修正引力中FLRW兼容张量与理想流体普适性
FLRW-Compatible Tensors and Perfect-Fluid Universality in Modified Gravity
- ETH Zurich（苏黎世联邦理工学院）
- Bilkent University（比尔肯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究在(D+1)维FLRW时空中证明，满足D>N的协变N阶张量可分解为度规与类时单位矢量的单项式，D>2时FLRW背景下修正引力的二阶修正项具理想流体形式，为相关方程提供张量分类并探讨应用。
AI中文摘要：
我们研究了配备Levi-Civita联络的(D+1)维Friedmann–Lemaître–Robertson–Walker时空中与FLRW兼容的张量场。我们证明，当空间均匀各向同性群不变的任意协变N阶张量场满足D>N时，其可有限分解为由度规张量g_{μν}和类时单位矢量u_μ构成的单项式，且标量系数仅依赖宇宙时。由此直接得出，当D>2时，FLRW背景场方程的类爱因斯坦重排中出现的任意二阶修正项均具有有效理想流体形式。因此，该结果为FLRW背景下修正引力方程的理想流体结构提供了任意阶张量分类，补充了现有的二阶普适性结果，还讨论了其在广义Friedmann方程和修正引力中测地线偏离方程的应用。
英文摘要：
We study FLRW-compatible tensor fields on Friedmann--Lemaître--Robertson--Walker spacetimes in $(D+1)$ dimensions equipped with Levi-Civita connection. We prove that any covariant rank-$N$ tensor field invariant under the spatial homogeneity and isotropy group, with $D>N$, admits a finite decomposition into monomials constructed from the metric tensor $g_{μν}$ and the unit timelike vector $u_μ$, with scalar coefficients depending only on cosmic time. As a direct consequence, any rank-two correction term appearing in an Einstein-like rearrangement of the FLRW background field equations has the effective perfect-fluid form for $D>2$. Thus, the result provides an arbitrary-rank tensorial classification underlying the perfect-fluid structure of modified gravity equations on FLRW backgrounds, complementing existing rank-two universality results. Applications to generalized Friedmann equations and to the geodesic deviation equation in modified gravity are also discussed.
