Cosmological Topologically Massive Gravitons and Photons
S. Carlip, S. Deser, A. Waldron, D. K. Wise
备注：
36 pages, 1 figure. v2: Expanded; exhibits localized normalizable wave packets and exact chiral pp-wave solutions. v3: Added references; clarification on bulk vs. boundary chirality. v4: Published version; changes include discussion of bulk solutions' asymptotic acceptability at all mu
We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS_3 backgrounds are not only shifted from their flat background values but, more surprisingly, split according to chirality. For all finite values of the topological mass, we find a single bulk degree of freedom with positive energy, and exhibit a complete set of normalizable, finite-energy wave packet solutions. This model can also be written as a sum of two higher-derivative SL(2,R) Chern--Simons theories, weighted by the central charges of the boundary conformal field theory. At two particular "critical" values of the couplings, one of these central charges vanishes, and linearized topologically massive gravity becomes equivalent to topologically massive electromagnetism; however, the physics of the bulk wave packets remains unaltered here.
It is shown that in some multi-supergraviton models, the contributions to the effective potential due to a non-trivial topology can be positive, giving rise in this way to a positive cosmological constant, as demanded by cosmological observations.
We investigate the topologically new massive gravity in three dimensions. It turns out that a single massive mode is propagating in the flat spacetime, comparing to the conformal Chern-Simons gravity which has no physically propagating degrees of freedom. Also we discuss the realization of the BMS/GCA correspondence.
I consider a simple model where the graviton mass and the cosmological constant depend on a scalar field with appropriate couplings and I calculate the graviton propagator and the resulting effective potential for the scalar field in order to examine issues of stability and symmetry breaking.
We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtai…
We show that the graviton acquires a mass in a de Sitter background given by $m_{g}^{2}=-{2/3}Λ.$ This is precisely the fine-tuning value required for the perturbed gravitational field to mantain its two degrees of freedom.
Relevant deformations of gravity present an exciting window of opportunity to probe the rigidity of gravity on cosmological scales. For a single-graviton theory, the leading relevant deformation constitutes a graviton mass term. In this paper, we investigate the classical and quantum stability of massive cosmological gravitons on generic Friedman backgrounds. For a Universe expanding towards a de Sitter epoch, we find that massive cosmological gravitons are self-protected against unitarity violations by a strong coupling phenomenon.
Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the "massive graviton") is switched on. An exact solution with this property is explicitly exhibited and possesses a slower fall-off than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a u(1) current algebra.…
We study the imprint of a massive scalar particle on cosmological correlation functions, and suggest the way to determine the mass of the newly introduced particle, which is expected to be around 10^14 GeV. After reviewing the basic theory by Maldacena and the effective field theory (EFT) of inflation by Cheung et al., we apply these two theories to construct new couplings of a massive scalar field with primordial fluctuations including an arbitrary number of gravitons. We compute some correlation functions including these couplings in the soft-graviton limit. We show that when the number of s…
Motivated by the interest raised by the problem of Lorenz-symmetry violating gauge theories in connetion with gravity models, this contribution sets out to provide a general method to systematically study the excitation spectrum of gravity actions which include a Lorentz-symmetry breaking Chern-Simons-type action term for the spin connection. A complete set of spin-type operators is found which accounts for the (Lorentz) violation parameter to all orders and graviton propagators are worked out in a number of different situations.
We consider Topologically Massive Gravity (TMG), which is three dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate g…
A qualitative discussion of possible features of a composite graviton arising out of open string field theory is provided along with expected modifications to the graviton propagator due to such a composite graviton model. Possible implications for the cosmological constant problem are also discussed.
Graviton fluctuations induce strong non-perturbative infrared renormalization effects for the cosmological constant. The functional renormalization flow drives a positive cosmological constant towards zero, solving the cosmological constant problem without the need to tune parameters. We propose a simple computation of the graviton contribution to the flow of the effective potential for scalar fields. Within variable gravity we find that the potential increases asymptotically at most quadratically with the scalar field. With effective Planck mass proportional to the scalar field, the solutions…
The graviton 1-loop partition function in Euclidean topologically massive gravity (TMG) is calculated using heat kernel techniques. The partition function does not factorize holomorphically, and at the chiral point it has the structure expected from a logarithmic conformal field theory. This gives strong evidence for the proposal that the dual conformal field theory to TMG at the chiral point is indeed logarithmic. We also generalize our results to new massive gravity.
We discuss the production and evolution of cosmological gravitons showing how the cosmological background affects their dynamics. Besides, the detection of cosmological gravitons could constitute an extremely important signature to discriminate among different cosmological models. Here we consider the cases of scalar-tensor gravity and $f(R)$ gravity where it is demonstrated the amplification of graviton amplitude changes if compared with General Relativity. Possible observational constraints are discussed.
Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four dimensions, we construct the three-dimensional equivalent of $x$-variables for conserved matter currents coupled to topologically massive gauge bosons or gravitons. Using these, we bootstrap various matter-coupled gauge-theory and gravitational scattering amplitudes, and conjecture that topologically massive gauge theory and topologically massive gravity are relat…
Wolfgang Kummer was a pioneer of two-dimensional gravity and a strong advocate of the first order formulation in terms of Cartan variables. In the present work we apply Wolfgang Kummer's philosophy, the `Vienna School approach', to a specific three-dimensional model of gravity, cosmological topologically massive gravity at the chiral point. Exploiting a new Chern-Simons representation we perform a canonical analysis. The dimension of the physical phase space is two per point, and thus the theory exhibits a local physical degree of freedom, the topologically massive graviton.
It is well known that gravitons can convert into photons, and vice versa, in the presence of cosmological magnetic fields. We study this conversion process in the context of atomic dark matter scenario. In this scenario, we can expect cosmological dark magnetic fields, which are free from the stringent constraint from the cosmic microwave observations. We find that gravitons can effectively convert into dark photons in the presence of cosmological dark magnetic fields. The graviton-dark photon conversion effect may open up a new window for ultra high frequency gravitational waves.
We revisit the proposal that the resolution of the Cosmological Constant Problem involves a sub-millimeter breakdown of the point-particle approximation for gravitons. No fundamental description of such a breakdown, which simultaneously preserves the point-particle nature of matter particles, is yet known. However, basic aspects of the self-consistency of the idea, such as preservation of the macroscopic Equivalence Principle while satisfying quantum naturalness of the cosmological constant, are addressed in this paper within a Soft Graviton Effective Theory. It builds on Weinberg's analysis o…
We present solutions describing spatially closed, open, or flat cosmologies in the massive gravity theory within the recently proposed tetrad formulation. We find that the effect of the graviton mass is equivalent to introducing to the Einstein equations a matter source that can consist of several different matter types -- a cosmological term, quintessence, gas of cosmic strings, and non-relativistic cold matter.
In this paper we study the cosmological constant emerging from the Wheeler-DeWitt equation as an eigenvalue of the related Sturm-Liouville problem. We employ Gaussian trial functionals and we perform a mode decomposition to extract the transverse-traceless component, namely, the graviton contribution, at one loop. We implement a noncommutative-geometry- induced minimal length to calculate the number of graviton modes. As a result, we find regular graviton fluctuation energies for the Schwarzschild, de Sitter, and anti-de Sitter backgrounds. No renormalization scheme is necessary to remove infi…
We show that cosmological topologically massive gravity at the chiral point allows not only Brown-Henneaux boundary conditions as consistent boundary conditions, but slightly more general ones which encompass the logarithmic primary found in 0805.2610 as well as all its descendants.
We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three-dimensional Riemann-Cartan space-times. We use the language of exterior differential forms and the properties of Majorana spinors on 3-dimensional space-times to explicitly demonstrate the local supersymmetry of the action density involved. Coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion-constraint imposed by the method of Lagrange multipliers. We compare these field equations with…
We study the effects of gravitationally-driven decoherence on tunneling processes associated with false vacuum decays, such as the Coleman--De~Luccia instanton. We compute the thermal graviton-induced decoherence rate for a wave function describing a perfect fluid of nonzero energy density in a finite region. When the effective cosmological constant is positive, the thermal graviton background sourced by a de Sitter horizon provides an unavoidable decoherence effect, which may have important consequences for tunneling processes in cosmological history. We discuss generalizations and consequenc…
We compute the graviton one-loop correction to the expectation value of the local expansion rate in slow-roll inflation, with both slow-roll parameters finite. The calculation is based on a recent method to explicitly construct gauge-invariant observables in perturbative quantum gravity at all orders in perturbation theory, and it is particularly suited in cases of highly-symmetrical space-time backgrounds. Our analysis adds to recent calculations of that correction in de Sitter space-time and in single-field inflation with constant deceleration. In the former case a vanishing one-loop correct…
We solve the equations of topologically massive gravity with potentially non-vanishing cosmological constant for homogeneous metrics without isotropy. We only reproduce known solutions. We also discuss their homogeneous deformations, possibly with isotropy. We show that de Sitter space and hyperbolic space cannot be infinitesimally homogeneously deformed in TMG. We clarify some of their Segre-Petrov types and discuss the warped de Sitter spacetime.
Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It p…
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $β$ and $γ$, equal to one in Einstein theory, can be obtained from static spherically symmetric solutions. For the graviton-dilaton system, as in Brans-Dicke or low energy string theory, we find that if $γ\ne 1$ for a charge neutral point star, then there exist naked singularities. Thus, if $γ$ is measured to be different from one, then it cannot be explained by these theories, without implying naked singularities. We also couple a cosmologic…
We propose a multi-graviton theory with non-nearest-neighbor couplings in the theory space. The resulting four-dimensional discrete mass spectrum reflects the structure of a latticized extra dimension. For a plausible mass spectrum motivated by the discretized Randall-Sundrum brane-world, the induced cosmological constant turns out to be positive and may serve as a quite simple model for the dark energy of our accelerating universe.
We reexamine a scenario in which photons and gravitons arise as Goldstone bosons associated with the spontaneous breaking of Lorentz invariance. We study the emergence of Lorentz invariant low energy physics in an effective field theory framework, with non-Lorentz invariant effects arising from radiative corrections and higher order interactions. Spontaneous breaking of the Lorentz group also leads to additional exotic but weakly coupled Goldstone bosons, whose dispersion relations we compute. The usual cosmological constant problem is absent in this context: being a Goldstone boson, the gravi…
The graviton is pictured as a bound state of a fermion and anti-fermion with the spacetime metric assumed to be a composite object of spinor fields, based on a globally Lorentz invariant action proposed by Hebecker and Wetterich. The additional degrees of freedom beyond those of the graviton are described by Goldstone boson gravitational degrees of freedom. If we assume that the fermion is a light neutrino with mass $m_nu\sim 10^{-3}$ eV, then we obtain the effective vacuum density ${\barρ}_λ\sim (10^{-3} eV)^4$, which agrees with the estimates for the cosmological constant from WMAP and SNIa …
We investigate the emission of gravitons by a cosmological brane into an Anti de Sitter five-dimensional bulk spacetime. We focus on the distribution of gravitons in the bulk and the associated production of `dark radiation' in this process. In order to evaluate precisely the amount of dark radiation in the late low-energy regime, corresponding to standard cosmology, we study numerically the emission, propagation and bouncing off the brane of bulk gravitons.
I discuss the status of present knowledge about a possible background of relic gravitons left by an early, pre-big bang cosmological epoch, whose existence in the past of our Universe is suggested by the duality symmetries of string theory.
The standard $Λ$-CDM predicts a growth of structures which tends to be higher than the values of redshift space distortion (RSD) measurements, if the cosmological parameters are fixed by the CMB data. In this paper we point out that this discrepancy can be resolved/understood if we assume that the graviton has a small but non-zero mass. In the context of the Minimal Theory of Massive Gravity (MTMG), due to infrared Lorentz violations measurable only at present cosmological scales, the graviton acquires a mass without being haunted by unwanted extra degrees of freedom. While the so-called self-…
The basic cosmological conjecture about the Dopplerian nature of redshifts may be false if gravitons are super-strong interacting particles. A quantum mechanism of classical gravity and the main features of a new cosmological paradigm based on it are described here.
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on …
We present the first direct and non-perturbative computation of the graviton spectral function in quantum gravity. This is achieved with the help of a novel Lorentzian renormalisation group approach, combined with a spectral representation of correlation functions. We find a positive graviton spectral function, showing a massless one-graviton peak and a multi-graviton continuum with an asymptotically safe scaling for large spectral values. We also study the impact of a cosmological constant. Further steps to investigate scattering processes and unitarity in asymptotically safe quantum gravity …
We argue that gravity theories in AdS4 are holographically dual to either of two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton acts as a source for the stress-energy tensor, and a dual CFT2 with a fixed dual graviton which acts as a source for a dual stress-energy tensor. The dual stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The two CFT's are related by a Legendre transformation generated by a gravitational Chern-Simons coupling. This duality is a gravitational version of electric-magnetic duality valid at any radius r, where the reno…
A new approach to the cosmological constant problem is proposed by modifying Einstein's theory of general relativity, using instead a scalar-tensor theory of gravitation. This theory of gravity crucially incorporates the concept of quantum symmetry breaking. The role of the cosmological constant $λ$ as a graviton mass in the weak-field limit is necessarily utilized. Because $λ$ takes on two values as a broken symmetry, so does the graviton mass -- one of which cannot be zero. Gravity now exhibits both long- and short-range forces, by introducing hadron bags into strong interaction physics usin…
We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are quantized by means of the fakeon prescription. The proof applies to renormalizable theories, including the ultraviolet complete theory of quantum gravity with fakeons formulated recently, as well as low-energy (nonrenormalizable) theories. We clarify a number of subtleties related to the study o…
The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by $k=0$ cosmological coordinates (also called conformal or Poincare coordinates). We show that this divergence can be removed by adding a linearized diffeomorphism to each mode function; i.e., by an explicit change of gauge. It follows that the graviton vacuum state is well-defined and de Sitter invariant in agreement with various earlier arguments.
I discuss various thoughts, old and new, about the cosmological constant (or dark energy) paradox. In particular, I suggest the possibility that the cosmological ``constant'' may decay as $Λ\sim α^2 m_N^3 / τ$, where $τ$ is the age of the universe.
We analyze the physics of massive spin 2 fields in (A)dS backgrounds and exhibit that: The theory is stable only for masses m^2 >= 2Λ/3, where the conserved energy associated with the background timelike Killing vector is positive, while the instability for m^2<2Λ/3 is traceable to the helicity 0 energy. The stable, unitary, partially massless theory at m^2=2Λ/3 describes 4 propagating degrees of freedom, corresponding to helicities (+/-2,+/-1) but contains no 0 helicity excitation.
Beginning with the Pauli-Fierz theory, we construct a model for multi-graviton theory. Couplings between gravitons belonging to nearest-neighbor ``theory spaces'' lead to a discrete mass spectrum. Our model coincides with the Kaluza-Klein theory whose fifth dimension is latticized. We evaluate one-loop vacuum energy in models with a circular latticized extra dimension as well as with compact continuous dimensions. We find that the vacuum energy can take a positive value, if the dimension of the continuous space time is $6, 10,...$. Moreover, since the amount of the vacuum energy can be an arbi…
We present the cosmological analysis of the Gauss-Bonnet quasi-dilaton massive gravity theory. This offers a gravitational theory with a non-zero graviton mass. We calculate the complete set of background equations of motion. Also, we obtain the self-accelerating background solutions and we present the constraints on parameters to indicate the correct sign of parameters. In addition, we analyse tensor perturbations and calculate the mass of graviton and find the dispersion relation of gravitational waves for two cases. Finally, we investigate the propagation of gravitational perturbation in th…
We consider cosmological topologically massive gravity at the chiral point with positive sign of the Einstein-Hilbert term. We demonstrate the presence of a negative energy bulk mode that grows linearly in time. Unless there are physical reasons to discard this mode, this theory is unstable. To address this issue we prove that the mode is not pure gauge and that its negative energy is time-independent and finite. The isometry generators L_0 and \bar{L}_0 have non-unitary matrix representations like in logarithmic CFT. While the new mode obeys boundary conditions that are slightly weaker than t…
The cosmological constant appearing in the Wheeler-De Witt equation is considered as an eigenvalue of the associated Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities tog…
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 apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the …
The graviton exchange effect on cosmological correlation functions is examined by employing the double-soft limit technique. A new relation among correlation functions that contain the effects due to graviton exchange diagrams in addition to those due to scalar-exchange and scalar-contact-interaction, is derived by using the background field method and independently by the method of Ward identities associated with dilatation symmetry. We compare these three terms, putting small values for the slow-roll parameters and $(1-n_{s}) = 0.042$, where $n_{s}$ is the scalar spectral index. It is argued…
Conversion of gravitational waves into electromagnetic radiation is discussed. The probability of transformations of gravitons into photons in presence of cosmological background magnetic field is calculated at the recombination epoch and during subsequent cosmological stages. The produced electromagnetic radiation is concentrated in the X-ray part of the spectrum. It is shown that if the early Universe was dominated by primordial black holes (PBHs) prior to Big Bang Nucleosynthesis (BBN), the relic gravitons emitted by PBHs would transform to an almost isotropic background of electromagnetic …
