pisin chen- cosmological constant as a manifestation of the hierarchy

8/3/2019 Pisin Chen- Cosmological Constant as a Manifestation of the Hierarchy

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Cosmological Constant as aManifestation of the Hierarchy

PC and Je-An Gu, astro-ph/0409238 (2004)PC, astro-ph/06112378 (2006)

PC and Je-An Gu, in preparation (2007)

Pisin Chen

Department of Physics and Institute of AstrophysicsNational Taiwan University

CosPA2007 Symposium, November 13-15, 2007 Taipei, Taiwan



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Cosmological Constant Problem

1. The smallness problemWhy is CC << SM?

2. The concordance problemWhy is Ω Λ

~ Ωm ~ Ωtotal ?

Coined by Michael Turner as the

“Nancy Keragan problem: Why me, why now?”



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Another Hierarchy in Physics

• Gravity is much weaker, or Planck scale (1019 GeV),

much larger, than that of SM gauge interactions:M Pl

M SM

Two well-known solutions:ADD : large (but flat) extra dimensionRS : warped geometry

~ 1016 .



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A Numerical Coincidence

• A remarkable numerical coincidence,

• Perhaps not accidental but implies a deeper connection:

• Caution: Unlike the 1st hierarchy that links 4 fundamental

interaction strengths, DE must be a secondary, derivedquantity.



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Analogy in Atomic Physics

• Bohr atom• Fundamental energy

scale in Schrodinger

equation: me

• Ground state energysuppressed by 2powers of finestructure constant

• Dark energy• Fundamental energy

scale in quantum

gravity: M Pl

• Dark energysuppressed by 2powers of “gravityfine structure

constant”



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Randall-Sundrum Warped Geometry

Y=0 Y=π

Visible brane Hidden branedx μ dx ν



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Randall-Sundrum Warped Geometry

Y=0 Y=π

Visible brane Hidden brane

dx μ dx ν

e-kay

M SM

~TeV

M Pl

~ 1016TeV

Weakness of gravity = smallness of graviton wavefunction at visible brane

~ 10-16

k~M Pl ,

M SM M Pl

= e-π ka



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Casimir Effect

QED vacuum fluctuations



10(a ∞)a

Casimir Energy

ρ casimir = ρ vac (| |) − ρ vac(a→∞)∞ a-4



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Casimir Energy vs. Vacuum Energy

py

p x

• Casimir energy: p x

= ‒ ρ, py

> 0.

py

cannot be tuned away.

• Conventional vacuum energy (brane tension): p x

= ‒ ρ, py

= 0.

py

can in principle be tuned away.



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Strategy for the Smallness of Dark Energy

Supersymmetry Brane World

BUT SUSY only on the brane

= 0vac:

boson fermion

+

ρ vac(4) ~ (mn

- mn-1 )Δmn

-2



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• It can be shown that this will induce a KK

gravitino mass-shift for the nth mode

• Graviton, on the other hand, remains massless

(at tree-level).



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• On the TeV brane,

• The normalization constant is

• Therefore on the TeV brane



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• By definition, the Casimir energy under SUSY

breaking is

which is

The mass shift can be show nto scale as



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Summary• Dark energy may very well be a cosmologicalconstant.• The numerical coincidence between the SM-Planck

and the SM-DE hierarchies implies a deeperconnection between the two.

• If true, the well-known smallness and concordanceproblems of CC can be understood.

• Casimir energy in a SUSY-breaking brane world

may provide the key to the solution of DE problem.• It is remarkable that, guided by our Ansatz, wemanage to construct a model for CC whose energy

scale is indeed suppressed by 2 powers of the“gravity fine structure constant” (the hierarchy)!

pisin chen- cosmological constant as a manifestation of the hierarchy

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