Slow-roll, acceleration, the Big Rip and WKB approximation in NLS-type formulation of scalar field cosmology

Abstract

Aspects of non-linear Schrödinger-type (NLS) formulation of scalar (phantom) field cosmology on slow-roll, acceleration, WKB approximation and Big Rip singularity are presented. Slow-roll parameters for the curvature and barotropic density terms are introduced. We reexpress all slow-roll parameters, slow-roll conditions and acceleration condition in NLS form. WKB approximation in the NLS formulation is also discussed when simplifying to linear case. Most of the Schrödinger potentials in NLS formulation are very slowly-varying, hence WKB approximation is valid in the ranges. In the NLS form of Big Rip singularity, two quantities are infinity in stead of three. We also found that approaching the Big Rip, $w_{\mathrm{eff}}\to -1+2/3q$, $(q<0)$ which is the same as effective phantom equation of state in the flat case.

[7 pages, no figure, more reference added, accepted by JCAP]

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Cited by in corpus (4)

• Observational constraints on phantom power-law cosmology
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• Phantom expansion with non-linear Schrödinger-type formulation of scalar field cosmology
• Non-linear Schrödinger-type formulation of scalar field cosmology: two barotropic fluids and exact solutions