论文标题
量子宇宙学的缓慢倾斜
Slow-roll approximation in quantum cosmology
论文作者
论文摘要
In minimally coupled scalar field theories with a potential of the slow-roll type, we give a detailed description of the complex $O(4)$-symmetric solutions to Einstein's equations on the four-ball which contribute to the no-boundary amplitude $Ψ_\textsf{NB}(b,χ)$ for a closed universe to contain a round three-sphere spatial slice of size $b$ covered标量字段的均值为$χ$。我们的推导证明了Hartle，Hawking和Hertog在Phys中的预期结果。 Rev. D 77（2008）123537 [Arxiv：0803.1663]，使Vilenkin在Phys中的结果锐化。 Rev. D 37（1988）888在Minisuperspace的经典制度中，并使用了复杂的慢速近似。我们的技术适用于Hartle-Hawking和Vilenkin波函数，它们都预测了通货膨胀宇宙家族，但在半经典近似中，每个成员的重量均以指数差异。
In minimally coupled scalar field theories with a potential of the slow-roll type, we give a detailed description of the complex $O(4)$-symmetric solutions to Einstein's equations on the four-ball which contribute to the no-boundary amplitude $Ψ_\textsf{NB}(b,χ)$ for a closed universe to contain a round three-sphere spatial slice of size $b$ covered homogeneously with the scalar field at value $χ$. Our derivation demonstrates a result anticipated by Hartle, Hawking and Hertog in Phys. Rev. D 77 (2008) 123537 [arXiv:0803.1663], sharpens Vilenkin's result in Phys. Rev. D 37 (1988) 888 in the classical regime of the minisuperspace and makes use of a complexified slow-roll approximation. Our technique applies to both the Hartle-Hawking and Vilenkin wave functions, which both predict a family of inflationary universes but weight each member exponentially differently in the semiclassical approximation.
