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The holographic $\Lambda(t)$CDM model in a non-flat universe is studied inthis paper. In this model, to keep the form of the stress-energy of the vacuumrequired by general covariance, the holographic vacuum is enforced to exchangeenergy with dark matter. It is demonstrated that for the holographic model thebest choice for the IR cutoff of the effective quantum field theory is theevent horizon size of the universe. We derive the evolution equations of theholographic $\Lambda(t)$CDM model in a non-flat universe. We constrain themodel by using the current observational data, including the 557 Union2 type Iasupernovae data, the cosmic microwave background anisotropy data from the 7-yrWMAP, and the baryon acoustic oscillation data from the SDSS. Our fit resultsshow that the holographic $\Lambda(t)$CDM model tends to favor a spatiallyclosed universe (the best-fit value of $\Omega_{k0}$ is -0.042), and the 95%confidence level range for the spatial curvature is $-0.101<\Omega_{k0}<0.040$.We show that the interaction between the holographic vacuum and dark matterinduces an energy flow of which the direction is first from vacuum to darkmatter and then from dark matter to vacuum. Thus, the holographic$\Lambda(t)$CDM model is just a time-varying vacuum energy scenario in whichthe interaction between vacuum and dark matter changes sign during theexpansion of the universe.

Holographic \Lambda(t)CDM model in a non-flat universe