Abstract

By using an extended spherical collapse model taking into account the effects of shear, vorticity, and dynamical friction we found the relationship between the turnaround radius, \({{R}_{t}}\), and mass, \({{M}_{t}}\), in \(\Lambda \)CDM and dark energy scenarios. We get a more general formula than that usually described in literature, showing a dependence of \({{R}_{t}}\) from shear, vorticity and dynamical friction. The \({{R}_{t}}{-} {{M}_{t}}\) relation differs from that obtained not taking into account shear, and rotation, and dynamical friction especially at galactic scales, differing for \( \simeq {\kern 1pt} 40\)% from the result given in literature. The theoretical turnaround–mass relation and the turnaround radius obtained from stable structures, can be used to put some constraints on the equation of state, \(w\), parameter. We compare the \({{R}_{t}}{-}{{M}_{t}}\) relationship obtained for different dark energy models to that obtained in the \(f(R)\) modified gravity (MG) scenario. The \({{R}_{t}}{-}{{M}_{t}}\) relationship in dark energy scenarios are tantamount to the prediction of the \(f(R)\) theories. Consequently, we must conclude that the \({{R}_{t}}{-}{{M}_{t}}\) relationship is not a good probe to test gravity theories beyond Einstein’s general relativity.

中文翻译：

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用结构最大尺寸探测修正的重力

摘要

通过使用扩展的球形塌陷模型，考虑了剪切，涡旋和动摩擦的影响，我们发现了转弯半径\（{{R} _ {t}} \）和质量\（{ M} _ {t}} \），在\（\ Lambda \） CDM和暗能量场景中。我们得到了比文献中通常描述的更通用的公式，该公式显示了\（{{R} _ {t}} \）与剪切力，涡旋和动力摩擦的关系。的\（{{R} _ {吨}} { - } {{M} _ {吨}} \）从该关系的不同得到的不考虑剪切和旋转，和动力摩擦特别是在星系秤，不同的对\（\ simeq {\ kern 1pt} 40 \）％从文献中给出的结果。从稳定结构获得的理论周转质量关系和周转半径可用于对状态方程\（w \），参数施加一些约束。我们将不同暗能量模型获得的\（{{R} _ {t}} {-} {{M} _ {t}} \）关系与\（f（R）\）修正引力中获得的关系进行比较（MG）场景。暗能量场景中的\（{{R} _ {t}} {-} {{M} _ {t}} \）关系等于\（f（R）\）理论的预测。因此，我们必须得出结论，\（{{R} _ {t}} {-} {{M} _ {t}} \）关系不是检验爱因斯坦广义相对论之外的引力理论的好方法。