标题： 基于曲率的广义引力理论和第五元素场的进动偏移 显示英文标题

标题： Precession shift in curvature based Extended Theories of Gravity and Quintessence fields

摘要： 在本文中，我们利用行星进动的数据来限制假想的新弱力的大小。我们考虑标量-张量四阶引力（STFOG）的弱场近似，其中包括几种修改引力模型。牛顿势的修正形式为类似杨-米尔斯势（第五种力），即$V(r) = {\alpha} \dfrac{e^{-\beta r}}{r}$，其中${\alpha}$是与势强度相关的参数，${\beta}$是与力的范围相关的参数。目前关于近日点进动的数据可以推断出引力模型中自由参数的约束。此外，非对易谱引力（NCSG）也被研究，它是STFOG的一个特例。在这里我们表明，行星的进动偏移可以将参数${\beta}$的界限提高几个数量级。最后，这种分析也应用于幂律势的情况，特别是参考了由暗能量场引起的施瓦茨希尔德几何变形，该暗能量场负责当前宇宙的加速阶段。 显示英文摘要

摘要： In this paper we constrain the sizes of hypothetical new weak forces by making use the data coming from the precession of Planets. We consider the weak field approximation of Scalar-Tensor Fourth Order Gravity (STFOG), which include several models of modified gravity. The form of the corrections to the Newtonian potential if of the form of Yukawa-like potential (5th force), i.e. $V(r) = {\alpha} \dfrac{e^{-\beta r}}{r}$, where ${\alpha}$ is the parameter related to the strength of the potential, and ${\beta}$ to the range of the force. The present data on periastron advance allow to infer a constraint on the free parameter of the gravitational models. Moreover, the Non-Commutative Spectral Gravity (NCSG) is also studied, being a particular case STFOG. Here we show that the precession shift of Planet allows to improve the bounds on parameter ${\beta}$ by several orders of magnitude. Finally such an analysis is studied to the case of power-like potential, referring in particular to deformation of the Schwarzschild geometry induced by a quintessence field, responsible of the present accelerated phase of the Universe.