We propose a new theoretical approach for a cosmological model, which starts from an exponential of the trace of the energy-momentum tensor-dependence on the gravitational action, to be summed to the Ricci scalar. We derive the referred field equations and Friedmann-like equations. We derive the scale factor, Hubble parameter and deceleration parameter, in terms of both time and redshift. In possession of those parameters in terms of the redshift, we confront their predictions with the observational Hubble dataset and the outcomes are pretty satisfactory so that the model can be seen as a new alternative to the cosmological constant problem. We also present the statefinder diagnostic and discuss profoundly the dynamical behaviour of the model.

中文翻译：

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$$R+e^T$$R+eT 宇宙学的可行性

我们为宇宙学模型提出了一种新的理论方法，该方法从能量-动量张量-依赖于引力作用的轨迹的指数开始，求和到 Ricci 标量。我们推导出所提及的场方程和类似弗里德曼的方程。我们根据时间和红移推导出比例因子、哈勃参数和减速参数。掌握了红移方面的这些参数，我们用哈勃观测数据集来面对他们的预测，结果非常令人满意，因此该模型可以被视为宇宙常数问题的新替代方案。我们还介绍了状态查找器诊断并深入讨论了模型的动态行为。