论文标题
在通货膨胀de Sitter时空中，无质量的最小量子标量与$ V（ϕ）= λϕ^4/4！+βd^3/3！$的非扰动分析
Non-perturbative analysis for a massless minimal quantum scalar with $V(ϕ)=λϕ^4/4!+βϕ^3/3!$ in the inflationary de Sitter spacetime
论文作者
论文摘要
我们认为具有不对称的自相互作用的无质量，最小的量子标量场理论，$ v（ϕ）= λϕ^4/4！+β+βϕ^3/3！$（$λ> 0 $）在通货膨胀的设备时段。电势从下方界定。虽然$β= 0 $的情况已经进行了很好的研究，但采用这种混合潜力的动机与以下事实：它可能会产生有限的负真空期望值为$ v（ϕ）$以及$ ϕ $的事实，导致了膨胀的综合体常数$λ$的动态性筛选，并在最初的条件下= 0 = 0 = 0 = 0. \ rangle $。在这项工作中，我们首先使用较晚时间，非扰动和红外有效的随机形式主义，计算$ ϕ，\，ϕ^2 $和$ v（ϕ）$的真空期望值。估计对通货膨胀$λ$的反应。我们还使用$ \ langle ϕ^2 \ rangle $来计算标量场的动态生成质量。接下来，我们使用量子场理论计算$ \ langleϕ^2 \ rangle $，使用schwinger-keldysh形式主义，使用量子场理论在一个和两个循环下以一个和两个循环来计算$ \ langle。这些结果表明，随着宇宙学时间的增长，非扰动的世俗对数。使用下一步，我们最近提出的重态化小组启发了形式主义，我们试图找出一个重新召集的$ \ langleϕ^2 \ rangle $。我们已经能够重新恢复其中的某些部分，其中仅包含当地自我能源的贡献。计算相应的动态生成的质量。随机和量子场理论的比较表明，尽管它们具有相似的定性行为，但它们在数值上有所不同。讨论了这种定量不匹配的可能原因。通过两种形式主义发现的结果，强烈的非古典作用的表现都得到了强调。
We consider a massless, minimally coupled quantum scalar field theory with an asymmetric self interaction, $V (ϕ) = λϕ^4/4!+βϕ^3/3!$ ($λ>0$) in the inflationary de Sitter spacetime. The potential is bounded from below. While the $β=0$ case has been much well studied, the motivation behind taking such a hybrid potential corresponds to the fact that it might generate finite negative vacuum expectation values of $V(ϕ)$ as well of $ϕ$, leading to some dynamical screening of the inflationary cosmological constant $Λ$, at late times, with the initial conditions, $\langle ϕ\rangle=0=\langle V(ϕ) \rangle $. In this work we first compute the vacuum expectation values of $ϕ,\, ϕ^2$ and $V(ϕ)$, using the late time, non-perturbative and infrared effective stochastic formalism. The backreactions to the inflationary $Λ$ are estimated. We also compute the dynamically generated mass of the scalar field using $\langle ϕ^2 \rangle$. We next compute $\langleϕ^2\rangle$ using quantum field theory with respect to the initial Bunch-Davies vacuum at one and two loops, using the Schwinger-Keldysh formalism. These results show non-perturbative secular logarithms, growing with the cosmological time. Using next a recently proposed renormalisation group inspired formalism, we attempt to find out a resummed $\langleϕ^2\rangle$. We have been able to resum some part of the same which contains contributions only from the local self energy. The corresponding dynamically generated mass is computed. Comparison of the stochastic and the quantum field theory results shows that they differ numerically, although they have similar qualitative behaviour. Possible reasons for such quantitative mismatch is discussed. The manifestation of strong non-classical effects in the results found via both the formalisms has been emphasised.
