NONTRIVIAL VACUA IN HIGHER-DERIVATIVE GRAVITATION

A discussion of an extended class of higher-derivative classical theor ies of gravity is presented. A procedure is given for exhibiting the n ew propagating degrees of freedom, at the full nonlinear level, by tra nsforming the higher-derivative action to a canonical second-order for m. For general fourth-order theories, described by actions which are g eneral functions of the scalar curvature, the Ricci tensor and the ful l Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non trivial, corresponding to de Sitter or anti-de Sitter solutions of the original theory. It is also shown that around any vacuum the elementa ry excitations remain the massless graviton, a massive scalar field, a nd a massive ghostlike spin-two field. The analysis is extended to act ions which are arbitrary functions of terms of the form del(2k)R, and it is shown that such theories also have a nontrivial vacuum structure .