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Register a new userCausality of Massive Spin 2 Field in External Gravity
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We investigate the structure of equations of motion and lagrangian constraints in a general theory of massive spin 2 field interacting with external gravity. We demonstrate how consistency with the flat limit can be achieved in a number of specific spacetimes. One such example is an arbitrary static spacetime though equations of motion in this case may lack causal properties. Another example is provided by external gravity fulfilling vacuum Einstein equations with arbitrary cosmological constant. In the latter case there exists one-parameter family of theories describing causal propagation of the correct number of degrees of freedom for the massive spin 2 field in arbitrary dimension. For a specific value of the parameter a gauge invariance with a vector parameter appears, this value is interpreted as massless limit of the theory. Another specific value of the parameter produces gauge invariance with a scalar parameter and this cannot be interpreted as a consistent massive or massless theory.
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The de Rham-Gabadadze-Tolley massive gravity admits pp-wave backgrounds on which linear fluctuations are shown to undergo time advances for all values of the parameters. The perturbations may propagate in closed time-like curves unless the parameter space is constrained to a line. These classical phenomena take place well within the theorys validity regime.
We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two dimensional sigma-model. In the lowest order in $alpha$ we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.
We investigate the problem of derivation of consistent equations of motion for the massive spin 2 field interacting with gravity within both field theory and string theory. In field theory we derive the most general classical action with non-minimal couplings in arbitrary spacetime dimension, find the most general gravitational background on which this action describes a consistent theory and generalize the analysis for the coupling with background scalar dilaton field. We show also that massive spin 2 field allows in principle consistent description in arbitrary background if one builds its action in the form of an infinite series in the inverse mass square. Using sigma-model description of string theory in background fields we obtain in the lowest order in $alpha$ the explicit form of effective equations of motion for the massive spin 2 field interacting with gravity from the requirement of quantum Weyl invariance and demonstrate that they coincide with the general form of consistent equations derived in field theory.
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 preparing and comparing with the dS conformal spin-2 massless case (dS linear quantum gravity) which will be considered in a forthcoming paper and for which specific quantization methods are needed.
We show how uncertainty in the causal structure of field theory is essentially inevitable when one includes quantum gravity. This includes the fact that lightcones are ill-defined in such a theory - independent of the UV completion of the theory. We include details of the causality uncertainty which arises in theories of quadratic gravity.
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