论文标题
在宇宙学有效的领域理论中出现的不稳定性：何时以及如何？
Instabilities Appearing in Cosmological Effective Field theories: When and How?
论文作者
论文摘要
非线性偏微分方程出现在许多物理领域中，我们在这里研究了一个典型的方程式，人们在有效的现场理论（EFT）中发现源自宇宙学研究。特别是，我们对等式$ \ partial_t^2 u（x，t）=α（\ partial_x u（x，x，t））^2 +β\ partial_x^2 u（x，t）$ in $ 1 +1 $尺寸。众所周知，在有限的时间（$α> 0 $）的有限时间内解决该方程式的解决方案。我们研究这种分歧的性质，这是参数$α> 0 $和$β\ ge0 $的函数。即使$β$与可能相信的很大，差异也不会消失（注意，由于我们考虑固定的初始数据，因此$α$和$β$无法缩放）。但是，当$α$固定时，出现$β$的增加将需要更长的时间。我们注意到有两种类型的差异，我们讨论了这两个差异作为参数选择的函数。除非对相应的方程式进行了修改，否则不可避免的爆炸是不可避免的。我们的结果扩展到$ 3+1 $尺寸。
Nonlinear partial differential equations appear in many domains of physics, and we study here a typical equation which one finds in effective field theories (EFT) originated from cosmological studies. In particular, we are interested in the equation $\partial_t^2 u(x,t) = α(\partial_x u(x,t))^2 +β\partial_x^2 u(x,t)$ in $1+1$ dimensions. It has been known for quite some time that solutions to this equation diverge in finite time, when $α>0$. We study the nature of this divergence as a function of the parameters $α>0 $ and $β\ge0$. The divergence does not disappear even when $β$ is very large contrary to what one might believe (note that since we consider fixed initial data, $α$ and $β$ cannot be scaled away). But it will take longer to appear as $β$ increases when $α$ is fixed. We note that there are two types of divergence and we discuss the transition between these two as a function of parameter choices. The blowup is unavoidable unless the corresponding equations are modified. Our results extend to $3+1$ dimensions.
