AI 中文总结
本研究构建类MOND引力理论的结构形成微扰框架，结合多组观测数据约束相关唯象场景，未发现偏离ΛCDM模型的显著证据，为检验该类引力修正的宇宙学可行性提供了系统框架。
AI 中文摘要
我们针对一类以广义非线性泊松方程为特征的类MOND（修改牛顿动力学）理论，构建了一套用于结构形成的微扰框架。我们推导了支配物质扰动的修正演化方程，得到了对应的线性增长方程，并通过对物质功率谱的单圈修正，将分析拓展至轻度非线性区域。除理论框架外，我们还基于两种唯象场景开展了宇宙学分析：一种由控制广义泊松方程中非线性程度的物理量进行参数化，另一种则描述MOND加速度标度与背景膨胀相关的宇宙学加速度之间的相互作用。我们利用最新的结构增长率测量值$fσ_8$、DESI-DR2重子声学振荡数据以及Ia型超新星汇编数据，对这些场景施加了约束。我们未发现偏离标准$Λ$CDM（Λ冷暗物质）宇宙学模型的统计显著性证据。在当前观测不确定度范围内，所得约束与广义相对论+$Λ$CDM场景完全一致。在非线性尺度上，我们注意到类MOND修正可以改变$P_{\rm NL}(k)$，并留下当前及未来高精度大尺度结构观测或可探测的特征。我们的结果建立了类MOND引力动力学与大尺度结构观测之间的系统性关联，为在宇宙学背景下评估受MOND启发的引力修正理论的唯象可行性提供了一套自洽的框架。
英文摘要
We develop a perturbative framework for structure formation in a broad class of MOND-like theories characterized by a generalized nonlinear Poisson equation. We derive the modified evolution equations governing matter perturbations and obtain the corresponding linear growth equation, extending the analysis into the mildly nonlinear regime through one-loop corrections to the matter power spectrum. Beyond the theoretical framework, we perform a cosmological analysis based on two phenomenological scenarios: one parametrized by a quantity controlling the degree of nonlinearity in the generalized Poisson equation, and another describing the interplay between the MOND acceleration scale and the cosmological acceleration associated with the background expansion. We constrain these scenarios using recent measurements of the growth rate of structure, $fσ_8$, DESI-DR2 baryon acoustic oscillation data, and Type Ia supernova compilations. We find no statistically significant evidence for departures from the standard $Λ$CDM cosmology. The inferred constraints are fully consistent with the GR + $Λ$CDM scenario within the current observational uncertainties. At nonlinear scales, we note that MOND-like modifications can alter $P_{\rm NL}(k)$ and leave signatures that current and future high-precision large-scale-structure observations may probe. Our results establish a systematic connection between MOND-like gravitational dynamics and large-scale structure observations, providing a consistent framework to assess the phenomenological viability of MOND-inspired modifications of gravity in a cosmological context.
Comments22 pages, 7 figures and 2 table. Comments are welcome!
