Dual models for p-form mimetic gravity and their connection to perfect fluids consisting of (p+1)-branes

Abstract

We propose an approach that allows one to reformulate n-dimensional p-form mimetic gravity (including usual mimetic gravity as particular case p=0) as nonlinear (n−p−1)-form electrodynamics via electric-magnetic duality. The resulting dual Lagrangian density is just the square root of the ordinary quadratic Lagrangian density of (n−p−1)-form electrodynamics. By applying field transformation in the action, we show that for the arbitrary p this dual theory transforms into the (p+1)-brane fluid: the model of the stack of the parallel (p+1)-dimensional branes foliating physical spacetime. As the structure of the field transformations depends on p, the sets of solutions in these models are related differently. We prove, that for p=0 and p=n−2 dual mimetic models describe usual particle fluid with the potential flow and to the (n−1)-brane fluid respectively. For other values of p not all mimetic solutions behave like that, in general, so we restrict ourselves only to the case n=4, p=1. In this case, we show, that mimetic formulation is dual to the well-known Nielsen-Olesen theory of “dual strings” and discuss the criterion indicating whether its solutions behave like string fluid. The cosmological solutions for these models in are also discussed.