Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action

• Published in: Science China. Physics, mechanics & astronomy Vol. 58; no. 7; pp. 99 - 108
• Main Authors: He, DongShan, Cai, QingYu
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.07.2015; Springer Nature B.V
• Subjects: Astronomy; Classical and Continuum Physics; Hamilton-Jacobi equation; Heating; Observations and Techniques; Physics; Physics and Astronomy; Quantum tunnelling; Scalars; 希尔伯特; 普朗克长度; 爱因斯坦; 真空泡; 粒子产生; 膨胀过程; 量化; 雅可比方程; vacuum bubble; Einstein-Hilbert action; inflation; 079801
• ISSN: 1674-7348; 1869-1927
• DOI: 10.1007/s11433-015-5659-6

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quan- tization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions, including the exponential expansion solutions of the scalar factor a for the bubble. We show that exponential expansion of the bubble continues with a short period, no matter whether the bubble is closed, fiat, or open. The exponential expansion ends spontaneously when the bubble becomes large, that is, the scalar factor a of the bubble approaches a Planck length lp. We show that it is the quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.