We discuss here a specific field-theory model, inspired from string theory, in which the generation of a matter-antimatter asymmetry in the Cosmos is due to the propagation of fermions in a non-trivial, spherically asymmetric (and hence Lorentz violating) gravitational background that may characterise the epochs of the early universe. The background induces different dispersion relations, hence populations, between fermions and antifermions, and thus CPT Violation (CPTV) already in thermal equilibrium. Species populations may freeze out leading to leptogenesis and baryogenesis. More specifically, after reviewing some generic models of background-induced CPTV in early epochs of the Universe, we consider a stringinspired scenario, in which the CPTV is associated with a cosmological background with torsion provided by the Kalb-Ramond (KR) antisymemtric tensor field of the string gravitational multiplet. In a four-dimensional space time this field is dual to a pseudoscalar "axion-like" field. The thermalising processes in this model are (right-handed) Majorana neutrino-antineutrino oscillations, which are induced in the presence of the KR axion background. These processes freeze out at a (high) temperature T-c >> m, where m is the Majorana neutrino mass, at which the KR background goes to zero or is diminished significantly, through appropriate phase transitions of the (string) universe. An additional, but equally important, role, of the KR field is that its quantum fluctuations and mixing with an ordinary axion, which couples to the Majorana neutrinos via appropriate Yukawa couplings, can also lead to the generation of a Majorana neutrino mass through quantum anomalies. This provides a novel way for generating neutrino masses, independent of the traditional seesaw mechanism.
