标题： de Sitter背景下无质量自相互作用标量场的平衡态 显示英文标题

标题： Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background

摘要： 研究了具有小质量的标量场在de Sitter背景下的每周自相互作用行为（包括双井相互作用势的情况）。 证明了在存在相互作用的情况下，标量场具有de Sitter不变的平衡量子态，无论质量项的符号为何。 进一步发展了随机方法，提出了一种计算de Sitter背景下标量场任意异常大的相关函数的方法，并给出了平衡态下两点相关函数、相关时间和空间物理相关半径的表达式。 后者不随时间变化，这意味着在平衡态下，尽管de Sitter时空的 $t=const$ 超曲面在膨胀，标量场正负值区域的特征尺寸平均而言保持不变。 显示英文摘要

摘要： Behaviour of a weekly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). Existence of the de Sitter invariant equilibrium quantum state of the scalar field in the presence of interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculation of an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in the equilibrium state, correlation time and spatial physical correlation radius are presented. The latter does not depend on time that implies that the characteristic size of domains with positive and negative values of the scalar field remains the same on average in the equilibrium state in spite of the expansion of the $t=const$ hypersurface of the de Sitter space-time.