String cosmology models predict a relic background of gravitational-wave (GW) radiation in the early universe. The GW energy spectrum of radiated power increases rapidly with the frequency, and therefore it becomes a potential and meaningful observation object for high-frequency GW detector. We focus on the stochastic background generated by superinflation in string theory and search for such signal in the observing data of Advanced LIGO and Virgo O1$\sim$O3 runs in a Bayesian framework. We do not find the existence of the signal, and thus put constraints on the GW energy density. Our results indicate that at $f=100\,\text{Hz}$, the fractional energy density of GW background is less than $1.7\times10^{-8}$ and $2.1\times10^{-8}$ for dilaton-string and dilaton only cases respectively, and further rule out the parameter space restricted by the model itself due to the non-decreasing dilaton and stable cosmology background ($\beta$ bound).

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使用 Advanced LIGO 和 Virgo 的 O1$\sim$O3 数据从弦宇宙学中搜索随机引力波背景

弦宇宙学模型预测了早期宇宙中引力波 (GW) 辐射的遗迹背景。辐射功率的引力波能谱随频率快速增加，因此成为高频引力波探测器潜在的、有意义的观测对象。我们关注弦理论中超膨胀产生的随机背景，并在贝叶斯框架下运行的 Advanced LIGO 和 Virgo O1$\sim$O3 的观测数据中寻找这种信号。我们没有发现信号的存在，因此对 GW 能量密度施加了限制。我们的结果表明，在 $f=100\,\text{Hz}$ 时，GW 背景的分数能量密度小于 $1.7\times10^{-8}$ 和 $2.1\times10^{-8}$ 对于膨胀- string 和 dilaton 分别只有情况，