论文标题
De Sitter空间中的全息Beta功能
Holographic beta function in de Sitter space
论文作者
论文摘要
缓慢的滚动参数略微打破了宇宙的比例不变性。慢速滚动可能是随机步行的双重掷骰。我们研究了保形零模的分布函数。我们将Sitter Entropy $ S_ {DS} $带有共形Zeromode $ρ（ω）$的分布熵。我们已经为我们的假设提供了令人信服的支持。半经典的证据是，两者都是由重力耦合给出的$ 1/g = \ log n/2 $，其中$ g = g_nh^2/π$和$ n $是电子折叠数字。我们显示了重新归一化的分布函数遵守引力fokker-Planck方程（GFP）和Langevin方程。在高斯近似值下，它们归结为一个简单的一阶部分微分方程。相同的方程是通过通货膨胀时空中的热力学参数得出的。 GFP确定了宇宙熵的熵的演变。它与$ g $的$β$函数一致。我们发现GFP的两种类型的解决方案：（1）紫外线完整时空和（2）具有功率电势的通货膨胀时空。最大熵原则有利于场景：（a）出生的小$ε$，（b）通过通货膨胀而大大生长。我们喜欢传达de de二元性的新兴概念。通货膨胀宇宙：（散装/几何）是边界上随机时空（宇宙学）的双重，因为两者都是GFP的解决方案。
The scale invariance of the universe is slightly broken by slow roll parameters. It is likely the slow roll is dual to the random walk. We investigate the distribution function of the conformal zeromode. We identify de Sitter entropy $S_{dS}$ with the distribution entropy of the conformal zeromode $ρ(ω)$. We have collected convincing support on our postulate. The semiclassical evidence is that the both are given by the gravitational coupling $1/g=\log N/2$ where $g=G_NH^2/π$ and $N$ is the e-folding number. We show the renormalized distribution function obeys gravitational Fokker-Planck equation (GFP) and Langevin equations . Under the Gaussian approximation, they boil down to a simple first order partial differential equation. The identical equation is derived by the thermodynamic arguments in the inflationary space-time. GFP determines the evolution of de Sitter entropy of the universe. It coincides with $β$ function of $g$. We find two types of the solutions of GFP:(1) UV complete spacetime and (2) inflationary spacetime with power potentials. The maximum entropy principle favors the scenario: (a) born small $ε$ and (b) grow large by inflation. We like to convey the emerging notion of de Sitter duality. The inflationary universe: (bulk/geometrical) is dual to the stochastic space-time on the boundary (cosmological horizon ) as the both are the solutions of GFP.
