AI 中文总结
本研究构建基于CosmoPower训练的神经网络模拟器，模拟修改引力对物质功率谱的非线性效应，可高效准确重建修改引力函数，适用于第四代巡天，还展示了三项实际应用。
AI 中文摘要
包含修改引力（MG）的非线性信息能为修改引力函数的模型无关重建提供更强的约束能力。但使用MGCAMB+ReACT计算非线性物质功率谱在重复似然评估中开销巨大，限制了对高维参数空间的探索。本研究中，我们构建了一个用于非线性修正$R_{\text{MG}}(k,z)=P_{\text{MG}}^{\text{NL}}(k,z)/P_{\text{MG}}^{\text{L}}(k,z)$的神经网络模拟器，它基于约$9\times10^5$个样本由\texttt{CosmoPower}训练，并通过代表性功率谱、独立验证集及合成数据的马尔可夫链蒙特卡洛（MCMC）测试完成验证。对于$\boldsymbol{\rm{\u039b}}$CDM模型和中等MG非线性修正，模拟功率谱在所有考虑的尺度范围内与参考预测的偏差小于1.5%；对于极端非线性情况，在$k<0.8\boldsymbol{\rm{Mpc}}^{-1}$时仍保持相同精度。在独立验证集上，平均残差接近零，$k<0.5\boldsymbol{\rm{Mpc}}^{-1}$时2$\boldsymbol{\rm{\u03c3}}$离散度低于1%，更小尺度上约为2%。合成数据的MCMC分析在 posterior不确定性内恢复了输入的$\boldsymbol{\rm{\u039b}}$CDM宇宙学参数及重建MG函数的广义相对论（GR）极限，表明该模拟器适用于类似第四代巡天的精度与可靠性。我们还展示了三项应用：利用$R_{\text{MG}}$区分线性功率谱几乎简并的模型、使用该模拟器为当前测光巡天的$3\times2$pt似然提供理论预测、通过主成分分析预测DESI+CSST的约束能力。
英文摘要
Including nonlinear information from modified gravity (MG) brings more constraining power to the model-independent reconstruction of MG functions. However, the calculation of the nonlinear matter power spectrum with MGCAMB+ReACT is expensive in repeated likelihood evaluations, which limits the exploration of the high-dimensional parameter space. In this work, we construct a neural-network emulator for the nonlinear correction $R_{\mathrm{MG}}(k,z)=P_{\mathrm{MG}}^{\mathrm{NL}}(k,z)/P_{\mathrm{MG}}^{\mathrm{L}}(k,z)$, which is trained with \texttt{CosmoPower} on approximately $9\times10^5$ samples and validated with representative spectra, an independent validation set, and MCMC tests with synthetic data. For $Λ$CDM and moderate MG nonlinear corrections, the emulated power spectra agree with the reference predictions to within $1.5\%$ over the full scale range considered. For the extreme nonlinear case, the same accuracy is retained for $k<0.8\,\mathrm{Mpc}^{-1}$. Over the independent validation set, the mean residual is close to zero, with the $2σ$ scatter below $1\%$ for $k<0.5\,\mathrm{Mpc}^{-1}$ and about $2\%$ on smaller scales. The synthetic data MCMC analyses recover the input $Λ$CDM cosmology and the GR limits of the reconstructed MG functions within the posterior uncertainties, showing the accuracy and reliability of the emulator for Stage-IV-like surveys. We also demonstrate three applications: using $R_{\mathrm{MG}}$ to distinguish models with nearly degenerate linear power spectra, using the emulator for theory predictions for current photometric-survey $3\times2$pt likelihoods, and forecasting DESI+CSST constraints with principal component analysis.
Comments36 pages, 16 figures, 5 tables
