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

TL;DR

This paper investigates how a higher-order generalized uncertainty principle affects the stochastic gravitational wave background from a QCD-scale phase transition, revealing potential for future quantum gravity constraints.

Contribution

It introduces the impact of a higher-order GUP on the QCD-scale SGWB, highlighting the role of the deformation parameter in modifying the spectrum.

Findings

Negative $eta_0$ leads to divergent SGWB spectrum, deemed phenomenologically inconsistent.

Positive $eta_0$ shifts the SGWB peak to lower frequencies and slightly increases peak energy density.

Larger $eta_0$ values can produce observable effects within experimental bounds.

Abstract

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.