1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology...
-
Upload
belinda-maxwell -
Category
Documents
-
view
215 -
download
0
Transcript of 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology...
![Page 1: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/1.jpg)
1
Cosmological Constant as a Manifestation of
the HierarchyPisin Chen
Leung Center for Cosmology and Particle AstrophysicsNational Taiwan University
&Kavli Institute for Particle Astrophysics and Cosmology
Stanford University
3rd Biennial Leopoldina Conference on Dark Energy, Munich, Oct. 7-11, 2008
PC, Nucl. Phys. Proc. Suppl.173, 137 (2007).PC and J-A. Gu, Mod. Phys. Lett. A22, 1995 (2007); arXiv:0712.2441
![Page 2: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/2.jpg)
2
SN Ia (SNLS, Higher-Z, Essence, low-Z stuff) + WMAP5 +BAO(SDSS)+ HST H0
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
Kowalski et al 08
w+=1
Where we Stand now
Brian Schmidt’s talk
If it looks like an apple and tastes like an apple, then it must be an apple! - PC
![Page 3: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/3.jpg)
3
Smallness of Dark Energy• Combination of recent data from WMAP3 + SDSS determines w = − 0.94 ± 0.09 for dark energy (DE) equation of state p = wρ. • SNLS gives w = −1.023 ± 0.090 (stat) ± 0.54(sys).
Why much smaller than standard model scale?
DE likely a bone fide CC: w = − 1.
• Observations
~ 10-15 !ρDE
1/4
MSM
If DE never changes in space and time, then it must be associated with fundamental properties of spacetime.
![Page 4: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/4.jpg)
4
Another Hierarchy in Physics
• Gravity is much weaker, or Planck scale (1019 GeV), much larger, than that of SM gauge interactions:
MPl
MSM
Two well-known solutions:ADD : large (but flat) extra dimensions RS : warped geometry in x-d
~ 1016 .
![Page 5: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/5.jpg)
5
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, derived quantity.
![Page 6: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/6.jpg)
6
Analogy in Atomic Physics
• Bohr atom• Fundamental energy
scale in Schrödinger equation: me
• Ground state energy suppressed by 2 powers of fine structure constant
• Dark energy• Fundamental energy
scale in quantum gravity: MPl
• Dark energy suppressed by 2 powers of “gravity fine structure constant”
![Page 7: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/7.jpg)
7
Randall-Sundrum Warped Geometry
Y=0Y=π
Visible brane Hidden brane
dxμdxν
Gravity lives in the bulk while gauge interactions live on the brane.
![Page 8: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/8.jpg)
8
Casimir Effect
QED vacuum fluctuations
![Page 9: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/9.jpg)
9(a ) a
Casimir Energy
casimir = vac (| |) vac(a ) ∞ a-4
![Page 10: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/10.jpg)
10
Casimir Energy vs. Vacuum Energy
py
px
• Casimir energy: px = ‒ρ, py > 0. py cannot be tuned away.• Conventional vacuum energy (brane tension): px = ‒ρ, py = 0. py can in principle be tuned away.
![Page 11: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/11.jpg)
11
Strategy for the Smallness of Dark Energy
Supersymmetry Brane World
BUT SUSY only on the brane
= 0vac:boson fermion
+
vac(4)
~ (mn - mn-1)2 mn
2
![Page 12: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/12.jpg)
12
• By definition, the Casimir energy under SUSY breaking is
which is
The KK mass shift can be shown to scale as
• The SUSY-KK graviton/gravitino energy spectrum, on the other hand, goes like
![Page 13: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/13.jpg)
13
Casimir Energy under SUSY-Breaking
Putting all these together, we find
![Page 14: 1 Cosmological Constant as a Manifestation of the Hierarchy Pisin Chen Leung Center for Cosmology and Particle Astrophysics National Taiwan University.](https://reader036.fdocuments.net/reader036/viewer/2022081516/56649ee45503460f94bf34d6/html5/thumbnails/14.jpg)
Summary
• Dark energy may very well be a cosmological constant.• The numerical coincidence between the SM-Planck and the SM-DE hierarchies suggests a deeper connection between the two. • This approach does not attempt to solve the “old” CC problem, i.e., the problem of 10120. Assuming that this old CC problem will be resovled someday, our model seems able to solve the “new” CC problem, i.e., the smallness of CC as inferred by observations.