$f(Q, T)$引力中的宇宙学重构：$\u039b$CDM背景与物质 sector 依赖性
Cosmological Reconstruction in $f(Q, T)$ Gravity: $Λ$CDM Background and Matter-Sector Dependence
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中文总结 AI 辅助
研究$f(Q, T)$引力中对应$\u039b$CDM背景的宇宙学重构，通过一阶线性微分方程求解$f(Q)$的解析解，证实该框架可实现$\u039b$CDM膨胀历史。
中文摘要 AI 辅助
本研究探讨$f(Q, T)$引力的宇宙学重构问题，其中$Q$是非度量标量，$T$是能量动量张量的迹。考虑函数形式$f(Q,T)=f(Q)+\lambda T$，针对弗里德曼-勒梅特-罗伯逊-沃尔克（FLRW）宇宙中的$\u039b$CDM膨胀历史重构$f(Q)$的显式形式。利用物质守恒方程并将宇宙学量用$Q$表示，将重构问题转化为$f(Q)$的一阶线性微分方程。针对多种物质构型获得$f(Q)$的解析解，包括类尘物质、状态方程参数$\u03c9=-1/3$的理想流体，以及具有随时间变化的正压指数的非等熵理想流体。此外，还考虑重构的e-folding形式，以用e-folding参数考察宇宙演化。所得$f(Q)$的形式证实，$\u039b$CDM膨胀历史可在$f(Q,T)$框架内跨不同物质 sector 成功实现。
英文摘要
In this work, we investigate the cosmological reconstruction of $f(Q, T)$ gravity, where $Q$ is the non-metricity scalar and $T$ is the trace of the energy-momentum tensor. We consider the functional form $f(Q,T)=f(Q)+λT$ and reconstruct explicit forms of $f(Q)$ corresponding to the $Λ$CDM expansion history in Friedmann-Lemaître-Robertson-Walker (FLRW) universe. By employing the matter conservation equation and expressing the cosmological quantities in terms of $Q$, the reconstruction problem is formulated as a first-order linear differential equation for $f(Q)$. Analytical solutions for $f(Q)$ are obtained for various matter configurations, including dust-like matter, a perfect fluid with equation-of-state parameter $ω=-1/3$, and a nonisentropic perfect fluid with a time-dependent barotropic index. Additionally, an e-folding formulation of the reconstruction is considered to examine the cosmological evolution in terms of the e-folding parameter. The resulting forms of $f(Q)$ confirm that the $Λ$CDM expansion history can be successfully realized within the $f(Q,T)$ framework across diverse matter sectors.
