  In this work we intend to address the matter-antimatter asymmetry via the
gravitational baryogenesis mechanism in the background of a quantum theory of
gravity. We investigate this mechanism under the framework of
Ho$\check{r}$ava-Lifshitz gravity. We will compute the baryon-to-entropy ratio
in the chosen framework and investigate its physical viability against the
observational bounds. We also conduct the above study for various sources of
matter like scalar field and Chaplygin gas as specific examples. We speculate
that quantum corrections from the background geometry will lead to interesting
results.
