具有边界项的非度量理论中的诺特对称性：精确解与贝叶斯宇宙学约束
Noether Symmetry in a Non-Metricity Theory with a Boundary Term: Exact Solutions and Bayesian Cosmological Constraints
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中文总结 AI 辅助
本研究通过诺特对称方法分析幂律$f(Q,B)$引力模型，获得精确解并发现其可解释宇宙加速膨胀，结合多种观测数据用MCMC约束参数，表明该模型是晚期宇宙学的可行替代方案。
中文摘要 AI 辅助
我们研究了幂律$f(Q, B)$引力模型的宇宙学意义，其中$Q$表示非度量标量，$B$是相关的边界项。我们采用诺特对称方法来识别引力拉格朗日量的可接受函数形式，并获得相应的守恒量和精确宇宙学解。利用精确解，我们发现对于该模型参数条件$\alpha+\beta>\frac{3}{2}$，模型表现出宇宙的加速阶段。此外，我们还使用贝叶斯马尔可夫链蒙特卡罗分析，用最近的观测数据讨论了该模型。我们考虑了宇宙计时器（CC）、Pantheon+ \\& SH0ES和DESI DR2观测的不同组合来约束模型参数和哈勃常数$H_0$。推断的$H_0$值取决于所采用的数据集组合，从CC+Pantheon+组合的较高值到CC+DESI DR2的较低值，后者得出$H_0=67.5^{+1.4}_{-1.6}\\,\mathrm{km\\,s^{-1}\\, Mpc^{-1}}$，与标准$\Lambda$CDM框架内普朗克2018年CMB优选值一致。推断的\\(H_0\\)强烈依赖于数据集，范围介于早期宇宙和局部校准测定值之间。我们进一步检查了后验协方差和相关矩阵，以识别参数简并性并评估MCMC约束的稳健性。背景演化也表现出晚期加速膨胀，并保持与观测约束兼容。这些结果表明，$f(Q, B)$模型为晚期宇宙学提供了一个可行的替代描述。
英文摘要
We investigate the cosmological implications of a power-law $f(Q, B)$ gravity model, where $Q$ denotes the non-metricity scalar and $B$ is the associated boundary term. We employ the Noether symmetry approach to identify the admissible functional form of the gravitational Lagrangian and to obtain the corresponding conserved quantities and exact cosmological solutions. Using the exact solution, we find that for this model parameter condition $α+β>\frac{3}{2}$, the model exhibits the accelerating phase of the Universe. Furthermore, we have also discussed the model with recent observational data using a Bayesian Markov Chain Monte Carlo analysis. We consider different combinations of Cosmic Chronometers (CC), Pantheon+ \& SH0ES, and DESI DR2 observations to constrain the model parameters and the Hubble constant $H_0$. The inferred value of $H_0$ depends on the adopted dataset combination, ranging from a higher value for the CC+Pantheon+ combination to a lower value for CC+DESI DR2, with the latter yielding $H_0=67.5^{+1.4}_{-1.6}\,\mathrm{km\,s^{-1}\, Mpc^{-1}}$, consistent with the Planck 2018 CMB-preferred value within the standard $Λ$CDM framework. The inferred \(H_0\) is strongly dataset dependent, spanning the range between the early-Universe and locally calibrated determinations. We further examine the posterior covariance and correlation matrices to identify parameter degeneracies and assess the robustness of the MCMC constraints. The background evolution also exhibits late-time accelerated expansion and remains compatible with the observational constraints. These results demonstrate that the $f(Q, B)$ model provides a viable alternative description of late-time cosmology.
发表机构
- Mukesh Patel School of Technology Management & Engineering, SVKM’s NMIMS（SVKM's NMIMS 穆凯什·帕特爾技術管理與工程學院）
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