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FRW minisuperspace with local N=4 supersymmetry and self‐interacting scalar field
Author(s) -
Vargas Moniz P.
Publication year - 2003
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200310003
Subject(s) - superpotential , physics , supersymmetry , friedmann–lemaître–robertson–walker metric , minisuperspace , mathematical physics , superspace , supermultiplet , theoretical physics , quantum mechanics , quantum , quantum cosmology , cosmology , quantum gravity , supergravity
A supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analysed from a quantum cosmological perspective. The corresponding Lorentz and supersymmetry constraints allow to establish a system of first order partial differential equations from which solutions can be obtained. We show that this is possible when the superpotential is expanded in powers of a parameter λ≪1. At order λ 0 we find the general class of solutions, which include in particular quantum states reported in the current literature. New solutions are partially obtained at order λ 1 , where the dependence on the superpotential is manifest. These classes of solutions can be employed to find states for higher orders in λ. Our analysis further points to the following: ( i ) supersymmetric wave functions can only be found when the superpotential has either an exponential behaviour, an effective cosmological constant form or is zero; ( ii ) If the superpotential behaves differently during other periods, the wave function is trivial ( $\rm {\Psi{_{SUSY}^{FRW}}}$ = 0, i.e., no supersymmetric states). We conclude this paper discussing how our FRW minisuperspace (with N = 4 supersymmetry and invariance under time‐reparametrization) can be relevant concerning the issue of supersymmetry breaking.