We apply a very simple procedure to construct non-singular cosmological models for flat Friedmann universes filled with minimally coupled scalar fields or by tachyon Born–Infeld-type fields. Remarkably, for the minimally coupled scalar field and the tachyon field, the regularity of the cosmological evolution, or in other words, the existence of bounce, implies the necessity of the transition between scalar fields with standard kinetic terms to those with phantom ones. In both cases, the potentials in the vicinity of the point of the transition have a non-analyticity of the cusp form that is characterized by the same exponent and is equal to 23. If, in the tachyon model’s evolution, the pressure changes its sign, then another transformation of the Born–Infeld-type field occurs: the tachyon transforms into a pseudotachyon, and vice versa. We also undertake an analysis of the stability of the cosmological evolution in our models; we rely on the study of the speed of sound squared.

中文翻译：

---

正则弗里德曼宇宙和物质变换

我们应用一个非常简单的过程来构建充满最小耦合标量场或快子玻恩-因费尔德型场的平面弗里德曼宇宙的非奇异宇宙学模型。值得注意的是，对于最小耦合标量场和快子场来说，宇宙演化的规律性，或者说，弹跳的存在，意味着标准动力学项标量场向幻影动力学项标量场之间过渡的必要性。在这两种情况下，转变点附近的势具有尖点形式的非解析性，其特征在于相同的指数并且等于 23。如果在快子模型的演化中，压力改变其符号，然后发生玻恩-因菲尔德型场的另一种转变：快子转变为伪快子，反之亦然。我们还对模型中宇宙演化的稳定性进行了分析；我们依靠对声速平方的研究。