标题： 研究$ f(Q) $引力中的早期和晚期时间阶段 显示英文标题

标题： Investigating early and late-time epochs in $ f(Q) $ gravity

摘要： 在接下来的工作中，提出了一种新的形式为$ f(Q)=Q(1+a)+b\frac{Q_0^2}{Q} $的混合模型，并使用早期和晚期约束条件进行了验证。 我们首先利用大爆炸核合成（BBN）时代的条件来约束这些模型，然后用它们研究宇宙通过减速参数的演化。 这种方法被应用于混合模型以及一种形式为$ \alpha_1 Q+\alpha_2 Q_0 $的简单模型，后者被发现可以简化为$\Lambda$CDM 模型。 研究了包含与$\Lambda$CDM 比较的宇宙时钟（CC）和 Pantheon+SH0ES 数据集的误差条图，用于受限的混合模型。 此外，我们针对三个数据集——CC、Pantheon+SH0ES 和重子声波振荡（BAO）——对模型进行了蒙特卡洛马尔可夫链（MCMC）抽样，以找到自由参数的最佳拟合范围。 结果表明，从 BBN 研究得出的模型参数（$a$）的约束范围与 MCMC 分析得到的范围存在重叠区域。 最后，我们使用 AIC 和 BIC 方法对我们的模型和$\Lambda$CDM 模型进行了统计学比较。 显示英文摘要

摘要： In the following work, a new hybrid model of the form $ f(Q)=Q(1+a)+b\frac{Q_0^2}{Q} $ has been proposed and confronted using both early as well as late-time constraints. We first use conditions from the era of Big Bang Nucleosynthesis (BBN) in order to constrain the models which are further used to study the evolution of the Universe through the deceleration parameter. This methodology is employed for the hybrid model as well as a simple model of the form $ \alpha_1 Q+\alpha_2 Q_0 $ which is found to reduce to $\Lambda$CDM. The error bar plot for the Cosmic Chronometer (CC) and Pantheon+SH0ES datasets which includes the comparison with $\Lambda$CDM, has been studied for the constrained hybrid model. Additionally, we perform a Monte Carlo Markov Chain (MCMC) sampling of the model against three datasets -- CC, Pantheon+SH0ES, and Baryon Acoustic Oscillations (BAO) to find the best-fit ranges of the free parameters. It is found that the constraint range of the model parameter ($a$) from the BBN study has a region of overlap with the ranges obtained from the MCMC analysis. Finally, we perform a statistical comparison between our model and the $\Lambda$CDM model using AIC and BIC method.