Running vacuum model in a non-flat universe

We investigate observational constraints on the running vacuum model （RVM） ofΛ=3ν（H;+K/a;）+c;in a spatially curved universe,whereνis the model parameter,K corresponds to the spatial curvature constant,a represents the scalar factor,and c;is a constant defined by the boundary conditions.We study the CMB power spectra with several sets ofνand K in the RVM.By fitting the cosmological data,we find that the best fittedχ;value for RVM is slightly smaller than that ofΛCDM in the non-flat universe,along with the constraints of■.In particular,our results favor the open universe in bothΛCDM and RVM.In addition,we show that the cosmological constraints of ■at 95%C.L.for the neutrino mass sum are relaxed in both models in the spatially curved universe.