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Power-law expansion cosmology in Schr\"odinger-type formulation
We investigate non-linear Schr\"{o}dinger-type formulation of cosmology of
which our cosmological system is a general relativistic FRLW universe
containing canonical scalar field under arbitrary potential and a barotropic
fluid with arbitrary spatial curvatures. We extend the formulation to include
phantom field case and we have found that Schr\"{o}dinger wave function in this
formulation is generally non-normalizable. Assuming power-law expansion, , we obtain scalar field potential as function of time. The
corresponding quantities in Schr\"{o}dinger-type formulation such as
Schr\"{o}dinger total energy, Schr\"{o}dinger potential and wave function are
also presented.Comment: 9 pages, 5 figures, Revtex 4, accepted by Astroparticle Physics, more
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