  We investigate the generation of the baryon asymmetry within the framework of
cosmological gra\-vi\-ta\-tional particle production, employing the Bogoliubov
approach. We examine two well-known baryogenesis scenarios, namely baryogenesis
in Grand Unified Theories (GUT) and leptogenesis, while considering reheating
temperatures sufficiently low for thermal processes to be negligible.
Considering $\alpha-$attractor T-models for the inflaton potential, we
demonstrate that GUT baryogenesis from scalar decays can be successful across a
large range of conformal couplings with gravity, without necessitating
substantial levels of CP violation. In the case of leptogenesis, we find that
the reheating temperature should be $T_{\rm RH}\lesssim 10^{6}~{\rm GeV}$ for
right-handed neutrino masses $M_1 \lesssim 6 \times 10^{12}~{\rm GeV}$ to
generate the observed asymmetry.
