Studies in supersymmetry and cosmology

The discussion of three studies in supersymmetry and one on the generation of a baryon asymmetry in the early universe are presented. Specifically, the following results are obtained: (i) It is possible to confine a supersymmetric system of fields wthout breaking supersymmetry. This is done by introducing external sources coupled to the fields and selecting them in such a way as to respect the supersymmetric invariance of the action. (ii) In a simple non-linear supersymmetric model, the classical soliton-like solutions are found to be pure gauge transformations of the ordinary bosonic solitons. The solutions are found under the assumption that the fields have to belong to a global Grassmann algebra consistent with supersymmetry. (iii) In the study of the quantum corrections to the classical states of (ii) it is found that the Grassmann character of the classical fields imposes too many constraints which are incompatible with the quantization scheme. A new anticommuting algebra is proposed to substitute the Grassmann algebra. (iv) In the context of the very early universe (GUT era), a very simple model for baryon production is discussed. It is shown that, under standard assumptions, it is unrealistic to view the early universe as in adiabatical expansion, close to equilibrium throughout the baryon-generation era