论文标题
在Sitter Spacetime中具有不对称自相互作用的无质量最小量子标量场
Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime
论文作者
论文摘要
无质量的最小耦合量子标量场，具有不对称的自相互作用，$ v（ϕ）= λϕ^4/4！+ βϕ^3/3！ $（带有$λ> 0 $的$）在$（3+1）$ - 尺寸通货膨胀de Sitter Spacetime中考虑。无论$β$的迹象如何，这种潜力都从下方界定。较早的计算主要考虑了四分之一的部分。这项研究背后的主要动机是评估$ v（ϕ）$和$ ϕ $的真空期望值，这两者都可能为负，因此可能导致对通货膨胀宇宙学恒定值的筛查。首先使用形式上的形式主义，对能量量张量中出现的立方势的重归于的量子校正是在两个环中计算的，在这种情况下，这是领先顺序。与上述宇宙学时代后期的结果相比，在两个循环下对动力学期限的量子校正是转向的。接下来，使用其中一些结果，我们通过计算$ {\ cal o}（β）$和$ {\ cal o}（λβ）$的ta t骨来计算$ ϕ $的重新归一化的真空期望值。由于De Sitter等轴测分解对数的出现，在这种情况下，t不能完全重新构成t，与平时不同。如预期的那样，所有这些结果表明，在宇宙学时代后期，对数具有世俗增长。接下来，我们使用最近提出的重态化组激发了形式主义来恢复扰动世俗效应，以计算宇宙学时代后期的非扰动$ \ langle ϕ \ rangle $。 $ \ langle ϕ \ rangle $ jut of $ v（ϕ）$的经典最小值=-3β/λ$的位置少于一个数量级。还提出了对这种$ \ langle ϕ \ rangle $可能筛选通货膨胀宇宙常数的估计。
Massless minimally coupled quantum scalar field with an asymmetric self interaction, $V(ϕ)=λϕ^4/4!+ βϕ^3/3! $ (with $λ>0$) is considered in the $(3+1)$-dimensional inflationary de Sitter spacetime. This potential is bounded from below irrespective of the sign of $β$. Earlier computations mostly considered the quartic part. Our chief motivation behind this study is to assess the vacuum expectation values of $V(ϕ)$ and $ϕ$, both of which can be negative, and hence may lead to some screening of the inflationary cosmological constant value. First using the in-in formalism, the renormalised quantum correction to the cubic potential appearing in the energy-momentum tensor is computed at two loop, which is the leading order in this case. The quantum correction to the kinetic term at two loop are subleading compared to the above result at late cosmological times. Next, using some of these results we compute the renormalised vacuum expectation value of $ ϕ$, by computing the tadpoles at ${\cal O}(β)$ and ${\cal O}(λβ)$. Due to the appearance of the de Sitter isometry breaking logarithms, the tadpoles cannot be completely renormalised away in this case, unlike the flat spacetime. All these results, as expected, show secularly growing logarithms at late cosmological times. We next use a recently proposed renormalisation group inspired formalism to resum perturbative secular effects, to compute a non-perturbative $\langle ϕ\rangle$ at late cosmological times. $\langle ϕ\rangle$ turns out to be approximately one order of magnitude less compared to the position of the classical minima $ϕ=-3β/λ$ of $V(ϕ)$. Estimation on the possible screening of the inflationary cosmological constant due to this $\langle ϕ\rangle$ is also presented.
