The utilization of Particle Physics for resolving several problems encountered in modern Cosmology has recently attracted much attention, since observational and experimental data are by now quite precise and place strong restrictions on theoretical models. In this scientific area, called usually Particle Cosmology, Cold Dark Matter (CDM) candidates are identified with certain stable particles, which are predicted by Supersymmetric (SUSY) models, whereas slowly evolving scalar fields can drive inflation. In this proposal we plan to restrict further observationally viable models of inflation combining them with other sectors of the theory related to some open problems of Particle Cosmology, such as SUSY breaking, CDM, and Baryogenesis via leptogenesis with constraints from unstable gravitino and neutrino oscillation parameters. Namely, adopting Induced-Gravity Inflation and unitarity safe versions of non-minimal inflation, we expect to shed light on the mechanism of SUSY breaking in the early universe working in the context of Supergravity and using a global R symmetry. One open possibility is the high scale SUSY which can be analyzed in conjunction with some mitigation of the gauge hierarchy problem, imposing the Veltman condition at a high scale. The stability of the electroweak vacuum for the higgs mass equal to 125.5 GeV will be also checked. In addition, we consider the embedding of non-minimal Higgs inflation in SUSY grand unified theories (GUTs) based on the Pati-Salam or the flipped SU(5) gauge groups and suggest scenaria which allow the activation of non-thermal leptogenesis. Moreover, we connect non-minimal inflation with CDM via ZDM, which is a type of CDM stabilized thanks to an unbroken discrete symmetry which may be remnant of a GUT. The implementation of our research requires model building, quantum field theoretic calculations and numerical and analytic investigation of the dynamical processes in the early Universe.