AI 中文总结
该研究在f(R,T)引力框架下提出非奇异对数弹跳宇宙学模型，通过假设对数标度因子实现平滑弹跳，验证其经典稳定性，获得耦合参数约束，发现其热力学行为在弹跳点处存在奇异。
AI 中文摘要
我们在修正f(R,T)引力框架下的空间平坦Friedmann-Robertson-Walker宇宙中，提出了一个非奇异弹跳宇宙学模型。假设一个随时间变化的对数标度因子，以实现从收缩相到膨胀相的平滑过渡，而不会遇到初始奇点。基于该假设，针对模型参数和物质-几何耦合参数的不同选择，获得了哈勃参数、减速参数、能量密度和压强的动力学演化，以确认成功弹跳的发生。我们还研究了有效状态方程参数，以表征不同演化阶段的宇宙流体。讨论了实现弹跳行为所必需的能量条件的违反情况。利用声速平方研究了模型的稳定性，发现其在允许的参数空间内保持为正，表明模型具有经典稳定性。此外，通过要求能量密度为正、压强为负以及宇宙演化可行，获得了对物质-几何耦合参数的约束，且该耦合参数的宇宙学约束与当前可用的致密天体约束兼容。通过检验热力学广义第二定律，研究了模型的热力学行为：总熵产生率在收缩相期间保持为负，在膨胀相期间符号变为正，但在弹跳点处变为奇异，反映了过渡阶段标准热力学描述的失效。
英文摘要
We present a nonsingular bouncing cosmological model in the framework of modified $f(R,T)$ gravity within a spatially flat Friedmann--Robertson--Walker universe. A logarithmic time-dependent scale factor is assumed to realize a smooth transition from a contracting phase to an expanding phase without encountering an initial singularity. Based on this assumption, the dynamical evolution of the Hubble parameter, deceleration parameter, energy density, and pressure is obtained for various choices of the model and the matter--geometry coupling parameter to confirm the occurrence of a successful bounce. The effective equation of state parameter is examined to characterize the cosmic fluid during different evolutionary phases. The violation of energy conditions, necessary for the realization of the bouncing behavior, is also discussed. The stability of the model is investigated using the squared speed of sound and is found to remain positive within the allowed parameter space, indicating classical stability. Furthermore, constraints on the matter--geometry coupling parameter are obtained by demanding positive energy density, negative pressure, and a viable cosmological evolution. The obtained cosmological constraint on the coupling parameter is also shown to be compatible with the currently available compact-object constraints. The thermodynamic behavior of the model is examined by testing the generalized second law of thermodynamics. The total entropy production rate remains negative during the contracting phase and changes its sign to positive during the expanding phase. However, it becomes singular at the bouncing point, reflecting the breakdown of the standard thermodynamic description during the transition phase.
Comments16 pages, 9 figures (Accepted for publication in Nuclear Physics B)
