arXiv 1907.035632019-07gr-qc

用$1+3$协变方法研究$f(T)$引力中的标量扰动

Scalar perturbations in $f(T)$ gravity using the $1+3$ covariant approach

Shambel Sahlu, Joseph Ntahompagaze, Amare Abebe, Alvaro de la Cruz-Dombriz, David F. Mota

备注：: Published version
DOI：: 10.1140/epjc/s10052-020-7961-3

摘要：

利用$1+3$协变形式，在扩展的远程平行$f(T)$引力理论的背景下研究了标准物质的宇宙标量扰动.在回顾了$f(T)$引力场方程的背景和引入协变扰动变量后，进行了通常的标量分解和谐波分解，并分析了一般$f(T)$引力理论中两种非相互作用流体（即挠尘和挠辐射混合物）在准静态近似下密度差的增长。特别应用于两类$f(T)$引力玩具模型，即$f(T) = μT_0 (T/T_0)^n$和$f(T) = T + μT_0 (-T/T_0)^n$，然后在各自的参数空间的观测可行的区域内进行，并检查了宇宙的扭转尘埃和扭转辐射时代的物质密度对比度的增长。在n的某些极限情况下，得到了在宇宙时间内振幅增大的尘埃扰动的精确解。同样，在扭转辐射的情况下，长波长和短波长模式进行处理，与振幅振荡或单调增长的时间。总体而言，注意到$f(T)$模型包含更丰富的观测上可行的结构增长情景，可以针对即将到来的观测数据进行测试，并且可以适应广义相对论和$Λ$ CDM限制中的大尺度结构功率谱的当前已知特征。

英文摘要：

The cosmological scalar perturbations of standard matter are investigated in the context of extended teleparallel $f(T)$ gravity theories using the $1+3$ covariant formalism. After a review of the background, gravitational field equations of $f(T)$ gravity and the introduction of the covariant perturbation variables, the usual scalar and harmonic decomposition have been performed, and the analysis of the growth of the density contrasts in the quasi-static approximation for two non-interacting fluids scenarios, namely torsion-dust and torsion-radiation mixtures is presented for the generic $f(T)$ gravity theory. Special applications to two classes of $f(T)$ gravity toy models, namely $f(T) = μT_0 (T/T_0)^n$ and $f(T) = T + μT_0 (-T/T_0)^n$, have then been made within the observationally viable regions of their respective parameter spaces, and the growth of the matter density contrast for both torsion-dust and torsion-radiation epochs of the Universe has been examined. The exact solutions of the dust perturbations, with growing amplitudes in cosmic time, are obtained for some limiting cases of n. Similarly, the long- and short-wavelength modes in the torsion-radiation case are treated, with the amplitudes either oscillating or monotonically growing with time. Overall, it is noted that $f(T)$ models contain a richer set of observationally viable structure growth scenarios that can be tested against up- and-coming observational data and can accommodate currently known features of the large-scale structure power spectrum in the general relativistic and $Λ$CDM limits.

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