标题： 共形相关的度量和拉格朗日量及其在宇宙学中的物理解释 显示英文标题

标题： Conformally related metrics and Lagrangians and their physical interpretation in cosmology

摘要： 共形相关的度量和拉格朗日量在标量-张量引力宇宙学的背景下被考虑。 在讨论了这个问题之后，我们提出一个引理，其中我们证明了两个共形相关的拉格朗日量的场方程也是共形相关的，当且仅当相应的哈密顿量为零。 然后我们证明，对于每一个非最小耦合的标量场，我们可以在一个共形相关的空间中关联一个具有适当势能的唯一最小耦合的标量场。 后一个结果意味着非最小耦合的标量场的场方程在共形层面上与最小耦合的标量场的场方程相同。 这一事实对于在共形等价系统中选择物理变量是相关的。 最后，我们发现上述命题可以扩展到一般的n维黎曼空间。 显示英文摘要

摘要： Conformally related metrics and Lagrangians are considered in the context of scalar-tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related Lagrangians are also conformally related if and only if the corresponding Hamiltonian vanishes. Then we prove that to every non-minimally coupled scalar field, we may associate a unique minimally coupled scalar field in a conformally related space with an appropriate potential. The latter result implies that the field equations of a non-minimally coupled scalar field are the same at the conformal level with the field equations of the minimally coupled scalar field. This fact is relevant in order to select physical variables among conformally equivalent systems. Finally, we find that the above propositions can be extended to a general Riemannian space of n-dimensions.