Emergent Dark Matter in Late Time Universe on Holographic Screen

We discuss a scenario that the dark matter in late time universe emerges as part of the holographic stress-energy tensor on the hypersurface in higher dimensional flat spacetime. Firstly we construct a toy model with a de Sitter hypersurface as the holographic screen in the flat bulk. After adding the baryonic matter on the screen, we assume that both of the dark matter and dark energy can be described by the Brown-York stress-energy tensor. From the Hamiltonian constraint equation in the flat bulk, we find an interesting relation between the dark matter and baryonic matter's energy density parameters, by comparing with the Lambda cold dark matter parameterization. We further compare this holographic embedding of emergent dark matter with traditional braneworld scenario and present an alternative interpretation as the holographic universe. It can be reduced to our toy constraint in the late time universe, with the new parameterization of the Friedmann equation. We also comment on the possible connection with Verlinde's emergent gravity, where the dark matter is treated 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 and the dark matter distribution in the galaxy scale can be derived.Comment: 28 pages, 2 figures; Matches published version and we thank the referees for many insightful comments; v3: typos in the Friedmann equations are fixe

Transport Coefficients from Extremal Gauss-Bonnet Black Holes

We calculate the shear viscosity of strongly coupled field theories dual to Gauss-Bonnet gravity at zero temperature with nonzero chemical potential. We find that the ratio of the shear viscosity over the entropy density is $1/4\pi$, which is in accordance with the zero temperature limit of the ratio at nonzero temperatures. We also calculate the DC conductivity for this system at zero temperature and find that the real part of the DC conductivity vanishes up to a delta function, which is similar to the result in Einstein gravity. We show that at zero temperature, we can still have the conclusion that the shear viscosity is fully determined by the effective coupling of transverse gravitons in a kind of theories that the effective action of transverse gravitons can be written into a form of minimally coupled scalars with a deformed effective coupling.Comment: 23 pages, no figure; v2, refs added; v3, more refs added; v4, version to appear in JHE

Shear Viscosity from the Effective Coupling of Gravitons

We review the progress in the holographic calculation of shear viscosity for strongly coupled field theories. We focus on the calculation of shear viscosity from the effective coupling of transverse gravitons and present some explicit examples.Comment: 10 pages, invited presentation for the 9th Asia-Pacific International Conference On Gravitation And Astrophysics (ICGA 9), June 28-July 2, 2009, Wuhan, China; for the proceedings to be published by World Scientifi

The discrete dynamics of nonlinear infinite-delay-differential equations

AbstractThis paper deals with numerical stability of nonlinear infinite-delay systems of the form y′(t) = ƒ(t,y(t),y(pt)) (p ∈ (0, 1), t > 0). Recently, linear stability properties of some numerical methods for infinite delay systems have been studied by several authors (cf. [1–9]). However, few results have been devoted to the nonlinear case. This paper considers global and asymptotic stability of one-leg θ-methods for the above nonlinear systems. Some stability criteria are obtained