Bottom-up approach to massive spin-two theory in arbitrary curved spacetime

TL;DR

This paper develops a method to analyze ghost-free massive spin-two theories in arbitrary curved spacetime, extending previous models by constraining nonminimal coupling terms through higher-order conditions.

Contribution

It introduces a systematic approach to solve ghost-freeness conditions at higher orders, broadening the class of viable massive spin-two theories beyond the linearized dRGT model.

Findings

Additional constraints on nonminimal couplings were derived from fourth order conditions.

The linearized dRGT model is a special case within the broader class of theories identified.

Higher order analysis can refine the parameter space for ghost-free massive spin-two theories.

Abstract

The linear theory of massive spin-two field in arbitrary curved background is investigated. In flat spacetime, the Fierz-Pauli model is well-known as the unique linear theory describing the massive spin-two field. On the other hand, in order to construct the massive spin-two theory in fixed curved background with arbitrary metric, infinite series of nonminimal coupling terms are necessary. In [Nucl. Phys. B 584 (2000) 615], Buchbinder et al. have derived the condition for the ghost-freeness and they have solved the condition in small curvature approximation. In the leading order approximation, three free parameters of the leading order nonminimal coupling terms are allowed. However, existence of the completion corresponding to all the three parameters is not guaranteed. On the other hand, recently, a class of the completion is obtained by linearizing the dRGT model. However, the leading order nonminimal coupling terms of the linearized dRGT model depend only on one free parameter. Therefore, possibility of a class larger than the linearized dRGT model has not been excluded. In this paper, we develop the method for solving the conditions for ghost freeness in higher order and investigate whether lower order nonminimal coupling terms can be constrained by higher order conditions or not. As a result, we obtain an additional constraint on the leading order nonminimal coupling terms from the fourth order condition. Although the leading order nonminimal coupling terms of the linearized dRGT model is still a subclass of our resulting nonminimal coupling terms in the leading order, a trivial extension of the linearized dRGT model is perfectly equivalent to our resulting action.