发表机构
Sultan Qaboos University; North-West University; National Institute for Theoretical and Computational Sciences (NITheCS)（苏丹卡布斯大学; 西北大学; 理论与计算科学国家研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导度规f(R)引力中无剪切宇宙扰动的一致性条件，发现无剪切扇区无张量引力波，标量辐射需满足约束闭合条件，矢量模式在正密度物质分支不存在，揭示了不同模式的传播特性与模型依赖性。
AI 中文摘要
我们推导了度规$f(R)$引力中Friedmann-Lemaître-Robertson-Walker宇宙学的线性无剪切扰动传播内容所满足的一致性条件。研究表明，无剪切约束的散度是总动量守恒方程，因此并不意味着测地流；其投影时间导数反而提供了一个非平凡的可积性条件，随后必须分别检验标量、矢量和张量扇区。无剪切性消除了独立的横向无迹电-磁外尔对，因此不存在普通的$+$或$×$张量引力波。标量子（scalaron）不会被代数消除，但其四变量调和系统必须保持在由无剪切约束及其所有时间导数生成的含时一致子空间内。对于空间平坦膨胀德西特片（de Sitter patch）中的测地无剪切汇，这排除了所有非零固定共动标量调和模式，包括$α,Λ>0$的健康$R+αR^2-2Λ$模型。矢量模式满足依赖于曲率的全局本征值条件，对于$f'>0$且$1+w>0$的正密度物质，其右侧为负，因此该分支上不存在非零矢量调和模式。常见的惯性$R^3$示例之所以能规避这一符号阻碍，仅因为它处于$f'<0$分支。因此，在施加的无剪切扇区中不存在张量辐射，而标量辐射虽未被运动学排除，但仍是一个依赖于模型和背景的约束闭合问题。
英文摘要
We derive the consistency conditions governing the propagating content of linear shear-free perturbations of Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in metric $f(R)$ gravity. The divergence of the shear-free constraint is shown to be the total momentum-conservation equation and therefore does not imply geodesic flow. Its projected time derivative instead supplies a nontrivial integrability condition. Scalar, vector, and tensor sectors must then be tested separately. Shear-freeness removes the independent transverse-traceless electric-magnetic Weyl pair, so no ordinary $+$ or $\times$ tensor gravitational wave survives. The scalaron is not removed algebraically, but its four-variable harmonic system must remain in the time-dependent consistent subspace generated by the shear-free constraint and all of its time derivatives. For a geodesic shear-free congruence in the spatially flat expanding de Sitter patch, this excludes every nonzero fixed comoving scalar harmonic, including the healthy $R+αR^2-2Λ$ model with $α,Λ>0$. Vector modes obey a curvature-dependent global eigenvalue condition whose right-hand side is negative for positive-density matter with $f'>0$ and $1+w>0$; hence no nonzero vector harmonic survives on that branch. The familiar coasting $R^3$ example evades this sign obstruction only because it lies on an $f'<0$ branch. Thus tensor radiation is absent in the imposed shear-free sector, whereas scalar radiation is not excluded kinematically but remains a model- and background-dependent constraint-closure question.
Comments9 pages
