变引力常数的Tsallis全息暗能量模型与ΛCDM模型：观测数据的统计分析及张力问题
Tsallis Holographic Dark Energy model with varying gravitational constant vs $Λ$CDM model: statistical analysis of observational data and tensions problem
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中文总结 AI 辅助
该研究对比变引力常数的Tsallis全息暗能量模型与ΛCDM，结合多类观测数据统计分析，发现前者更受偏好，且可部分降低宇宙学张力的显著性。
中文摘要 AI 辅助
我们研究充满Tsallis全息暗能量（THDE）的平直Friedmann-Robertson-Walker宇宙的宇宙学演化，假设引力常数G随时间按幂律参数化关系变化，满足d ln G / d ln a = α_G = 常数。在此框架下，全息暗能量密度为ρ_DE ∝ L^(2γ - 4)，其中L为未来事件视界，γ为Tsallis非加性参数。我们针对模型参数C、γ和α_G的不同取值，研究宇宙的过去与未来演化。通过结合Pantheon+ Ia型超新星样本、直接哈勃参数测量H(z)及重子声学振荡（BAO）数据等观测数据集，检验该模型的可行性。采用马尔可夫链蒙特卡罗（MCMC）方法及偏差信息准则（DIC）、贝叶斯因子、可疑度度量等贝叶斯分析工具，我们与标准ΛCDM模型开展严格的统计比较。结果显示，变引力常数的模型比ΛCDM更受观测数据偏好；结合数据的最优拟合结果对应C < 1的THDE模型。此外，我们利用不一致指数、Q_DMAP统计量及贝叶斯可疑度分析数据集的内部一致性，发现变G且C < 1的THDE模型可部分缓解不同探针间的张力，将张力显著性从约7.4σ降至约5.3σ。
英文摘要
We investigate the cosmological evolution of a flat Friedmann--Robertson--Walker Universe filled with Tsallis holographic dark energy (THDE) under the assumption that the gravitational constant $G$ varies with time according to the power-law parametrisation $d\ln G / d\ln a = α_G = \mathrm{const}$. In this framework, the holographic dark energy density is given by $ρ_{\mathrm{DE}} \propto L^{2γ- 4}$, where $L$ is the future event horizon and $γ$ is the Tsallis non-additivity parameter. We study both the past and future evolution of the Universe for various values of the model parameters $C$, $γ$, and $α_G$. The viability of the model is tested against a combination of observational data, including the Pantheon+ Type Ia supernova sample, direct Hubble parameter measurements $H(z)$, and baryon acoustic oscillation (BAO) data. Using Markov Chain Monte Carlo (MCMC) methods and Bayesian analysis tools such as the Deviance Information Criterion (DIC), the Bayes factor, and the suspiciousness metric, we perform a rigorous statistical comparison with the standard $Λ$CDM model. Our results show that models with a varying gravitational constant are preferred over $Λ$CDM. The best fit to the combined data is obtained for the THDE model with $C < 1$. Furthermore, we analyse the internal consistency of the data sets using the Index of Inconsistency, the $Q_{\mathrm{DMAP}}$ statistic, and Bayesian suspiciousness. We find that the THDE model with varying $G$ and $C < 1$ partially alleviates the tensions between different probes, reducing the significance from $\sim 7.4σ$ to $\sim 5.3σ$.
