Title: Strong gravitational lensing in $f\left(χ\right)=χ^{3/2}$ gravity Show Chinese title

Title: 强引力透镜在$f\left(χ\right)=χ^{3/2}$引力中

Abstract: We discuss the phenomenology of gravitational lensing in the purely metric $f\left(\chi\right)$ gravity, an $f(R)$ gravity where the action of the gravitational field depends on the source mass. We focus on the strong lensing regime in galaxy-galaxy lens systems and in clusters of galaxies. Using an approximate metric solution accurate to second order of the velocity field $v/c$, we show how, in the $f\left(\chi\right)=\chi^{3/2}$ gravity, the same light deflection can be produced by point-like lenses with masses smaller than in General Relativity; this mass difference increases with increasing impact parameter and decreasing lens mass. However, for sufficiently massive point-like lenses and small impact parameters, $f\left(\chi\right)=\chi^{3/2}$ and GR yield indistinguishable light deflection angles: this regime occurs both in observed galaxy-galaxy lens systems and in the central regions of galaxy clusters. In the former systems, the GR and $f\left(\chi\right)$ masses are compatible with the mass of standard stellar populations and little or no dark matter, whereas, on the scales of the core of galaxy clusters, the presence of substantial dark matter is required both in General Relativity, and in our approximate $f\left(\chi\right)=\chi^{3/2}$ point-like lens solution. We thus conclude that our approximate metric solution of $f\left(\chi\right)=\chi^{3/2}$ is unable to describe the observed phenomenology of the strong lensing regime without the aid of dark matter. Show Chinese abstract

Abstract: 我们讨论纯度规引力$f\left(\chi\right)$中的引力透镜现象，这是一种$f(R)$引力，其中引力场的作用依赖于源质量。我们关注星系-星系透镜系统和星系团中的强透镜效应。利用速度场的二阶近似度规解$v/c$，我们展示了在$f\left(\chi\right)=\chi^{3/2}$引力中，可以通过质量小于广义相对论中的点状透镜产生相同的光偏转；这种质量差异随着影响参数的增加和透镜质量的减少而增大。然而，对于足够大质量的点状透镜和小影响参数，$f\left(\chi\right)=\chi^{3/2}$和 GR 会产生无法区分的光偏转角：这种情形既出现在观测到的星系-星系透镜系统中，也出现在星系团的中心区域。在前一种系统中，GR 和$f\left(\chi\right)$的质量与标准恒星种群的质量相容，并且几乎没有暗物质，而在星系团核心尺度上，广义相对论和我们近似的$f\left(\chi\right)=\chi^{3/2}$点状透镜解都需要存在大量的暗物质。 因此我们得出结论，我们的近似度量解$f\left(\chi\right)=\chi^{3/2}$在没有暗物质帮助的情况下无法描述强引力透镜效应的观测现象。