Dark Energy and the Cosmic Coincidence

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Dark Energy and the Cosmic Coincidence
Hyeong-Chan Kim(???), Jae-Weon Lee(KIAS),
Jungjai Lee(???)
hep-th/0702121
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Energy budget of the universe
Eq. of state
Acceleration Force
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Concordance model
,
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The Cosmological constant problem in detail
Quantum field
Huge sum of harmonic oscillators
UV cutoff a 1/Mp
L IR cutoff

• Naive expectation

Sum of all oscillators
Zero point Energy
But

• Observed

accidental coincidence or hidden law?
for

• 1) Why it is so small?
  Holographic principle
• 2) Why it is not zero?
  Entanglement energy
• 3) Why now(Cosmic coincidence problem)?
  Inflation

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Coincidence problem (why now?)
Why now question is meaningful only when now
(1010 years1060 tP) exists. -gt now exists
only when there was an inflation -gt the cosmic
coincidence might be related to inflation
Inflation with N60 solves the coincidence
problem (Li)
We confirm this with detailed calculation.
!
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Holographic principle

• all of information in a volume can be described
  by physics
• in the Area
• the maximum entropy in the volume is
  proportional to its Area.

QFT over-counts d.o.f.!
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Holographic dark energy
Only modes with Schwarzschild radius
survives (Cohen et al)
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Relation between a and L
UV
IR
L
a
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History of the universe
Accelerating expansion
Decelerating expansion
Inflation
Inflection time
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ta
tf
Inflationary phase (ti ltt lt tf) Hi Mi2/MP.
Number of efold N Hi(tf-ti)

• Power Law expansion phase (tgt tf)
• RDE (tlt ta) followed by DDE (tgt ta) . (Ignore
  MDE)
• ta is the inflection time R(ta)0.
• (tf/ta)1/2 is a constant.

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Event horizon and particle horizon
,
WMAP team
t
?
But who knows the end of the universe???
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Event horizon in Penrose Diagram
The horizon is a boundary surface such that any
light departing from outside the surface cannot
arrive the origin however time past.
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Evolution of the distance to the event horizon

• During the inflationary phase

The initial condition
Assumption The distance to the horizon is finite.
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Evolution of the distance to the event horizon

• Power law expansion phase

Comparing at ttf
Now, the inflection time ta is given by the
initial condition
For GUT scale inflation, tf 107, N 66, we have
ta 1060. ? Holographic Dark energy model solves
the cosmic coincidence problem.
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Another coincidence

• This relation also explains the strange
  coincidence of the expansion of the scale factor
  during the inflation R(tf)/R(ti) eN and that
  from the inflation to the present R(t0)/R(tf) eN
  .
• R(t) t1/2 before ta .

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Evolution of density
The dark energy density and the matter(radiation)
energy density. ??(t0)2x10-123 is comparable to
the observed value.
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Evolution of R_h and R
N65.69, n20, Mi1016GeV.
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Evolution of the equation state and ratio of the
Dark Energy
?? (t0)0.72, ??-0.93 are comparable to the
observed values.
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Conclusions
Is it just a miraculous coincidence or the
solution of the cosmological constant problem?
Thank you very much