This research investigates the impact of modified gravity on cosmic scales, focusing on $f(Q)$ cosmology. By applying energy conditions, the study reconstructs various $f(Q)$ models, considering an accelerating Universe, quintessence, and a cosmological constant $\mathrm{\Lambda }$. Using up-to-date observational data, including the Supernova Pantheon sample and cosmic chronometer data, Hubble constants $H_0$ are estimated as $70.37_{-0.92}^{+0.84}$ km/s/Mpc (from $H(z)$ data) and $70.02_{-0.25}^{+0.44}$ km/s/Mpc (from pantheon compilation of SN Ia data). The matter energy density parameter (${\mathrm{\Omega }}_{0m}$) is calculated as $0.26_{-0.010}^{0.015}$ (OHD) and $0.27_{-0.014}^{0.025}$ (SN Ia). Furthermore, as a function of red-shift $z$, explicit expressions of $f(Q)$ and the EOS parameter $\omega$ are produced, and their graphical analysis describes the late time acceleration of the Universe without the usage of dark energy.

这项研究研究了修正引力对宇宙尺度的影响，重点是 $f(Q)$ 宇宙学。通过应用能量条件，该研究重建了各种 $f(Q)$ 模型，考虑了加速宇宙、本质和宇宙常数 $\mathrm{\Lambda }$ 。使用最新的观测数据，包括超新星万神殿样本和宇宙天文钟数据，哈勃常数 $H_0$ 估计为 $70.37_{-0.92}^{+0.84}$ km/s/Mpc（来自 $H(z)$ km/s/Mpc（来自 SN Ia 数据的万神殿编译）。物质能量密度参数（ ${\mathrm{\Omega }}_{0m}$ ）计算为 $0.26_{-0.010}^{0.015}$ （OHD）和 $0.27_{-0.014}^{0.025}$ （SN Ia）。此外，作为红移 $z$ 的函数，生成了 $f(Q)$ 和 EOS 参数 $\omega$ 的显式表达式，并且它们的图形分析描述了后期加速不使用暗能量的宇宙。