我們列出了可行重力模型的條件，然後在程式 MGCAMB 及 CosmoMC 的使用下，討論及比較可行 f(R) 模型在 ΛCDM 背景下及修改宇宙演化背景下的觀測限制。我們所討論的模型為: Exponential 模型、Tsujikawa 模型、Staroinsky 模型，和 Hu-Sawicki 模型。我們發現某些模型的有些參數在宇宙演化背景被修正的情況下，限制範圍有明顯的改變。在觀察微中子的總質量的限制範圍繪圖後，我們發現當宇宙演化背景被修改時，Starobinsky (n=1) 模型和 Hu-Sawicki (p=2) 模型的微中子總質量的限制範圍遭到了明顯的壓縮。

We discuss the cosmological constraints on viable f(R) models with the ΛCDM and modified backgrounds, respectively, by using the programs of MGCAMB and CosmoMC. We study the viable f(R) gravity theories of the Exponential, Tsujikawa, Starobinsky, and Hu-Sawicki models. We find out that the constraints of some parameters of the f(R) models with modified backgrounds deviate from their counterparts that evolve with the ΛCDM one. By comparing the contour plots of the total neutrino mass Σmν of the f(R) models with different backgrounds, we observe apparent suppression of the ranges of Σmν in the Starobinsky (n=1) and Hu-Sawicki (p=2) models, when the background evolution of the universe is modified.

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