基于MCMC分析的真实$f(G)$引力框架的观测约束与宇宙增长指数

中文摘要 AI 辅助

我们对修正的高斯-博内引力，即$f(G)$引力，进行了全面的观测分析，同时研究了背景宇宙膨胀和亚视界线性物质扰动。我们考虑了两种可行的函数形式：反正切参数化（模型I）和广义多项式幂律模型（模型II）。利用马尔可夫链蒙特卡洛（MCMC）集成采样器，我们通过背景和结构增长观测来约束其参数空间。我们的分析采用了宇宙计时器（CC）、Pantheon+ Ia型超新星汇编（PP）、红移空间畸变（RSD）以及暗能量光谱仪器第一年重子声学振荡测量（DESI BAO）的累积组合。DESI BAO数据的加入使得哈勃常数$H_0$和当前物质密度参数$\Omega_{m0}$的优选值出现明显下移。对于模型II，完整分析得到$H_0=64.02^{+4.13}_{-3.08}\\ \mathrm{km\\,s^{-1}\\,Mpc^{-1}}$和$\Omega_{m0}=0.249^{+0.047}_{-0.038}$。我们进一步使用$\Delta\mathrm{AIC}_c$、$\Delta\mathrm{BIC}$和$\Delta\mathrm{DIC}$评估了模型相对于$\Lambda$CDM的统计性能。对于模型II，完整数据集给出$\Delta\mathrm{AIC}_c=4.233$和$\Delta\mathrm{DIC}=5.971$，偏向于$\Lambda$CDM基线。在扰动层面，两种模型都表现出与大规模结构观测相容的稳定增长历史。模型预测了晚期膨胀动力学在$z\approx0.5005$（模型I）和$z\approx0.6086$（模型II）处的转变，突出了它们宇宙学演化的差异。

英文摘要

We present a comprehensive observational analysis of modified Gauss--Bonnet, or $f(G)$, gravity by investigating both the background cosmological expansion and sub-horizon linear matter perturbations. We consider two viable functional forms: an arctangent parameterization (Model~I) and a generalized polynomial power-law model (Model~II). Using a Markov Chain Monte Carlo (MCMC) ensemble sampler, we constrain their parameter spaces through background and structure-growth observations. Our analysis employs cumulative combinations of Cosmic Chronometers (CC), the Pantheon+ Type Ia Supernovae compilation (PP), Redshift-Space Distortions (RSD), and the Year-1 Baryon Acoustic Oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI BAO). The inclusion of DESI BAO data produces a noticeable downward shift in the preferred values of the Hubble constant, $H_0$, and present matter density parameter, $Ω_{m0}$. For Model~II, the full analysis yields $H_0=64.02^{+4.13}*{-3.08},\mathrm{km,s^{-1},Mpc^{-1}}$ and $Ω*{m0}=0.249^{+0.047}_{-0.038}$. We further assess the statistical performance of the models relative to $Λ$CDM using $Δ\mathrm{AIC}_c$, $Δ\mathrm{BIC}$, and $Δ\mathrm{DIC}$. For Model~II, the full dataset gives $Δ\mathrm{AIC}_c=4.233$ and $Δ\mathrm{DIC}=5.971$, favoring the $Λ$CDM baseline. At the perturbation level, both models exhibit stable growth histories compatible with large-scale structure observations. The models predict transitions in the late-time expansion dynamics at $z\approx0.5005$ and $z\approx0.6086$ for Models~I and II, respectively, highlighting differences in their cosmological evolution.

发表机构

• Symbiosis Institute of Technology, Nagpur Campus, Symbiosis International (Deemed University), Pune, India（印度浦那西姆比奥斯国际（认定）大学纳格浦尔校区西姆比奥斯技术学院）
• Department of Education, East African University Rwanda, Nyagatare, Rwanda（卢旺达尼亚加塔雷东非大学卢旺达教育学院）
• Department of Physics, College of Science and Technology, University of Rwanda,Kigali, Rwanda（卢旺达基加利卢旺达大学科学与技术学院物理系）
• Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa, Saudi Arabia（沙特阿拉伯艾哈萨费萨尔国王大学理学院数学与统计系）
• Department of Mathematics, Jadavpur University, Kolkata, India（印度加尔各答贾达普大学数学系）

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28 pages, 7 figures