Supersymmetric Cosmology and Dark Energy

Abstract: Using the superfield approach we construct the n= 2 super-symmetric lagrangian for the FRW Universe with perfect fluid as matter fields.The obtained supersymmetric algebra allowed us to take the square root ofthe Wheeler-DeWitt equation and solve the corresponding quantum constraint.This model leads to the relation between the vacuum energy density and theenergy density of the dust matter.IntroductionThis paper is for the anniversary volume on the occasion 50th birthday, SergeiOdintsov, our colleague and friend who made an extensive contribution to thecosmological and astrophysics fields.Some time ago we have used the superfield formulation to investigate super-symmetric cosmologicalmodels [1]. The main idea is to extend the group of localtime reparametrization of the cosmological models to the local time supersym-metry which is a subgroup of the four dimensional space-time supersymmetry.This local supersymmetry procedure has the advantage that, by defining thesuperfields on superspace, all the component fields in a supermultiplet can bemanipulated simultaneously in a manner that automatically preserves super-symmetry. Besides, the fermionic fields are obtained in a clear manner as thesupersymmetric partners of the cosmological bosonic variables.