Motivated by the mathematic theory of split-complex numbers (or hyperbolicnumbers, also perplex numbers) and the split-quaternion numbers (orcoquaternion numbers), we define the notion of split-complex scalar field andthe split-quaternion scalar field. Then we explore the cosmic evolution ofthese scalar fields in the background of spatially flatFriedmann-Robertson-Walker Universe. We find that both the quintessence fieldand the phantom field could naturally emerge in these scalar fields.Introducing the metric of field space, these theories fall into a subclass ofthe multi-field theories which have been extensively studied in inflationarycosmology.
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