In this paper, we investigate the scalar field dark energy (DE) models within the context of $F(T,T_G)$ gravity. Scalar field models are known for their dynamic nature. Parameters in the dynamical equation of state are responsible for the acceleration of the cosmos in recent epochs. We determined that the power-law cosmology fits the OHD and Pantheon data nicely. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo (MCMC) method, we examine the three sets of the model parameters $H_0=63.26_{-0.97}^{+0.77}$$q=-0.039_{0.0029}^{+0.0029}$ obtained by 57 points of the $H(z)$ data, $H_0=70.93_{-0.0037}^{+0.0024}$$q=-0.3384_{0.0026}^{+0.0027}$ 1048 points of the Pantheon data and $H_0=70.76732_{-0.00088}^{+0.0030}$$q=-0.6478_{0.0075}^{+0.0093}$ by using joint data ($H(z)+\mathrm{\text{BAO}}+\mathrm{\text{Pantheon}}$), respectively. We solved the modified Einstein’s field equations by taking the bulk-viscosity component $\xi ={\xi }_0{\rho }^{\alpha }$. We also establish a correspondence between the $F(T,T_G)$ gravity model and scalar field DE models such as quintessence, $k$-essence, and DBI-essence. The nature of scalar fields and their corresponding potentials are being graphically analyzed. To check the validity of $F(T,T_G)$ gravity model, we also analyze the behavior of energy conditions.

在本文中，我们研究了标量场暗能量（DE）模型$F(\mathrm{时间},{\mathrm{时间}}_G）$重力。标量场模型以其动态特性而闻名。动态状态方程中的参数是近代宇宙加速的原因。我们确定幂律宇宙学非常适合 OHD 和 Pantheon 数据。使用贝叶斯分析和似然函数结合马尔可夫链蒙特卡罗 (MCMC) 方法，我们检查了三组模型参数$H_0=63。26_{-0。97}^{+0。77}$$q=-0。039_{0。0029}^{+0。0029}$获得57分$H(z）$数据，$H_0=70。93_{-0。0037}^{+0。0024}$$q=-0。3384_{0。0026}^{+0。0027}$1048 点的 Pantheon 数据和$H_0=70。76732_{-0。00088}^{+0。0030}$$q=-0。6478_{0。0075}^{+0。0093}$通过使用联合数据（$H(z）+\mathrm{\text{宝奥}}+\mathrm{\text{万神殿}}$）， 分别。我们通过采用体积粘度分量来求解修正的爱因斯坦场方程$\Psi ={\Psi }_0{\rho }^{\alpha }$。我们还建立了以下之间的对应关系：$F(\mathrm{时间},{\mathrm{时间}}_G）$引力模型和标量场DE模型等精髓，$k$-精华和DBI-精华。标量场的性质及其相应的势正在以图形方式进行分析。检查有效性$F(\mathrm{时间},{\mathrm{时间}}_G）$引力模型中，我们还分析了能量条件的行为。