Running vacuum model in a non-flat universe

We investigate observational constraints on the running vacuum model (RVM) of Lambda = 3 nu(H-2 + K/a(2)) + c(0) in a spatially curved universe, where nu is the model parameter, corresponds to the spatial curvature constant, a represents the scalar factor, and c(0) is a constant defined by the boundary conditions. We study the CMB power spectra with several sets of nu and K in the RVM. By fitting the cosmological data, we find that the best fitted chi value for RVM is slightly smaller than that of Lambda CDM in the non-flat universe, along with the constraints nu <= O(10(-4)) of (68% C.L.) and vertical bar Omega(K) = -K/(aH)(2)vertical bar <= O(10(-2)) (95% C.L.). In particular, our results favor the open universe in both Lambda CDM and RVM. In addition, we show that the cosmological constraints of Sigma m(nu) = 0.256(-0.234)(+0.224) (RVM) and Sigma m(nu) = 0.257(-0.234)(+0.219) (Lambda CDM) at 95% C.L. for the neutrino mass sum are relaxed in both models in the spatially curved universe.