In addition, combining our theoretical results with the observational data, we constraint the GUP parameter β 0, whose bound is between 8.4 × 10 ¹⁰ ∼ 1.1 × 10 ¹³. In particular, our results satisfy all of Sakharov's conditions, which indicates that the scheme of explaining baryon asymmetry in the framework of higher-order GUP is feasible. Those modifications break the thermal equilibrium of the Universe, and in turn produce a non-zero asymmetry factor η. It is demonstrated that the entropy and the Friedman equation of the Universe deviate from the original cases due to the effect of the higher-order GUP. In this paper, we investigate the gravitational baryogenesis for the generation of baryon asymmetry in the early Universe by using a new higher-order generalized uncertainty principle (GUP). However, the original mechanism of gravitational baryogenesis in the radiation-dominated era leads to the asymmetry factor η equal to zero, which indicates this mechanism may not generate a sufficient baryon asymmetry in the early Universe. The gravitational baryogenesis plays an important role in the study of baryon asymmetry. The CUORE experiment is a ton-scale array of $$\hbox $$ Λ Λ ¯ asymmetry is in agreement with and compatible in precision to the most precise previous measurement ⁴. The region in which ΩB and ΩDM can be explained simultaneously almost coincides with the area inside the red line, see . They were chosen independently for the blue and red lines displayed here. The CP-violating phases that maximize the efficiency of baryogenesis and DM production are different. In the region within the red line, thermal production of N1 (resonant and non-resonant) is sufficient to explain all the observed DM. In the region between the blue lines, a CP-asymmetry that explains the observed BAU can be produced during the thermal production of N2,3. The regions above the green lines of different shades are excluded by the NuTeV , CHARM and CERN PS191 experiments, as indicated in the plot. In the region below the black dotted BBN line, the lifetime of N2,3 particles in the early universe is larger than 0.1 s, leading to the danger that their decay spoils the agreement between BBN calculations and the observed light element abundances. In the regions below the black dashed ‘seesaw’ line there exists no choice of νMSM parameters that is in accordance with experimental constraints on the active neutrino mixing matrix. Constraints on the sterile neutrino mass M and mixing U² = tr(θ†θ) in the νMSM as found in for normal (upper panel) and inverted (lower panel) hierarchy of active neutrino masses.