This paper concerned with the effect of generalized uncertainty principle (GUP) on the stochastic gravitational wave (SGW) background signal that produced during first order cosmological QCD phase transition in early universe. A modified formula of entropy is used to calculate the temporal evolution of temperature of the universe as a function of the Hubble parameter. The pressure that results from the recent lattice calculations, which provides parameterizations of the pressure due to u, d, s quarks and gluons, with trace anomaly is used to describe the equation of state around QCD epoch. A redshift in the peak frequency of SGW at current epoch is calculated. The results indicate an increase in the frequency peak due to GUP effect, which improves the ability to detect it. Taking into account bubble wall collisions (BWC) and turbulent magnetohydrodynamics (MHD) as a source of SGW, a fractional energy density is investigated. It is found that the GUP effect weakens the SGW signal generated during QCD phase transition in comparison to its counterpart in the absence of GUP. These results support understanding the cosmological QCD phase transition and test the effectiveness of the GUP theory.

中文翻译：

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广义不确定性原理与随机引力波背景谱

本文关注的是广义不确定性原理（GUP）对早期宇宙一阶宇宙学QCD相变过程中产生的随机引力波（SGW）背景信号的影响。修改后的熵公式用于计算作为哈勃参数函数的宇宙温度的时间演化。由最近的晶格计算产生的压力，它提供了由于 u、d、s 夸克和胶子引起的压力的参数化，带有痕量异常，用于描述 QCD 时期周围的状态方程。计算当前时期 SGW 峰值频率的红移。结果表明，由于 GUP 效应，频率峰值增加，从而提高了检测它的能力。考虑到气泡壁碰撞 (BWC) 和湍流磁流体动力学 (MHD) 作为 SGW 的来源，研究了分数能量密度。发现与不存在 GUP 的情况相比，GUP 效应减弱了 QCD 相变期间产生的 SGW 信号。这些结果支持理解宇宙学 QCD 相变并测试 GUP 理论的有效性。