An Overview of Recent Developments in Bimetric Theory
In this paper, Schmidt-May and von Strauss provide a comprehensive review of recent advancements in bimetric theories, which serve as an extension of nonlinear massive gravity frameworks to include multiple interacting spin-2 fields. The primary focus is on ghost-free models, which are imperative to stabilize these interactions. Such models typically necessitate intricate tuning of parameters to avoid the appearance of problematic Boulware-Deser ghosts, thereby ensuring theoretical consistency.
The paper begins by addressing historical attempts at massive gravity, illustrating the challenges in constructing stable models. Notably, the Fierz-Pauli action laid foundational groundwork, but longstanding issues like the vDVZ discontinuity and the Boulware-Deser ghost highlighted the profound complexities involved. The recent surge of interest was kindled by de Rham, Gabadadze, and Tolley (dRGT), who proposed a nonlinear theory free of the Boulware-Deser ghost in the decoupling limit. This was later extended by Hassan-Rosen to incorporate completely dynamical systems with bimetric interactions between two metrics, each satisfying its own Einstein-Hilbert action.
Bimetric theories distinguish themselves by coupling two metric fields, each with its gravitational dynamics, via a specific interaction potential. This potential is a sophisticated mix of elementary symmetric polynomials related to the eigenvalues of the square-root of their inverse metric product. Consistency and stability are achieved by demanding the precise cancellation of unwanted degrees of freedom beyond the seven permissible (two from a massless spin-2 field and five from a massive one) to avoid the Boulware-Deser ghost manifestation. The paper highlights Hassan and Rosen's metric formulation as a cornerstone of these developments: an elegant construction ensuring ghost-free actions characterized by a finite number of terms, thanks to their antisymmetric structure.
The expansive scope of the review encompasses linear stability analyses on arbitrary backgrounds, revealing intriguing insights into how perturbations around cosmological solutions unfold within bimetric frameworks. The gravitational sector potentially embraces a newly significant vacuum structure with indirect avenues for Modified Source Couplings via effective metrics, circumstantially rekindling the GR analog for substance interaction models.
The review explores prospects of partial masslessness, whereby the gauge symmetries at particular parameter conditions, especially in higher dimensions, portend exciting theoretical possibilities with conformal extensions bearing resemblance to gravity’s conventional symmetry. This domain borders the frontier of more speculative regimes wherein solutions like conformal gravity emerge. Further advancement could unveil novel symmetry protection scenarios, with implications for technical naturalness in cosmological constants.
Fascinatingly, the exploration also extends to multimetric interactions. These interactions necessitate sophisticated ADM formalism adaptations to continually eschew inconsistencies inherent in traditional loop couplings indicative of graviton entanglements. An emphasis on graph-theoretical representations succinctly captures these couplings, directing future exploration away from geometrical ambiguities toward stable algebraic constructs.
In conclusion, the paper not only consolidates current understandings and theoretical developments of interacting spin-2 fields but also pinpoints intriguing challenges and unexplored avenues within the theoretical groundworks of bimetric gravity. It offers invaluable insight into the promising territory of multimetric interactions, inviting a deeper probe into the realms where higher-spin interactions and gauge symmetries might harmoniously interlace. As the theoretical implications remain a vibrant area of research, further explorations are likely to uncover a wealth of structures and symmetries, enriching our understanding of gravitational paradigms.