In this thesis the role of a CPT violating (CPTV) background ﬁeld B0 is consid-ered as a mechanism for leptogensis. The beneﬁts of such an approach are that the lepton asymmetry can be produced via tree-level decays of a single heavy right-handed neutrino species that is already present in the see-saw mechanism. This model can then be considered as a minimal/economical extension by building on a current explanation for the light masses of the Standard Model (SM) neutrinos. The fact that the lepton asymmetry can be produced with tree-level processes further shows the simplicity of this approach. The Boltzmann equations are derived for such a system of particles interacting in the presence of the CPTV background and are solved semi-analytically in the high temperature regime above the decoupling temperature of equilibrium dynamics. Although the semi-analytical solution to the Boltzmann equations is only valid in the high temperature regime we are able to improve the validity of this solution to regions outside this regime by the method of Padé approximants. This method increases the conﬁdence of the high temperature regime solution when considering the point of decoupling. Our model of leptogenesis begins by considering a constant CPTV background and shows that in such a scenario a lepton asymmetry is indeed produced. The microscopic nature of the background ﬁeld is then investigated, by considering the Kalb-Ramond (KR) axion ﬁeld b(x)
, part of the massless multiplet of string theory. The CPTV background can be identiﬁed as the time derivative of this axion ﬁeld B0 = b
˙. The equations of motion of the KR axion ﬁeld yields the following temperature dependence for the CPTV background ﬁeld B0(T)∼T3
. Such a temperature dependence causes the ﬁeld to decrease to negligible levels beyond current experimental detection.