Exact inflationary cosmologies with exit: from an inflaton complex field to an `anti-inflaton' one

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We study Barrow's method for the case of a complex scalar field and present exact solutions to Einstein's equations. There are two results from the investigation of these solutions. First, the complex fields give us an inflationary cosmology with a natural exit as distinct from models with a real inflaton. Second, the complex inflaton leads to very small inflation. We suppose that a satisfactory model may contain two scalar fields: one real and one complex. The real field (the inflaton) must lead to power-law inflation and the complex field (the `anti-inflaton') must lead to exit from inflation. So the complex scalar field can be useful in the hybrid models as the field that triggers the end of inflation.

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