1. Spontaneous creation of the universe from nothing
蔡庆宇
中国科学院武汉物理与数学研究所
2019/4/26

4. Acknowledgements Dongshan He (何东山) Dongfeng Gao (高东峰)
Financial support from CAS.
报告分一下几个部分：1，什么是黑洞信息丢失问题；2.一些没有成功的方案；3.隧穿图像下的黑洞辐射；4.证明信息可以转移出黑洞；5.黑洞辐射谱特性研究；6.实验检验黑洞信息问题

5. Outline Motivation de Broglie-Bohm quantum trajectory theory
Vacuum inflation
Discussion

6. The expansion of the universe

7. Problems after Big Bang
Flatness
Horizon
Primordial monopole ……

8. Inflation theory
1. A. A. Starobinsky, JETP Lett. “Spectrum of relict gravitational radiation and the early state of the universe ”，
30, 682 (1979)
2. A. H. Guth, "The inflationary universe: A possible solution to the horizon and flatness problems,"
Phys. Rev. D 23, 347 (1981)
3. A. D. Linde, "A new inflationary universe scenario: A possible solution of the horizon, flatness,
homogeneity, isotropy and primordial monopole problems," Phys. Lett. B 108, 389 (1982).
4. A. Vilenkin, "The birth of inflationary universes," Phys. Rev. D 27, 2848 (1983).
5. S.W. Hawking,“The Quantum State of the Universe”, Nucl. Phys. B 239, 257 (1984)

9. Slow-roll scalar field model for inflation
A scalar field rolling down a potential energy hill.
What’s the scalar field?
A Higgs field?

10. A universe from nothing
Once a small true vacuum bubble is created, it will expand exponentially to become large. The early universe appears after the vacuum bubble becomes enough large.
When the vacuum bubble becomes very large, it stops growing up, and the inflation ends.

11. Outline Motivation de Broglie-Bohm quantum trajectory theory
Vacuum inflation
Discussion

12. de Broglie-Bohm quantum trajectory theory
Traditional quantum mechanics of Copenhagen has no the law of causation (Why EPR paradox?).
De Broglie, Bohm and Holland suggested a hidden variable theory for quantum mechanics.
They are equivalent mathematically, while with quite different explanation for the world.

13. de Broglie-Bohm quantum trajectory theory

14. Quantum trajectory in atomic physics

16. Outline Motivation de Broglie-Bohm quantum trajectory theory
Vacuum inflation
Discussion

17. The Wheeler-DeWitt equation for vacuum bubble
The action of the minisuperspace model,
Wheeler-DeWitt equation for true vacuum bubbles

18. Quantum trajectory theory to WDWE
We can get

19. Guidance relation
From
We can get
and
The guidance relation

20. For a closed bubble, k=1

21. The power for vacuum inflation
The quantum and classical potential (p=-2, or 4)
The summation of classical and quantum potential
The power for inflation
With

22. For an open bubble, k=-1
v(a)=-a2

23. For the flat bubble, k=0

24. Inflation ends

26. Outline Motivation de Broglie-Bohm quantum trajectory theory
Vacuum inflation
Discussion

27. After BICEP2
Testing scalar field?
Testing the quantum potential?

28. Media

29. “Last month saw the publication of a paper that may be as important to our understanding of the Big Bang as was the detection of gravitational waves. A team from the Wuhan Institute of Physics and Mathematics in China has made the first rigorous mathematical proof that the Big Bang could have spontaneously generated from nothing. The Wuhan team, led by Qing-yu Cai, developed new solutions to the Wheeler-DeWitt equation, which sought to combine quantum mechanics and general relativity in the mid-20th century. “

30. Summary
A small true vacuum bubble can expand exponentially no matter whether the bubble is closed, flat, or open (p=-2, or 4).
Quantum potential plays a role of the cosmological constant and provides the power for the exponential expansion.
Quantum trajectory method: Quantization of action. （Interdisciplinary Research）

31. Thank you!