1. Qing-Guo Huang based on arXiv:1201.2443 (to appear in PLB) done with F.L.Lin Institute of High Energy Physics, CAS State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS 05/22/2012 1

2. 2 Supernova cosmology project collaboration, S. Perlmutter et al, APJ 517(1999)565 Supernova search team collaboration, A.G. Riess et al, APJ 116(1998)1009

3. 3

4. 4

5.  Why is the cosmological constant so small? 5

6.  Why is it comparable to nowadays matter energy density? (cosmic coincidence) (Anthropic???) scale factor a(t) cosmological constant matter radiation 6

7.  Why is there a positive cosmological constant? 7  Why it is exponentially small compared to known fundamental energy scale?  How does it fit in a self-consistent quantum theory?

8.  Why is there a positive cosmological constant? 8  Why it is exponentially small compared to known fundamental energy scale?  How does it fit in a self-consistent quantum theory?

9. 9

10. 10 ‘t Hooft, gr-qc/9310026 Susskind, hep-th/9409089

11. Black Hole M, Q, J Black Hole M, Q, J ??? Classical picture 11

12. Black Hole Hawking Radiation Quantum picture 12 e-e- e+e+

13. Complementarity principle for black hole: The process of formation and evaporation of a black hole, as viewed by a distant observer, can be described entirely within the context of standard quantum theory. In particular, there exists a unitary S-matrix which describes the evolution from infalling matter to outgoing Hawking radiation. No information loss. ‘t Hooft, Nucl.Phys.B 335(1990)138 Susskind, Thorlacius, Uglum, Phys.Rev.D 48(1993)3743 13

14. Black Hole complementarity principle 14 e-e- e+e+

15. de Sitter space is the maximally symmetric vacuum solution to Einstein equations with a positive cosmological constant Λ. FRW coordinates Static coordinates 15

16. observer-dependent horizon Gibbons, Hawking, Phys.Rev.D 15(1977)2738 16 R observer

17. Similar to black hole, Complementarity principle for de Sitter space: To an observer who never crosses the horizon, the horizon can absorb, thermalize and re-emit all information that falls on it. No information loss. Banks, Fischler, hep-th/0102077 Banks, Fischler, Paban, JHEP 0212(2002)062 Dyson, Lindesay, Susskind, JHEP 0208(2002)045 Susskind, hep-th/0204027 Dyson, Kleban, Susskind, JHEP 0210(2002)011 17

18. Question: How fast we can re-construct one qubit from Hawking radiation? 18

19.  Suppose the degrees of freedom are arranged in a D dimensional system.  The total number of d.o.f scales with N.  Awaring of thermalization is process of diffusion in which the initial perturbation spreads in space to a distance of order t 1/2. size ~ N 1/D power law 19

20. 20 scrambling time for de Sitter space Susskind, arXiv:1101.6048

21. 21 inflation  Flatness, horizon, structure formation, ……  It must end in the early universe.

22. 22 During inflation  Alice crosses Bob’s event horizon at a moment t c.  Based on the complementarity principle, Bob can reconstruct it after the moment of t c +t *. Bob Alice

23. 23  Inflation must end in the early universe (t end ). At the end of inflation, the proper distance between Alice and Bob is  The minimum distance for the case in which Bob can re-construct the qubit from Hawking radiation during inflation is given by

24. 24 Question: Whether can we clone a q-bit if inflation lasted long enough?

25. 25  How far a photon can travel in an expanding universe after inflation?  Since L r,m -> ∞ in a decelerating universe, Bob can get the qubit carried by Alice after inflation sooner or later, and therefore the qubit can be cloned.

26. 26 Quantum superposition + Unitarity Wootters and Zurek, Nature 299(1982)802 two arbitrary states: If we can clone an unknown quantum state, if U is unitary This is not the case for two arbitrary states!

27. 27 Naively,

28. 28 A better estimation, Assuming that the vacuum energy driving inflation instantaneously decays into radiation at the end of inflation, we roughly have

29. 29  A positive cosmological constant is postulated to preserve the unitarity in quantum mechanics if a long-lasting inflation happened in the early universe.  The scale of cosmological constant can be exponentially small compared to inflation scale.  In fact, a similar argument for more general dark energy is also applicable. Our arguments cannot be used to select dark energy models.  The fate of our universe should be in a state with accelerating expansion.

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