Phantom without phantom or how the PT symmetry saves us from the Big Rip

Abstract

We consider the PT symmetric flat Friedmann model of two scalar fields with positive kinetic terms. While the potential of one ("normal") field is taken real, that of the other field is complex. We study a complex classical solution of the system of the two Klein-Gordon equations together with the Friedmann equation. The solution for the normal field is real while the solution for the second field is purely imaginary, realizing classically the "phantom" behavior. The energy density and pressure are real and the corresponding geometry is well-defined. The Lagrangian for the linear perturbations has the correct potential signs for both the fields, so that the problem of stability does not arise. The background dynamics is determined by an effective action including two real fields one normal and one "phantom". Remarkably, the phantom phase in the cosmological evolution is transient and the Big Rip never occurs. Our model is contrasted to well-known quintom models, which also include one normal and one phantom fields.

revised and enlarged version, to be published in Int. J. Mod. Phys. D, the title is changed

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• Constraining dark energy with gamma-ray bursts
• General solution of scalar field cosmology with a (piecewise) exponential potential
• Archimedean-type force in a cosmic dark fluid: III. Big Rip, Little Rip and Cyclic solutions
• Quantum cosmology of the multi-field scalar matter: some exact solutions
• Chameleon Cosmology Model Describing the Phantom Divide Line Crossing
• The relation between Geometry and Matter in classical and quantum Gravity and Cosmology