Holographic Dark Energy in Non-conserved Gravity Theory

Recently, reconsidering Rastall idea T_( μ;ν)^ν=a_(,μ) through relativistic thermodynamics gives the new form for scalar field a which led us to construct modern modified theory of gravity debugged ‘non-conserved gravity theory’ [1]. This theory unlike other modified theories of gravity cannot explain directly the current acceleration expansion in absence of the cosmological constant and or existence of other forms of dark energy. Hence, in this study we have reinvestigated holographic dark energy ρ_X~H^2 in the non-conserved theory of gravity. In this context and depending on our interpretation on continuity equation, we face with two models wherein non-conservation term is part of matter evolution and or it is considered as part of effective dark energy. As shown, second model can explain current acceleration epoch with and or without interaction between matter and dark energy while first model only satisfy observation when there is mutual interaction between matter and dark energy sectors.