Stability of a modified Jordan–Brans–Dicke theory in the dilatonic frame,General Relativity and Gravitation

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Stability of a modified Jordan–Brans–Dicke theory in the dilatonic frame
General Relativity and Gravitation ( IF 2.1 ) Pub Date : 2020-07-01 , DOI: 10.1007/s10714-020-02718-7
Genly Leon , Andronikos Paliathanasis , Luisberis Velazquez Abab

We investigate the Jordan–Brans–Dicke action in the cosmological scenario of FLRW spacetime with zero spatially curvature and with an extra scalar field minimally coupled to gravity as matter source. The field equations are studied in two ways. The method of group invariant transformations, i.e., symmetries of differential equations apply in order to constraint the free functions of the theory and determine conservation laws for the gravitational field equations. The second method that we apply for the study of the evolution of the field equations is the stability analysis of equilibrium points. Particularly, we find solutions with $$w_{\text {tot}}=-\,1$$ , and we study their stability by means of the Center Manifold Theorem. We show this solution is an attractor in the dilatonic frame but it is an intermediate accelerated solution $$a \simeq e^{A t^p}, p:=\frac{2}{2+l}, \quad \frac{32}{57+6 \omega _0}

中文翻译：

膨胀坐标系中修正的 Jordan-Brans-Dicke 理论的稳定性

我们研究了 FLRW 时空宇宙学场景中的 Jordan-Brans-Dicke 作用，其中空间曲率为零，并且具有与重力最小耦合的额外标量场作为物质源。场方程有两种研究方式。群不变变换的方法，即微分方程的对称性，用于约束理论的自由函数并确定引力场方程的守恒定律。我们用于研究场方程演化的第二种方法是平衡点的稳定性分析。特别是，我们找到了 $$w_{\text {tot}}=-\,1$$ 的解，并通过中心流形定理研究了它们的稳定性。

更新日期：2020-07-01

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