In the recently suggested modified non-metricity gravity theory with boundary term in a flat FLRW spacetime universe, dark energy scenarios of cosmological models are examined in this study. An arbitrary function, $f(Q,C)=Q+\alpha C^2$, has been taken into consideration, where $Q$ is the non-metricity scalar, $C$ is the boundary term denoted by $C=\ddot{R}-Q$, and $\alpha$ is the model parameter, for the action that is quadratic in $C$. The Hubble function $H(z)=H_0{[c_1{(1+z)}^n+c_2]}^{\frac{1}{2}}$, where $H_0$ is the current value of the Hubble constant and $n,c_1$ and $c_2$ are arbitrary parameters with $c_1+c_2=1$, has been used to examine the dark energy characteristics of the model. We discovered a transit phase expanding universe model that is both decelerated in the past and accelerated in the present, and we discovered that the dark energy equation of state (EoS) ${\omega }^{(de)}$ behaves as $(-1\le {\omega }^{(de)}<2)$. The Om diagnostic analysis reveals the quintessence behavior in the present and the cosmological constant scenario in the late-time universe. Finally, we calculated the universe’s current age, which was found to be quite similar to recent data.

在最近提出的修改后的非度量引力理论中，在平坦的 FLRW 时空宇宙中使用边界项，本研究对宇宙学模型的暗能量场景进行了研究。任意函数，$F（问,C）=问+\alpha C^2$，已被考虑在内，其中$问$是非度量标量，$C$是边界项，表示为$C=\ddot{右}-问$， 和$\alpha$是模型参数，对于二次的动作$C$。哈勃函数$H（z）=H_0{[C_1{（1+z）}^n+C_2]}^{\frac{1}{2}}$， 在哪里$H_0$是哈勃常数的当前值，$n,C_1$和$C_2$是任意参数$C_1+C_2=1$，已用于检查模型的暗能量特性。我们发现了一个过渡相膨胀宇宙模型，它在过去减速，现在加速，并且我们发现暗能量状态方程（EoS）${\omega }^{（de）}$表现为$（-1\le {\omega }^{（de）}<2）$。 Om 诊断分析揭示了当前宇宙的本质行为和晚期宇宙的宇宙学常数情景。最后，我们计算了宇宙当前的年龄，发现它与最近的数据非常相似。