Abstract
Motivated by the mathematic theory of split-complex numbers (or hyperbolic numbers, also perplex numbers) and the split-quaternion numbers (or coquaternion numbers), we define the notion of split-complex scalar field and the split-quaternion scalar field. Then we explore the cosmic evolution of these scalar fields in the background of spatially flat Friedmann-Robertson-Walker Universe. We find that both the quintessence field and the phantom field could naturally emerge in these scalar fields. Introducing the metric of field space, these theories fall into a subclass of the multi-field theories which have been extensively studied in inflationary cosmology.
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