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

TL;DR

This paper reformulates p-form mimetic gravity as nonlinear electrodynamics and reveals its duality to (p+1)-brane fluids, providing new insights into their solutions and cosmological implications.

Contribution

It introduces a duality between p-form mimetic gravity and (p+1)-brane fluids, extending the understanding of their solution structures and connections to known theories.

Findings

Dual models relate to perfect fluids of (p+1)-branes.

For p=0 and p=n-2, models describe particle and (n-1)-brane fluids.

In 4D with p=1, duality links mimetic gravity to Nielsen-Olesen string theory.

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.