In the current study, we have investigated a modified $f\left(Q\right)$-gravity theory in an anisotropic, locally rotationally symmetric (LRS) Bianchi type-I spacetime universe model. The arbitrary function $f\left(Q\right)=Q+\Lambda$, where $\Lambda$ is the “cosmological constant,” and $Q$ is the non-metricity scalar, has been taken into consideration. To obtain the exact solution of the modified field equations, we considered a dusty string fluid matter source and the shear scalar ($\sigma$) is proportional to the expansion scalar ($\theta$). The resultant Hubble function has been fitted with observational datasets $H\left(z\right)$ and SNe Ia datasets of apparent magnitude $m\left(z\right)$ in order to obtain the best fit values for the cosmological parameters. And utilizing these best fit values throughout the investigation, the many cosmic phenomena are examined. We have investigated the cosmographic coefficients like $H,q,j,s$ to see if an accelerated dual mode expanding dark energy (DE) model of the universe exists. Our Om diagnostic study shows that our universe model is a quintessence example of a dark energy model. We have also calculated the universe’s present age.

在当前的研究中，我们研究了一种改良的$F（问）$-各向异性、局部旋转对称 (LRS) Bianchi I 型时空宇宙模型中的引力理论。任意函数$F（问）=问+\Lambda$， 在哪里$\Lambda$是“宇宙常数”，并且$问$是非度量标量，已被考虑在内。为了获得修正场方程的精确解，我们考虑了尘埃弦流体物质源和剪切标量（$\sigma$) 与展开标量 ($\theta$）。由此产生的哈勃函数已与观测数据集相匹配$H（z）$和 SNe Ia 视星等数据集$米（z）$以获得宇宙学参数的最佳拟合值。在整个调查过程中利用这些最佳拟合值来检查许多宇宙现象。我们研究了宇宙学系数，例如$H,q,j,s$看看宇宙的​​加速双模膨胀暗能量 (DE) 模型是否存在。我们的 Om 诊断研究表明，我们的宇宙模型是暗能量模型的典型例子。我们还计算了宇宙目前的年龄。