标题： 关于宇宙学背景下$f(R)$引力微分同胚对称性的注记 显示英文标题

标题： Notes on diffeomorphisms symmetry of $f(R)$ gravity in the cosmological context

摘要： 我们研究在限制的$f(R)$引力背景下度量扰动，在这种情况下引入了一个偏离时空完整微分同构性的参数。 我们证明可以选取该参数以消除通常$f(R)$引力中存在的感应各向异性应力。 此外，为了防止矢量和张量度量扰动的不稳定性，得到了模型的一些约束条件。 显示英文摘要

摘要： We study the metric perturbations in the context of restricted $f(R)$ gravity, in which a parameter for deviation from the full diffeomorphisms of space-time is introduced. We demonstrate that one can choose the parameter to remove the induced anisotropic stress, which is present in the usual $f(R)$ gravity. Moreover, to prevent instability for the vector and tensor metric perturbations, some constraints on the model are obtained.