Ghost condensation and subluminal propagation on low derivative backgrounds

Abstract

We show a new class of interaction terms with higher derivatives that can be added to every low derivative real scalar, such that the first order perturbations induced by the higher derivative terms on the low derivative background are ghost-free. This follows without imposing additional constraints. Furthermore, we show a related class of theories with an additional stabilizer variable and a constraint which are ghost-free without restricting to a perturbative expansion. In this case the field equation followed by the stabilizer variable may have interesting physical applications: namely, in contrast to some models with first-order derivative interactions with applications for dark energy and inflation, these constrained second-order derivative self-interactions do not necessarily affect the luminal propagation, hence, avoiding the common superluminality issues of the former.