论文标题
通货膨胀期间的近似$ u（1）$对称的角模式的相关长度
Correlation length of the angular mode for an approximate $U(1)$ symmetry during inflation
论文作者
论文摘要
众所周知，在DE Sitter膨胀背景下，光标度场获得了波动。这种波动可以通过Affleck-Dine机制提供重生的初始条件，其中通常假设$ U（1）_b $对称性。但是，以这种方式对巴里昂数量产生的解释与角模式的相关长度密切相关。在这项工作中，我们计算出具有大约$ u（1）$对称性的模型的角模式的相关长度。我们发现，对于一个巨大的几乎非相互作用的字段，角模式的相关长度取决于模型的质量参数，并且类似于$ h^{ - 1} \ exp（h^2/m^2）$。通过具有随机来源的Affleck-dine机制将此结果应用于baryogeny，我们发现，对于$ M \ ll \ Mathcal O（0.1）H $（假设$ n _*= 60 $）可以比我们当前的baryon horiz Horizon大小大得多，这样我们才能使用Baryon数量密度大得多，这样我们才能使用Baryon-raryon-ryon-ryon-ryon-ryon-ryon-ryon-ryon-rarion-rich区域。如果这不是事实，那么在早期，我们的宇宙将包括众多含巴能的富含巴里木和反巴里族的区域，平均巴里昂数字接近零。
It is known that a light scalar field obtains fluctuations in the de Sitter inflationary background. Such fluctuations could provide an initial condition for baryogenesis through the Affleck-Dine mechanism, where an approximate $U(1)_B$ symmetry is usually assumed. However, an interpretation of the baryon number generation in this way is strongly related to the correlation length of the angular mode. In this work, we calculate the correlation length of the angular mode for a model exhibiting an approximate $U(1)$ symmetry. We find that for a massive nearly non-interacting field, the correlation length of the angular mode is determined by the mass parameter of the model and it is similar to $H^{-1} \exp(H^2/m^2)$. Applying this result to baryogenesis via the Affleck-Dine mechanism with a stochastic origin, we find that only for $m \ll \mathcal O(0.1) H$(assuming $N_*=60$) can the correlation length of the baryon number density be much larger than our current horizon size, such that we live in the baryon-rich region. If this is not true, in the early time our universe would consist of numerous patches of baryon-rich and anti-baryon-rich regions with the average baryon number being nearly zero.
