论文标题
高斯bonnet重力的Lorentzian路径综合
Surprises in Lorentzian path-integral of Gauss-Bonnet gravity
论文作者
论文摘要
在本文中，我们研究了四个时空维度中的小苏普斯空间近似中高斯重力的Lorentzian路径综合性，并研究了从一种构型到另一种构型的过渡幅度。过去的研究激发了我们在初始边界上施加诺伊曼边界条件，因为它们导致了波动的稳定行为。过渡幅度是精确计算的，同时结合了来自Gauss Bonnet重力部门的非平凡贡献。涉及使用Picard-Lefschetz方法的鞍点分析使我们能够进一步了解过渡幅度的性质。小规模的宇宙本质上是欧几里得的，这是由指数上升的波功能所示。它达到了峰值，之后波功能变为振荡，表明时间的出现和宇宙的洛伦兹阶段。当宇宙的波功能完全独立于初始条件时，我们还注意到一个有趣的假设情况，当宇宙常数和高斯 - 骨网耦合具有特定的关系时，这种情况就会发生。但是，这并不意味着初始动量是任意的，因为它需要固定为特定的值，该值是通过要求在初始时间定期进行定期和波动的稳定性而选择的。
In this paper we study the Lorentzian path-integral of Gauss-Bonnet gravity in the mini-superspace approximation in four spacetime dimensions and investigate the transition amplitude from one configuration to another. Past studies motivate us on imposing Neumann boundary conditions on initial boundary as they lead to stable behaviour of fluctuations. The transition amplitude is computed exactly while incorporating the non-trivial contribution coming from the Gauss-Bonnet sector of gravity. A saddle-point analysis involving usage of Picard-Lefschetz methods allow us to gain further insight of the nature of transition amplitude. Small-size Universe is Euclidean in nature which is shown by the exponentially rising wave-function. It reaches a peak after which the wave-function becomes oscillatory indicating an emergence of time and a Lorentzian phase of the Universe. We also notice an interesting hypothetical situation when the wave-function of Universe becomes independent of the initial conditions completely, which happens when cosmological constant and Gauss-Bonnet coupling have a particular relation. This however doesn't imply that the initial momentum is left arbitrary as it needs to be fixed to a particular value which is chosen by demanding regularity of Universe at an initial time and the stability of fluctuations.
