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Qing-Guo Huang

based on arXiv:1201.2443 (to appear in PLB) done with F.L.Lin

Institute of High Energy Physics, CASState Key Laboratory of Theoretical Physics,

Institute of Theoretical Physics, CAS

05/22/2012

Cosmological Constant, inflation

and no-cloning theorem

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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

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“Old” Cosmological Constant Problem

Why is the cosmological constant so small?

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Why is it comparable to nowadays matter energy density? (cosmic coincidence) (Anthropic???)

scale factor a(t)

Ener

gy d

ensit

y

cosmological constant

matter

radiation

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“New” Cosmological Constant Problem

Why is there a positive cosmological constant?

Why it is exponentially small compared to known fundamental energy scale?

How does it fit in a self-consistent quantum theory?

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“New” Cosmological Constant Problem

Why is there a positive cosmological constant?

Why it is exponentially small compared to known fundamental energy scale?

How does it fit in a self-consistent quantum theory?

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New conceptual insightsfrom

Quantum + Gravity

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Holography

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

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Black HoleM, Q, J

???Classical picture

Information loss paradox

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Black Hole

Hawking Radiation Quantum picture

e-

e+

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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)138Susskind, Thorlacius, Uglum, Phys.Rev.D 48(1993)3743

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Black Hole

complementarity principle

e-

e+

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de Sitter spacede Sitter space is the maximally symmetric vacuum solution

to Einstein equations with a positive cosmological constant Λ.

FRW coordinates

Static coordinates

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observer-dependent horizon

Gibbons, Hawking, Phys.Rev.D 15(1977)2738

R

observer

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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/0102077Banks, Fischler, Paban, JHEP 0212(2002)062

Dyson, Lindesay, Susskind, JHEP 0208(2002)045Susskind, hep-th/0204027

Dyson, Kleban, Susskind, JHEP 0210(2002)011

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Question:

How fast we can re-construct one qubit from Hawking radiation?

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Conventional local system

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 t1/2.

size ~ N1/D

power law

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Horizon: Fast scrambler

scrambling time for de Sitter space

Susskind, arXiv:1101.6048

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

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Alice-Bob thought experiment

During inflation

Alice crosses Bob’s event horizon at a moment tc.

Based on the complementarity principle, Bob can reconstruct it after the moment of tc+t* .

Bob

Alice

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Inflation must end in the early universe (tend). 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

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Question:

Whether can we clone a q-bit if inflation lasted long enough?

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How far a photon can travel in an expanding universe after inflation?

Since Lr,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.

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No-cloning theoremQuantum 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!

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Our proposal: Cosmological constant for preserving unitarity

Naively,

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A better estimation,

Assuming that the vacuum energy driving inflation instantaneously decays into radiation at the end of inflation, we roughly have

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Conclusions and Discussions 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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Thank You!