Multi-graviton Theories Research Articles

Deconstructing dimensions and massive gravity

We show that the ghost-free models of massive gravity and their multi-graviton extensions follow from considering higher dimensional General Relativity in Einstein–Cartan form on a discrete extra dimension, according to the dimensional deconstruction paradigm. We show that dimensional deconstruction is equivalent to a truncation of the Kaluza–Klein tower at the nonlinear level. Higher dimensional gravity is not recovered from a lower dimensional multi-graviton theory in the limit of a continuous extra dimension (infinite Kaluza–Klein tower) due to the appearance of a low strong coupling scale that depends on IR physics. This strong coupling scale, which is associated with the mass of the lowest Kaluza–Klein mode, controls the onset of the Vainshtein mechanism and is crucial to the theoretical and observational viability of the truncated theory.

Classical and quantum cosmology of multigravity

Recently, a multigraviton theory on a simple closed circuit graph corresponding to the discretization of S1 compactification of the Kaluza–Klein (KK) theory has been considered. In the present paper, we extend this theory to that on a general graph and study what modes of particles are included. Furthermore, we generalize it in a possible nonlinear theory based on the vierbein formalism and study classical and quantum cosmological solutions in the theory. We found that scale factors in a solution for this theory repeat acceleration and deceleration.

Interacting string multi-verses and holographic instabilities of massive gravity

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 of the scalar mode of the graviton are suppressed. Our examples require a fine tuning of the boundary conditions in AdS. Without it, the spacetime background backreacts in order to erase the effects of the graviton mass.

Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals

The question of graviton cloning in the context of the bulk/boundary correspondence is considered. It is shown that multi-graviton theories can be obtained from products of large-N CFTs. No more than one interacting massless graviton is possible. There can be however, many interacting massive gravitons. This is achieved by coupling CFTs via multi-trace marginal or relevant perturbations. The geometrical structure of the gravitational duals of such theories is that of product manifolds with their boundaries identified. The calculational formalism is described and the interpretation of such theories is discussed.

No multi-graviton theories in the presence of a Dirac field

The cross-couplings among several massless spin-two fields (described in the free limit by a sum of Pauli-Fierz actions) in the presence of a Dirac field are investigated in the framework of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincare invariance, (background) Lorentz invariance and the preservation of the number of derivatives on each field, we prove that there are no consistent cross-interactions among different gravitons in the presence of a Dirac field. The basic features of the couplings between a single Pauli-Fierz field and a Dirac field are also emphasized.

MULTI-GRAVITON THEORY FROM A DISCRETIZED RS BRANE-WORLD AND THE INDUCED COSMOLOGICAL CONSTANT

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 latticed 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.

Multi-graviton theory, a latticized dimension and the cosmological constant

Beginning with the Pauli–Fierz theory, we construct a model for multi-graviton theory. Couplings between gravitons belonging to nearest-neighbour ‘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 spacetime is 6, 10, …. Moreover, since the amount of vacuum energy can be an arbitrary small value depending on the choice of parameters in the model, our models are useful for explaining the small positive dark energy in the present universe.

Multi-graviton theory, latticized dimensions and the cosmological constant(Quantum Field Theories: Fundamental Problems and Applications)

Multi-graviton theory, latticized dimensions and the cosmological constant(Quantum Field Theories: Fundamental Problems and Applications)

Multi-graviton theories: yes-go and no-go results.

We report yes-go and no-go results on consistent cross-couplings for a collection of gravitons. Motivated by the search of theories where multiplets of massless spin-two fields cross-interact, we look for all the consistent deformations of a positive sum of Pauli-Fierz actions. We also investigate the problem of deforming a (positive and negative) sum of linearized Weyl gravity actions and show explicitly that there exists multi-Weyl-graviton theories. As the single-graviton Weyl theory, these theories do not have an energy bounded from below.

Inconsistency of interacting, multi-graviton theories

We investigate, in any space–time dimension ⩾3, the problem of consistent couplings for a (finite or infinite) collection of massless, spin-2 fields described, in the free limit, by a sum of Pauli–Fierz actions. We show that there is no consistent (ghost-free) coupling, with at most two derivatives of the fields, that can mix the various “gravitons”. In other words, there are no Yang–Mills-like spin-2 theories. The only possible deformations are given by a sum (or integral) of individual Einstein–Hilbert actions. The impossibility of cross-couplings subsists in the presence of scalar matter. Our approach is based on the BRST-based deformation point of view and uses results on the so-called “characteristic cohomology” for massless spin-2 fields which are explained in detail.