论文标题
lorentzian量子宇宙学在新颖的高斯 - 骨网络重力中，来自picard-lefschetz方法
Lorentzian quantum cosmology in novel Gauss-Bonnet gravity from Picard-Lefschetz methods
论文作者
论文摘要
在本文中，我们研究了四个时空维度的新型高斯河内（NGB）重力中经典和量子宇宙学的某些方面。从一般性的Friedmann-Lema-Robertson Walker（FLRW）开始，尊重均匀性和各向同性，在任意时空尺寸$ D $中，我们在四个时空维度中找到了理论的作用，其中限制$ d \ to 4 $在按零件进行集成后平稳地获得。高斯 - 骨网耦合的特殊重新缩放为$ d-4 $，导致对该行动的非平凡贡献。我们研究了一阶NGB耦合的运动方程系统。然后，我们继续将过渡概率从一个直接在洛伦兹签名中直接使用到另一个几何形状到另一个几何。我们利用WKB近似和Picard-Lefschetz（PL）理论的组合来实现我们的目标。 PL理论允许直接在洛伦兹（Lorentzian）签名中分析路径融合，而无需进行灯芯旋转。由于动作的非线性性质引起的并发症，我们计算了NGB耦合中一阶的过渡幅度。我们发现，即使分析是扰动进行的，也从NGB耦合到过渡幅度的非平凡校正。我们使用此结果来研究经典边界条件的情况。
In this paper we study some aspects of classical and quantum cosmology in the novel-Gauss-Bonnet (nGB) gravity in four space-time dimensions. Starting with a generalised Friedmann-Lemaître-Robertson Walker (FLRW) metric respecting homogeneity and isotropicity in arbitrary space-time dimension $D$, we find the action of theory in four spacetime dimension where the limit $D\to4$ is smoothly obtained after an integration by parts. The peculiar rescaling of Gauss-Bonnet coupling by factor of $D-4$ results in a non-trivial contribution to the action. We study the system of equation of motion to first order nGB coupling. We then go on to compute the transition probability from one $3$-geometry to another directly in Lorentzian signature. We make use of combination of WKB approximation and Picard-Lefschetz (PL) theory to achieve our aim. PL theory allows to analyse the path-integral directly in Lorentzian signature without doing Wick rotation. Due to complication caused by non-linear nature of action, we compute the transition amplitude to first order in nGB coupling. We find non-trivial correction coming from the nGB coupling to the transition amplitude, even if the analysis was done perturbatively. We use this result to investigate the case of classical boundary conditions.
