标题： 能量动量平方引力中的非奇异反弹模型 显示英文标题

标题： Non-Singular Bouncing Model in Energy Momentum Squared Gravity

摘要： 这项工作旨在研究各向同性流体配置$\mathcal{T}_{\alpha\beta}$和 Friedmann-Lemaître-Robertson-Walker 度规方案的宇宙弹跳特性。 这项工作是在新颖的$f(\mathcal{G},\mathcal{T}_{\alpha \beta} \mathcal{T}^{\alpha \beta})$引力下进行的，假设了一个具体模型，即$f(\mathcal{G},\mathcal{T}^2)=\mathcal{G}+\alpha \mathcal{G}^2+2\lambda \mathcal{T}^2$，其中$\alpha$和$\lambda$是常数，作为自由参数。 {项$\mathcal{G}$和$\mathcal{T}^2$分别作为高斯-博内不变量和能量-动量迹的平方项被包含在引力作用中，且与$\mathcal{T}^2=\mathcal{T}_{\alpha \beta} \mathcal{T}^{\alpha \beta}$成比例。}采用哈勃参数的具体函数形式，以提供宇宙学参数的演化。 一个著名的状态方程参数，$\omega(t)=-\frac{k \log (t+\epsilon )}{t}-1$被用来表示能量密度、物质压力和能量条件的动力学行为。 还提供了详细的图形分析以回顾弹跳现象。 此外，所有自由参数都以一种方式设定，使假设的哈勃参数起到弹跳解的作用，并确保能量条件的可行性。 最后，检查了弹跳模型的所有必要条件。 显示英文摘要

摘要： This work is concerned to study the bouncing nature of the universe for an isotropic configuration of fluid $\mathcal{T}_{\alpha\beta}$ and Friedmann-Lema\^{i}tre-Robertson-Walker metric scheme. This work is carried out under the novel $f(\mathcal{G},\mathcal{T}_{\alpha \beta} \mathcal{T}^{\alpha \beta})$ gravitation by assuming a specific model i.e, $f(\mathcal{G},\mathcal{T}^2)=\mathcal{G}+\alpha \mathcal{G}^2+2\lambda \mathcal{T}^2$ with $\alpha$ and $\lambda$ are constants, serving as free parameters. {The terms $\mathcal{G}$ and $\mathcal{T}^2$ served as an Gauss-Bonnet invariant and square of the energy-momentum trace term as an inclusion in the gravitational action respectively, and is proportional to $\mathcal{T}^2=\mathcal{T}_{\alpha \beta} \mathcal{T}^{\alpha \beta}$.} A specific functional form of the Hubble parameter is taken to provide the evolution of cosmographic parameters. A well known equation of state parameter, $\omega(t)=-\frac{k \log (t+\epsilon )}{t}-1$ is used to represent the dynamical behavior of energy density, matter pressure and energy conditions. A detailed graphical analysis is also provided to review the bounce. Furthermore, all free parameters are set in a way, to make the supposed Hubble parameter act as the bouncing solution and ensure the viability of energy conditions. Conclusively, all necessary conditions for a bouncing model are checked.