It is also shown that when the tangential pressures vanish, the bounce and singularity conditions reduce to that of the dust case studied earlier. The collapsing interior is matched with an exterior which is asymptotically de Sitter or anti de Sitter, depending on the sign of cosmological constant. The junction conditions for matching the cloud to exterior are specified. Th…
We construct different neutral blackfold solutions in Anti-de Sitter and de Sitter background spacetimes in the limit where the cosmological scale is taken to be much larger than the transverse horizon size. This includes a class of blackfolds with horizons that are products of odd-spheres times a transverse sphere, for which the thermodynamic stability is also studied. Moreover, we exhibit a specific case in which the same blackfold solution can describe different limiting black hole spacetimes therefore illustrating the geometric character of the blackfold approach. Furthermore, we show that…
Behaviour of a weekly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). Existence of the de Sitter invariant equilibrium quantum state of the scalar field in the presence of interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculation of an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in…
In this paper we provide the criteria for any generally covariant, parity preserving, and torsion free theory of gravity to possess a stable de Sitter (dS) or anti-de Sitter (AdS) background. By stability we mean the absence of tachyonic or ghost-like states in the perturbative spectrum that can lead to classical instabilities and violation of quantum unitarity. While we find that the usual suspects, the F(R) and F(G) theories, can indeed possess consistent (A)dS backgrounds, G being the Gauss-Bonnet term, another interesting class of theories, string-inspired infinite derivative gravity, can …
