AI 中文总结
该研究提出用马赫主义解释平坦星系旋转曲线，将BTFR改写为宇宙学形式，通过高红移观测验证，发现数据支持准德西特宇宙，为马赫原理提供了新证据。
AI 中文摘要
我们探讨了对盘状星系渐近平坦旋转曲线相关现象进行马赫主义解释的可能性，为Λ冷暗物质（ΛCDM）范式和修正牛顿动力学（MOND）提供了另一种选择。我们认为MOND加速度标度a₀可能不是新的基本常数，而是可观测宇宙宇宙学标度的体现（a₀ ~ c²/Rᵤ ~ c⁴/GMᵤ ~ c/tᵤ）。我们将重子塔利-费希尔关系（BTFR）改写为宇宙学形式：M_bar/Mᵤ = (V/c)⁴，表明当局部加速度足够小以感知全局宇宙边界时，会出现向非牛顿区域的转变，并显示任何马赫主义解释都必须满足这种形式的关系。此外，该框架自然预测BTFR归一化会随可观测宇宙质量的演化而发生宇宙学演化。我们将这些预测与近期高红移观测（z ~ 2和z ~ 5）进行对比检验，发现数据更支持平坦、仅含重子物质、Λ主导的准德西特宇宙（Ωₘ ≈ 0.05，Ω_Λ ≈ 0.95），而非标准MOND或ΛCDM参数。这些结果表明，至少在某些版本中，平坦星系旋转曲线可被解释为支持马赫原理的有力证据。
英文摘要
We explore the possibility of a Machian interpretation for the phenomena associated with asymptotically flat rotation curves in disk galaxies, providing an alternative to both the Lambda-Cold Dark Matter ($Λ$CDM) paradigm and MOdified Newtonian Dynamics (MOND). We argue that the MOND acceleration scale $a_0$ is likely not a new fundamental constant, but rather a manifestation of the cosmological scales of the observable Universe ($a_0 \sim c^2/R_u \sim c^4/GM_u \sim c/t_u$). We rewrite the Baryonic Tully-Fisher Relation (BTFR) in a cosmological format, $\frac{M_{\rm bar}}{M_{u}} = \left( \frac{V}{c} \right)^4$, suggesting that the transition to the non-Newtonian regime occurs when local accelerations become small enough to feel the global cosmic boundary, and showing that any Machian interpretation must fulfill a relation of this form. Furthermore, this framework naturally predicts a cosmological evolution of the BTFR normalization as the mass in the observable Universe evolves. We test these predictions against recent high-redshift observations ($z \sim 2$ and $z \sim 5$), finding that the data favor a flat, baryon-only, $Λ$-dominated quasi-de Sitter universe ($Ω_m \approx 0.05$, $Ω_Λ\approx 0.95$) over standard MOND or $Λ$CDM parameters. These results suggest that flat galactic rotation curves may be interpreted as compelling evidence in favor of Mach's Principle, in at least some of its versions.
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