Braneworld Mimetic Cosmology

We extend the idea of mimetic gravity to a Randall-Sundrum II braneworld model. As for the 4-dimensional mimetic gravity, we isolate the conformal degree of freedom of 5-dimensional gravity in a covariant manner. We assume the bulk metric to be made up of a non-dynamical scalar field $\Phi$ and an auxiliary metric $\tilde{{\cal{G}}}_{AB}$ so that ${\cal{G}}_{AB}= \tilde{{\cal{G}}}^{CD}\,\Phi_{,C}\,\Phi_{,D}\,\tilde{{\cal{G}}}_{AB}$ where $A, B, ...$ are the bulk spacetime indices. Then we show that the induced conformal degree of freedom on the brane as an induced scalar field, plays the role of a mimetic field on the brane. In fact, we suppose that the scalar degree of freedom which mimics the dark sectors on the brane has its origin on the bulk scalar field, $\Phi$. By adopting some suitable mimetic potentials on the brane, we show that this brane mimetic field explains the late time cosmic expansion in the favor of observational data: the equation of state parameter of this field crosses the cosmological constant line in near past from quintessence to phantom phase in a redshift well in the range of observation. We show also that this induced mimetic scalar field has the capability to explain initial time cosmological inflation. We study parameter space of the models numerically in order to constraint the models with Planck2015 data set.Comment: 17 pages, 7 figure