In the present investigation we use observational data of \( f \sigma _ {8} \) to determine observational constraints in the plane \((\Omega _{m0},\sigma _{8})\) using two different methods: the growth factor parametrization and the numerical solutions method for density contrast, \(\delta _{m}\). We verified the correspondence between both methods for three models of accelerated expansion: the \(\Lambda CDM\) model, the \( w_{0}w_{a} CDM\) model and the running cosmological constant RCC model. In all case we consider also the curvature as free parameter. The study of this correspondence is important because the growth factor parametrization method is frequently used to discriminate between competitive models. Our results we allow us to determine that there is a good correspondence between the observational constrains using both methods. We also test the power of the \( f\sigma _ {8} \) data to constraints the curvature parameter within the \( \Lambda CDM \) model. For this we use a non-parametric reconstruction using Gaussian processes. Our results show that the \( f\sigma _ {8}\) data with the current precision level does not allow to distinguish between a flat and non-flat universe.

在本研究中，我们使用观测数据\（f \ sigma _ {8} \）通过两种不同方法确定平面\（（\ Omega _ {m0}，\ sigma _ {8}）\）上的观测约束：生长因子参数化和密度对比的数值解决方法\（\ delta _ {m} \）。我们针对三种加速扩展模型验证了这两种方法之间的对应关系：\（\ Lambda CDM \）模型，\（w_ {0} w_ {a} CDM \）模型和运行中的宇宙学常数RCC模型。在所有情况下，我们还将曲率视为自由参数。这种关系的研究很重要，因为生长因子参数化方法经常用于区分竞争模型。我们的结果使我们能够确定使用这两种方法的观测约束之间是否存在良好的对应关系。我们还测试了\（f \ sigma _ {8} \）数据的能力，以约束\（\ Lambda CDM \）模型中的曲率参数。为此，我们使用使用高斯过程的非参数重建。我们的结果表明，具有当前精度水平的\（f \ sigma _ {8} \）数据无法区分平面和非平面宇宙。