CLASSICAL NATURE OF THE INFLATON FIELD WITH SELF-INTERACTION
CLASSICAL NATURE OF THE INFLATON FIELD WITH SELF-INTERACTION
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具有自相互作用的暴胀场的经典性质
DOI：
10.1143/ptp.100.547
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发表时间：
1997
影响因子：
--
通讯作者：
M. Sakagami
中科院分区：
文献类型：
--
作者：
Takahiro Tanaka;M. Sakagami
考虑自相互作用的影响，详细研究了>.∠4势的暴胀场的量子涨落动力学。我们发现自交互有效地将初始纯态驱动为混合态，这可以理解为统计系综。此外，发现平方场算子的期望值被转换为该统计系综的方差，而没有给出波动幅度的任何显着变化。这些结果验证了在宇宙原始波动幅度的标准评估中假设的量子到经典转变的假设。暴胀宇宙情景令人满意地解释了宇宙的各个方面，例如在微波背景辐射和大尺度结构中观察到的均匀性、各向同性和原始涨落的幅度。 1）然而，最近的几篇论文指出了对原始波动评估分析的不完整性。在大多数暴胀宇宙情景中，宇宙不均匀性的根源可以追溯到宇宙长度尺度加速膨胀所产生的暴胀场的量子涨落。在这种情况下，量子涨落的放大特征是状态向量的大量压缩。解释这个状态向量的困难在于，线性场算子的期望值没有表现出不均匀性，而是消失，而平方场算子的期望值变得非常大。通常，一旦感兴趣的波动规模超过哈勃视界尺度，人们就会将此量子态解释为就好像它相当于一个统计系综，在期望值的意义上与相应的量子算符具有相同的方差量。这里我们将基于这种临时分类分析的计算称为“标准计算”。为了证明标准计算的合理性，Starobinsky 2) 提出了一种宇宙暴胀情景的随机方法，随后许多作者进行了研究。 3)研究了定义为空间平均场算子期望值的阶次参数的演化。如果身体
Taking into account the effect of self-interaction, the dynamics of the quantum fluc tuations of the inflaton field with a >.¢4 potential is studied in detail. We find that the self-interaction efficiently drives the initial pure state into a mixed state, which can be understood as a statistical ensemble. Further, the expectation value of the squared field op erator is found to be converted into the variance of this statistical ensemble without giving any significant change in the amplitude of fluctuations. These results verify the ansatz of the quantum-to-classical transition that has been assumed in the standard evaluation of the amplitude of the primordial fluctuations of the universe. The inflationary universe scenarios satisfactorily explain various aspects of the universe, such as homogeneity, isotropy and the amplitude of the primordial fluctu ations observed in the microwave background radiation and in the large-scale struc ture. 1) However, an incompleteness in the analysis of the evaluation of the primordial fluctuations has been pointed out in several recent papers. In most of inflationary universe scenarios, the seed of the inhomogeneity of the universe is traced back to the quantum fluctuations of the inflaton field generated by the accelerated expansion of the cosmic length scale. In this context, the amplifica tion of quantum fluctuations is characterized by a large amount of squeezing of the state vector. A difficulty in interpreting this state vector exists in the fact that the expectation value of the linear field operator does not exhibit inhomogeneities, but rather vanishes, while that of the squared field operator becomes very large. Usually, one interprets this quantum state as if it were equivalent to a statistical ensemble which has the same amount of variance as the corresponding quantum operator in the sense of an expectation value, once the scale of the fluctuations of interest ex ceeds the Hubble horizon scale. Here we refer to the calculation based on this ad hoc classicalization ansatz as "the standard calculation" . In order to justify the standard calculation, a stochastic approach to the infla tionary universe scenario was proposed by Starobinsky 2) and later investigated by many authors. 3) The evolution of the order parameter that is defined as the ex pectation value of the spatially averaged field operator was studied. If the physical