We consider the chiral cosmological model consisting of two scalar fields minimally coupled to gravity. In the context of a Friedmann–Lematre–Robertson–Walker (FLRW) spacetime, and for massless fields in the presence of a cosmological constant, we present the general solution of the field equations. The minisuperspace configuration that possesses maximal symmetry leads to scenarios which—depending on the admissible value of the parameters—correspond to a quintessence, quintom or phantom case. The canonical quantization of the model retrieves this distinction as different families of quantum states. The crossing of the phantom line is related to the existence of free or bound states for the Casimir operator of the symmetry algebra of the fields. The classical singularity, which is present in the quintessence solution, is also resolved at the quantum level.

我们考虑由与重力最小耦合的两个标量场组成的手性宇宙学模型。在弗里德曼-勒马特-罗伯逊-沃克 (FLRW) 时空的背景下，对于存在宇宙常数的无质量场，我们提出了场方程的一般解。拥有最大对称性的微型超空间配置导致场景——取决于参数的可接受值——对应于典型、典型或幻影情况。该模型的规范量化将这种区别检索为不同的量子态族。虚线的交叉与场的对称代数的 Casimir 算子的自由或束缚态的存在有关。经典奇点，存在于精华解中，