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We investigate thoroughly the temporal evolution of the universe temperatureas a function of the Hubble parameter associated with the StochasticGravitational Wave (SGW), that formed at the cosmological QCD phase transitionepoch to the current epoch, within the Generalized Uncertainty Principle (GUP)framework. Here we use GUP version which provide constraints on the minimummeasurable length and the maximum observable momentum, that characterized by afree parameter $\alpha$. We study the effect of this parameter on the SGWbackground. We show that the effect can slightly enhance the SGW frequency inthe lower frequency regime which might be important in the detection of SGW inthe future GW detection facilities.

Minimal length, maximal momentum and stochastic gravitational waves spectrum generated from cosmological QCD phase transition