Emergent Dark Matter in Late Universe on Holographic Screen

Abstract

We discuss a scenario that the dark matter in late universe emerges as the holographic stress energy tensor on the hypersurface in higher dimensional flat bulk. Firstly we construct a toy model with a de Sitter hypersurface as the holographic screen in flat spacetime. After adding the baryonic matter on the screen, both of the dark matter and dark energy can be described by the Brown-York stress energy tensor. From the Hamiltonian constraint equation in higher dimensional spacetime, we find an interesting relation between the dark matter and baryonic matter density parameters, by using the Lambda cold dark matter parameterization. We further combine this holographic embedding of emergent dark matter with brane world scenario and present a new parameterization for the Friedmann equation, which can be reduced to our toy constraint in the current universe. We also comment on the connection with the Verlinde's emergent gravity, where the dark matter is regarded as the elastic response of the baryonic matter on the de Sitter spacetime background. We show that from the holographic de Sitter model with elasticity, the Tully-Fisher relation of the dark matter distribution in the galaxy scale can be derived.