In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory of axion field arising from Type IIB string theory compacted to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For a massless axion field, in all three formalisms, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

中文翻译：

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De Sitter空间中弦轴场真空波动引起的两点相关函数的宇宙光谱：量子纠缠作用的研究

在这项工作中，我们研究了量子纠缠对二分相关量子场理论系统中均方真空波动的两点相关函数和相关原始功率谱的影响。我们认为的场论是将IIB型弦理论压缩到四个维度而产生的有效轴场理论。我们用三种不同的方法来计算真空涨落的功率谱表达式，即（1）具有量子纠缠态的场算子扩展（FOE）技术，（2）具有混合量子态的简化密度矩阵（RDM）形式主义和（3） ）非纠缠态（NES）的方法。对于无质量的轴突场，在所有三种形式主义中，我们以领先的顺序再现了文献中众所周知的精确的尺度不变功率谱。我们观察到由于量子纠缠，这些形式论的次要术语是不同的。因此，这样的校正项打破了在超地平线范围内对FOE，RDM和NES形式主义进行分析时的简并性。另一方面，对于大量的轴场，我们会从尺度不变性那里获得一些偏差，并在小尺度上精确地量化功率谱的频谱倾斜。除此之外，对于无质量和大质量的轴场，我们发现了大规模纠缠的结果，表明FOE，RDM和NES的功率谱具有明显的特征。我们还发现，这样的大规模效应等于或大于de Sitter空间的曲率半径。最重要的是，在不久的将来，如果实验探索早期的宇宙现象，人们就能发现如此小的量子效应。