An interacting dark energy model in a non-flat universe

In this paper, an interacting dark energy model in a non-flat universe is studied, with taking interaction form $C=alpha Hrho _{de}$ C = α H ρ d e . And in this study a property for the mysterious dark energy is aforehand assumed, i.e. its equation of state $w_{Lambda }=-1$ w Λ = - 1 . After several derivations, a power-law form of dark energy density is obtained $rho _{Lambda } propto a^{-alpha }$ ρ Λ ∝ a - α , here $a$ a is the cosmic scale factor, $alpha $ α is a constant parameter introducing to describe the interaction strength and the evolution of dark energy. By comparing with the current cosmic observations, the combined constraints on the parameter $alpha $ α is investigated in a non-flat universe. For the used data they include: the Union2 data of type Ia supernova, the Hubble data at different redshifts including several new published datapoints, the baryon acoustic oscillation data, the cosmic microwave background data, and the observational data from cluster X-ray gas mass fraction. The constraint results on model parameters are $Omega _{K}=0.0024,(pm 0.0053)^{+0.0052+0.0105}_{-0.0052-0.0103}, alpha =-0.030,(pm 0.042)^{+0.041+0.079}_{-0.042-0.085}$ Ω K = 0.0024 ( ± 0.0053 ) - 0.0052 - 0.0103 + 0.0052 + 0.0105 , α = - 0.030 ( ± 0.042 ) - 0.042 - 0.085 + 0.041 + 0.079 and $Omega _{0m}=0.282,(pm 0.011)^{+0.011+0.023}_{-0.011-0.022}$ Ω 0 m = 0.282 ( ± 0.011 ) - 0.011 - 0.022 + 0.011 + 0.023 . According to the constraint results, it is shown that small constraint values of $alpha $ α indicate that the strength of interaction is weak, and at $1sigma $ 1 σ confidence level the non-interacting cosmological constant model can not be excluded.