AI 中文总结
本研究通过多探针贝叶斯分析系统约束线性Herglotz型$f(R,T)$引力的参数，验证了其可提供符合观测的晚期膨胀描述，且具备区别于标准模型的宇宙学特征。
AI 中文摘要
我们研究了线性Herglotz型$f(R,T)$引力模型$f(R,T)=R+αT$的观测可行性，该模型同时包含几何-物质耦合与非守恒引力动力学。与此前基于示例性参数选择的分析不同，我们对四维参数空间$\{H_0,A,w,Φ_0\}$开展了系统的贝叶斯估计，其中$A$表征物质-几何耦合，$w$为有效状态方程参数，$Φ_0$表示当前的Herglotz场值。我们通过对参数空间内每一点的耦合Herglotz宇宙学方程进行数值积分，得到背景演化过程。研究分别独立及联合使用了宇宙钟（CC）、DESI DR2重子声学振荡（BAO）和Union3 Ia型超新星数据。联合分析在68%置信度下得到$H_0=66.67^{+1.32}_{-1.28}\mathrm{km\\\\,s^{-1}\\\\,Mpc^{-1}}$、$A=1.57^{+0.66}_{-0.51}$、$w=-0.992^{+0.136}_{-0.119}$、$Φ_0=-0.062^{+0.185}_{-0.157}$。在CC数据覆盖的红移范围内，重构的哈勃膨胀与平坦$Λ$CDM模型的预测高度吻合。但减速参数、有效状态方程、$Om(z)$诊断量和状态 finder$\{r,s\}$轨迹与标准协和模型存在显著偏离，偏离幅度和红移演化特征取决于所采用的观测数据集。这些结果表明，Herglotz型$f(R,T)$引力能够为晚期膨胀提供符合观测的描述，同时保留背景哈勃历史之外可区分的宇宙学特征。
英文摘要
We investigate the observational viability of the linear Herglotz-type $f(R,T)$ gravity model, $f(R,T)=R+αT$, which incorporates both geometry--matter coupling and non-conservative gravitational dynamics. Unlike previous analyses\cite{Wazny:2025jth} based on illustrative parameter choices, we perform a systematic Bayesian estimation of the four-dimensional parameter space $\{H_0,A,w,Φ_0\}$, where $A$ characterizes the matter--geometry coupling, $w$ is the effective equation-of-state parameter, and $Φ_0$ denotes the present-day Herglotz field. The background evolution is obtained by numerically integrating the coupled Herglotz cosmological equations at every point in the parameter space. We employ Cosmic Chronometer (CC), DESI DR2 baryon acoustic oscillation (BAO), and Union3 Type-Ia supernova data, both independently and in combination. The joint analysis yields $H_0=66.67^{+1.32}_{-1.28}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $A=1.57^{+0.66}_{-0.51}$, $w=-0.992^{+0.136}_{-0.119}$, and $Φ_0=-0.062^{+0.185}_{-0.157}$ at $68\%$ credibility. The reconstructed Hubble expansion closely follows the flat $Λ$CDM prediction over the redshift range probed by the CC data. However, the deceleration parameter, effective equation of state, $Om(z)$ diagnostic, and statefinder $\{r,s\}$ trajectories exhibit appreciable departures from the concordance model, with the magnitude and redshift evolution depending on the observational dataset. These results demonstrate that Herglotz-type $f(R,T)$ gravity can provide an observationally viable description of the late-time expansion while retaining distinguishable cosmological signatures beyond the background Hubble history.
Comments21 pages, 9 figures
