本研究探討觀測資料對於在非平坦宇宙中跑動宇宙學常數模型 (RVM) 限制。在 本模型中，跑動宇宙學常數可表示為 Λ = 3ν(H^2 + K/a^2) + c_0 ，其中 H 為哈伯參數，ν 為 RVM 模型參數，K 描述空間的曲率，a 為宇宙尺度因子，c_0 為受邊界條件限制的常數。研究中利用不同 ν 和 Ω_K^0 = −K/(aH_0)^2 的參數組合，來繪製 RVM 和 ΛCDM 模型的理論 CMB 功率譜。利用不同的觀測資料組合擬合模 型，本研究發現在非平坦宇宙中 RVM 模型的卡方檢定值，χ^2，較 ΛCDM 模型之卡方檢定值為小，並且限制了 RVM 模型中的 ν ≤ O(10^(−4)) (68 % 信賴水準) 以及 |Ω_K^0|≤ O(10^(−2)) (95% 信賴水準)。本研究的結果顯示 RVM 和 ΛCDM 模型 在非平坦宇宙下較偏好開放宇宙形式，並在 95% 的信賴水準下，限制了兩模型 的微中子質量和為 Σmν = 0.256(+0.224)(−0.234) (RVM) 以及 Σmν = 0.257(+0.219)(−0.234)(ΛCDM)。

This study investigate observational constraints on the running cosmological constant model, or running vacuum model (RVM), of Λ = 3ν(H^2 + K/a^2) + c_0 in the spatially curved universe, where H stands for the Hubble parameter, ν is the model parameter, K corresponds to the spatial curvature constant, a represents the scale factor, and c0 is a constant defined by the boundary conditions. The CMB power spectra with several sets of ν and Ω_K^0 = −K/(aH_0)^2 in RVM are studied. By fitting the cosmological data, it is found that the best fitted χ^2 value of RVM is slightly smaller than that of ΛCDM in the non-flat universe, along with the constraints of ν ≤ O(10^(−4)) (68 % C.L.) and |Ω_K^0|≤ O(10^(−2)) (95 % C.L.). In particular, our results favor the open universe in both ΛCDM and RVM. Moreover, it is shown that the cosmological constraints of Σmν = 0.256(+0.224)(−0.234) (RVM) and Σmν = 0.257(+0.219)(−0.234) (ΛCDM) at 95% C.L. for the neutrino mass sum are relaxed in both models in the spatially curved universe.

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