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

Gravitational Baryogenesis in Ho$\check{r}$ava-Lifshitz gravity