Towards the extended SU(2) Proca theory

Abstract

In this work, we explore the construction of the most general vector-tensor theory with an SU(2) global symmetry in the vector sector as a proposal for a modified theory of gravity. We start with a general Lagrangian containing terms involving symmetric and/or antisymmetric combinations of the covariant derivative of the vector field plus an arbitrary function of the vector field times the Ricci scalar. Then, we study the degeneracy of the full theory to determine whether it can be healthy or not. We find relations among some of the free functions in the Lagrangian that are necessary for the healthiness of the theory in correspondence with the several ways in which the kinetic matrix can be turned degenerate. Finally, we take the decoupling limit of the theory and find additional conditions on the free functions that are necessary for the healthiness of the longitudinal modes.

arXiv commentLaTeX file in revtex4-1 style, 21 pages, no figures. v3: a few changes made to improve the presentation but, more importantly, to discuss the issue of the number of zero eigenvalues and its relation with the number of unphysical degrees of freedom that are removed. As a result, the two classes of theories discussed in previous versions merge into just one class of theories. v4: published version

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