arXiv 2001.106832020-01gr-qc

关于真空f（R）引力的微扰约束

On perturbative constraints for vacuum f(R) gravity

Daniel Molano, Fabián Darío Villalba, Leonardo Castañeda, Pedro Bargueño

备注：: 23 pages, 2 figures. Accepted for publication in Classical and Quantum Gravity
DOI：: 10.1088/1361-6382/ab8051

摘要：

微扰技术对于修正的引力理论很重要，因为它们允许计算与广义相对论的偏差，而不需要求助于精确解，而精确解可能很难找到。当应用于诸如$f(R)$重力的模型时，这些技术在涉及高阶导数的场方程中引入校正。这样的修正必须小心处理，以具有良好定义的微扰方案，这可以通过微扰约束的方法来实现，其中作用量中的附加项的系数用作感兴趣的量的展开参数。在这项工作中，我们实现了一个微扰的框架，比较解决方案，在修改后的引力理论与爱因斯坦场方程的解决方案，通过以下的指导方针，微扰理论构建在广义相对论与微扰约束的基本原理。通过使用这种形式主义，我们证明了一个一致的$f(R)$微扰理论在真空中，对于一类重要的$f(R)$功能，产生没有额外的影响，从广义相对论微扰理论的预期。从这个结果，我们认为，有根本的限制，解释为什么一些$f(R)$模型的解决方案可以从广义相对论的对应断开，在这个意义上，从$f(R)$行动导致广义相对论的限制并没有相应地转换的解决方案。

英文摘要：

Perturbative techniques are important for modified theories of gravity since they allow to calculate deviations from General Relativity without recurring to exact solutions, which can be difficult to find. When applied to models such as $f(R)$ gravity, these techniques introduce corrections in the field equations that involve higher order derivatives. Such corrections must be handled carefully to have a well defined perturbative scheme, and this can be achieved through the method of perturbative constraints, where the coefficient of the additional term in the action is used as expansion parameter for the quantities of interest. In this work, we implement a perturbative framework that compares solutions in modified theories of gravity with solutions of the Einstein field equations, by following the guidelines of perturbation theory constructed in General Relativity together with the perturbative constraints rationale. By using this formalism, we demonstrate that a consistent $f(R)$ perturbation theory in vacuum, for an important class of $f(R)$ functions, produces no additional effects with respect to what is expected from the perturbation theory of General Relativity. From this result, we argue that there are fundamental limitations that explain why the solutions of some $f(R)$ models can be disconnected from their general relativistic counterparts, in the sense that the limit that leads from the $f(R)$ action to General Relativity does not transform the solutions accordingly.

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