The applicability of a linearized perturbed FLRW metric to the late, lumpy universe has been subject to debate. We consider in an elementary way the Newtonian limit of the Einstein equations with this ansatz for the case of structure formation in late-time cosmology, on small and large scales, and argue that linearizing the Einstein tensor produces only a small error down to arbitrarily small, decoupled scales (e.g. Solar system scales). On subhorizon patches, the metric scale factor becomes a coordinate choice equivalent to choosing the spatial curvature, and not a sign that the FLRW metric cannot perturbatively accommodate very different local physical expansion rates of matter; we distinguish these concepts, and show that they merge on large scales for the Newtonian limit to be globally valid. Furthermore, on subhorizon scales, a perturbed FLRW metric ansatz does not already imply assumptions on isotropy, and effects beyond an FLRW background, including those potentially caused by non-linearities of general relativity (GR), may be encoded into non-trivial boundary conditions. The corresponding cosmologies have already been developed in a Newtonian setting by Heckmann and Schücking and none of these boundary conditions can explain the accelerated expansion of the universe. Our analysis of the field equations is confirmed on the level of solutions by an example of pedagogical value, comparing a collapsing top-hat overdensity (embedded into a cosmological background) treated in such perturbative manner to the corresponding exact solution of GR, where we find good agreement even in the regimes of strong density contrast.
Finding Schwarzschild metric component grr and FLRW's k without solving the Einstein's equation, rather by a synergistic matching between geometric results enfranchised by Newtonian gravity
Einstein's $R^{\hat{0} \hat{0}}$ equation for non-relativistic sources derived from Einstein's inertial motion and the Newtonian law for relative acceleration
Gravitational orbits in the expanding universe revisited
在膨胀宇宙中，修正的牛顿引力轨道方程表明，像星系和行星系统这样的局部引力束缚系统不受宇宙膨胀的影响。这个结果是在标准FLRW度量所描述的空间扩展的假设下得出的。本文应用另一种度规，导出了共形FLRW度规所描述的空间展开的修正牛顿方程。如Vavryčuk（Frontiers in Physics，2022）所示，这个度量是有利的，因为它正确地预测了宇宙的时间膨胀，并适合SNe Ia光度观测，而不需要引入暗能量。令人惊讶的是，基于共形FLRW度规的牛顿方程的行为完全不同于基于标准FLRW度规的牛顿方程。与通常认为局域系统抵抗空间膨胀的观点相反，共形度规的结果表明，所有局域系统都按照哈勃流膨胀。以旋涡星系的数值模拟为例，说明了局域系统随宇宙时间的演化。螺旋星系的大小与观测一致，并且典型的螺旋图案得到了很好的再现。该理论预测了平坦的旋转曲线，而没有假设星系周围有暗物质。该理论解决了对$Λ$ CDM模型的挑战，如暗卫星星系问题，重子Tully-Fisher关系或径向加速度关系。此外，太阳系中的谜题也得到了成功的解释，如先驱者异常、年轻太阳的微弱悖论、月球和泰坦的轨道异常或古代火星上存在河流。
Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
本文提出了一种求解一阶后牛顿（PN）展开场方程的方法。我们的计算推广了Bini和Damour以及随后Kavanagh等人的工作，考虑史瓦西背景下的偏心轨道。我们推导出所有$\ell$模式的粒子位置的延迟度规扰动的表达式。我们发现，尽管第一次出现，Regge-Wheeler规范度规扰动是$C^0$在所有$\ell$的粒子。作为第一次使用我们的解决方案，我们计算规范不变量$\langle U \rangle$通过4PN，同时扩大偏心率通过$e^{10}$。通过预测每个PN阶的$e\to 1$奇异行为，我们大大提高了我们的结果的精度为大$e$。我们使用$\langle U \rangle$通过$e^{10}$和在质量比的线性顺序找到有效的单体势$\hat Q$的4PN贡献。
Non-vacuum relativistic extensions of MOND using metric theories of gravity with curvature-matter couplings and their applications to the accelerated expansion of the Universe without dark components
A Tighter Test of Local Lorentz Invariance using PSR J2317+1439
引力是一种长程力，人们可能{ \it a priori}期望宇宙的全球物质分布为局部引力物理学选择一个优选的静止框架。用两个参数$\hatα_1$和$\hatα_2$描述双星强引力场背景下的优选标架效应现象。这些参数在广义相对论中完全消失，并在弱场极限下简化为两个参数化后牛顿（PPN）参数$α_1$和$α_2$。我们导出了$|\hatα_1| < 1.7\times 10^{-4}$（90%~ C. L.）使用非常低的偏心率脉冲双星PSR J2317+1439，在以前的限制上提高了3倍。
