基於 Planck 與 DESI 數據對動態暗能量模型的觀測約束

Abstract

本研究基於 Planck 2018 的宇宙微波背景（CMB）觀測數據與 DESI的重子聲學震盪（BAO）測量，針對動態暗能量模型進行觀測約束與理論回測。本文首先回顧了標準宇宙學模型（Λ-CDM）及其核心方程，並分析了現有模型在哈勃常數 H0 張力及結構生長速率等觀測上的偏差。研究中採用經超新星 Ia 校準的哈勃常數與 DESI 物質密度參數作為初始條件，提出一個可變狀態方程 wϕ (a) 的暗能量模型，並結合 CMB 角尺度 θ∗ 及 DESI 各項距離量進行模型擬合。結果顯示，本模型在描述宇宙膨脹歷史及結構形成方面，能有效降低與觀測數據的誤差，優於傳統Λ-CDM 及 DESI 公布的數個傳統模型 (w-CDM 及 w0 wa -CDM)。最後，本文亦討論未來將結構生長速率 f σ8 納入分析的潛力，期望進一步提升模型的普適性與預測能力。

This study utilizes observational data from the Planck 2018 Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillation (BAO) measurements by the Dark Energy Spectroscopic Instrument (DESI) to constrain and theoretically backtest dynamical dark energy models. We first review the standard cosmological model (Λ-CDM) and its core equa-tions, analyzing deviations in existing models regarding the Hubble con-stant H0 tension and structure growth rate. Adopting supernova Ia-calibrated H0 and DESI matter density parameters Ωm as initial conditions, we pro-pose a dark energy model with a variable equation of state wϕ (a). This model incorporates the CMB angular scale θ∗ and DESI distance measure-ments for cosmological fitting. Results demonstrate that our model effec-tively reduces residuals in describing cosmic expansion history and struc-ture formation, outperforming conventional Λ-CDM and several bench-mark models (including w-CDM and w0 wa -CDM) published by DESI. Fi-nally, we discuss the potential of incorporating the structure growth rate fσ8 in future analyses to enhance model generalizability and predictive capability.