对数Herglotz $f(R,T)$ 引力的宇宙学动力学与观测约束

中文摘要 AI 辅助

我们研究了一个由 $f(R,T)=R+\beta\ln(-T/T_0)$ 描述的对数 Herglotz 型 $f(R,T)$ 引力模型的宇宙学动力学和观测可行性。假设空间平坦的 Friedmann--Lemaître--Robertson--Walker 背景和无压物质，修正场方程被表述为一个涉及 Herglotz 场和归一化物质密度的耦合动力系统。对有效 Herglotz 扇区采用了一个现象学闭合关系，使得背景演化可以通过数值方法确定。该模型使用宇宙学计时器测量、DESI DR2 重子声学振荡汇编和 Union3 超新星样本进行约束，在贝叶斯马尔可夫链蒙特卡罗框架内考虑单独和组合数据集。组合分析提供了背景膨胀的统计上一致的描述。重建的膨胀历史给出了当今有效状态方程 $w_{\rm eff,0}\simeq-0.702$，并展示了从晚期加速膨胀向更高红移处减速膨胀的预期转变。我们进一步研究了 $Om(z)$ 诊断和 statefinder 参数。这些结果表明，对数 Herglotz 模型为均匀且各向同性的晚期膨胀历史提供了一致的现象学描述，同时允许偏离标准 $\Lambda$CDM 背景。

英文摘要

We investigate the cosmological dynamics and observational viability of a logarithmic Herglotz-type $f(R,T)$ gravity model described by $f(R,T)=R+β\ln(-T/T_0)$. Assuming a spatially flat Friedmann--Lemaître--Robertson--Walker background and pressureless matter, the modified field equations are formulated as a coupled dynamical system involving the Herglotz field and the normalized matter density. A phenomenological closure relation is adopted for the effective Herglotz sector, allowing the background evolution to be determined numerically. The model is constrained using Cosmic Chronometer measurements, the DESI DR2 baryon acoustic oscillation compilation, and the Union3 supernova sample, considering both individual and combined datasets within a Bayesian Markov-chain Monte Carlo framework. The combined analysis provides a statistically consistent description of the background expansion. The reconstructed expansion history yields a present-day effective equation of state $w_{\rm eff,0}\simeq-0.702$ and exhibits the expected transition from accelerated expansion at late times toward decelerated expansion at higher redshifts. We further investigate the $Om(z)$ diagnostic and statefinder parameter. These results indicate that the logarithmic Herglotz model provides a consistent phenomenological description of the homogeneous and isotropic late-time expansion history, while allowing departures from the standard $Λ$CDM background.

发表机构

• Vellore Institute of Technology（维罗尔理工学院）

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