The stochastic gravitational wave background from QCD phase transition in the framework of higher-order GUP

This work studies the impact of a new higher-order generalized uncertainty principle (GUP) on the stochastic gravitational wave background (SGWB) associated with a QCD-scale first-order phase transition. Assuming a strongly first-order transition at the QCD-scale as a phenomenological benchmark, the analysis shows that the sign and magnitude of the dimensionless deformation parameter ${\beta }_0$ play a crucial role. For negative ${\beta }_0$, the thermodynamic quantities of the radiation fluid develop a maximal temperature beyond which entropy and pressure vanish, and the SGWB spectrum exhibits divergent behavior at high temperatures, so this branch is discarded as phenomenologically inconsistent. For positive ${\beta }_0$, the higher-order GUP shifts the SGWB peak frequency towards lower values and slightly enhances the peak energy density, with the size of the effect controlled by ${\beta }_0$. For natural values ${\beta }_0=\mathcal{O}\left(1\right)$ the corrections at QCD temperatures are strongly suppressed, whereas larger benchmark values still compatible with existing experimental and cosmological bounds can induce appreciable shifts in the SGWB spectrum. A future detection of a QCD-scale first-order SGWB would therefore allow the framework developed here to be used to translate the measured signal into constraints on the higher-order GUP parameter, providing an indirect probe of quantum gravity effects.