Nobuchika Okada (KEK)

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Brane World Cosmologies
Nobuchika Okada (KEK)
IX Workshop on High Energy Physics Phenomenology
03 January 14 January, 2006
Institute of Physics, Sachivalaya Marg,
Bhubaneswar
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1. Introduction
The Standard Big Bang Cosmology
Robertson-Walker metric
Einstein equation
with
Friedmann eq.
For radiation
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Thermal history of the universe
Inflation?
Reheating ? most of the particles are in thermal
equilibrium
high
decoupling from thermal plasma production from
thermal plasma
Temp.
Radiation dominated era
Big Bang Nucleosynthesis
low
Equal epoch
Matter dominated era
Time
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Interesting topics in particle cosmology ?
Cosmology needs New Physics
Example Inflation inflation models
(inlfaton, inflaton potential,..)
Baryogenesis models producing baryon asymmetry
in the universe Dark Matter no candidate in
the Standard Model
These topics have been studied for many years
based on the 4D Standard Cosmology (standard
expansion law)
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Note that final results depend on the
cosmological model
If the expansion low of the early universe is
non-standard, the results can be altered from
those in the standard cosmology
Brane world cosmology is a well-known example
such a non-standard cosmological model
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2. Brane world cosmology
Randall Sundrum, PRL 83 (1999) 3370 PRL 83
(1999) 4699
Randall-Sundrum model (static solution)
3-brane
5th dim. is compactified on
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Solving Einsteins equations with cosmological
constants in bulk

on branes
Metric ansatz
4 dimensional Poincare invariance
Others 0
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?
?
IF
satisfied
? Solution consistent with the orbifold Z2
symmetry
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4-dim. effective Planck scale
Solution
5D Planck scale AdS curvature Warp factor
with a constraint
Free parameters
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Graviton KK mode
KK mode decomposition
Mode equation
(volcano potential)
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KK mode configuration
localize around y0 brane localize around ypi
brane
Graviton KK mode mass
KK mode configuration
We live here
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Which brane are we living on?
Two cases 1) IR brane at ypi (RS 1)
2) UV brane at y0 (RS 2)
(1) RS 1 model
SM
Warp down of the scale ? solution to hierarchy
problem
with
Strong interactions among KK gravitons and SM
particles
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(2) RS 2 model
SM
Weak interactions among KK gravitons and SM
particles
Alternative to compactification
Even in the limit , we can
reproduce 4D gravity correctly
Newton potential for continuum KK mode
4D gravity
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Brane world cosmology
Shiromizu et al., PRD 62, 024012 (2000) Binetury
et al., PLB 477, 285 (2000) Langlois, PTP Suppl.
148, 181 (2003), references therein
Original RS model ? static solution
We want a realistic cosmological solution
Metric ansatz
Einstein equation
Assume stabilization of the 5th dimension
with the junction conditions
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Effective Freedmann equation on a brane
By tuning
the Standard Cosmology
New term dominating when
New term so-called dark radiation with C
being a constant free parameter
Note to reproduce the 4D Standard Cosmology at
low scale
RS type model
RS 2 type model
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Modified Freedmann equation in Brane World
Cosmology
where
Cosmological constraint BBN constraint
Not to spoil the success of BBN ?
at
We take C0 for simplicity
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Radiation dominated era
transition temperature

• Brane World Cosmology era
• ? Standard Cosmology era

Standard cosmology is recovered at low
temperature!
If the transition temperature is low
enough, the non-standard expansion law affects
some physics processes and the final result
can be altered from those examined in the SC.
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Thermal history of the brane universe
Inflation?
Temp.
Reheating ? most of the particles are in thermal
equilibrium
high
Non-standard
decoupling from thermal plasma production from
thermal plasma
Radiation dominated era
Standard
Big Bang Nucleosynthesis
low
Equal epoch
Matter dominated era
Time
Model independent BBN cosmological constraint ?
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3. Brane world cosmological effects
3-1 Chaotic inflation on the brane
Maartens et al., , PRD 62, 041301 (2000)
E.O.M of inflaton
Slow-roll parameters
Number of e-folds
If , inflation takes place in
brane cosmology era ? Enhances slow-roll and the
e-folding number in any model
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Example) the simplest chaotic inflation
with
is found to be consistent with observed
anisotropies in the CMB
Low scale inflation ? we can take any
?? in 4D standard cosmology
? fixed, high scale inflation
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3-2 thermal relic density of dark matter
NO Seto, PRD 70, 083531, 2004
After WMAP results
The flat universe dominated by unknown energy
densities
Dark energy 73 Dark matter 23 Baryon
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Candidate for the Dark Mater
No candidate in the Standard Model!
Neutral, stable, suitable mass interaction etc.
?
Weak Interacting Massive Particle (WIMP) in
physics beyond SM
Example neutral LSP in SUSY model with
R-parity ? neutralino
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Relic abundance of the dark matter
Boltzmann equation
average of annihilation cross section
?
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Example
In the limit
Brane world case
The standard case
Enhancement of the relic density in the brane
world cosmology
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Application neutralino dark matter in minimal
SUGRA model
WMAP data
Very narrow allowed region!
Lahanas Nanopoulos, PLB 568 (2003) 55
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How is the allowed region changed in the brane
world cosmology?
Nihei, NO Seto, PRD 71, 063535 (2005)
Numerical analysis
Modification of the code DarkSUSY (Gondolo et
al., JCAP 0407, 008 (2004))
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Nihei, NO Seto, PRD 71, 063535 (2005)
Standard Cosmology
Allowed region shrinks and eventually
disappears as M5 decreases
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WMAP 2 sigma
Region shrinks
Allowed region appears by the enhancement
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Application 2 wino-like dark matter in anomaly
mediation model
In AMSB, neutralino is wino-like ? annihilation
process is very effective
? large
neutralino mass is favored

• If we consider the wino-like dark matter in the
  brane world cosmology
• Enhancement of relic density
• neutralino mass becomes small

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Model AMSB universal soft scalar mass _at_ GUT
scale
Nihei, N.O. Seto, hep-ph/0509231
Standard Cosmology
Rough estimation gives
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3-3. cosmological gravitino problem
Gravitino couples to ordinary matters through
only gravitational couplings ? long life time

• If gravitino has mass smaller than 10 TeV, it
  decays after BBN
• decay products would destroy successfully
  synthesized light
• nuclei by photo-dissociation and
  hadro-dissociation

To avoid this problem, number density of the
gravitino produced from the thermal plasma is
severely constrained ? upper bound on the
reheating temperature after infaltion
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The Boltzmann equation relevant to the gravitino
production process
?
Kawasaki Moroi, PTP 93, 879 (1995) Kawasaki,
Kohri Moroi, Astro-ph/0402249
For
Gravitino problem
is problematic
in inflation scenario thermal
leptogenesis scenario
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Kawasaki, Kohri Moroi, astro-ph/0402249
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Brane world cosmological solution to the
gravitino problem
NO Seto, PRD 71, 023517, 2004
The Boltzman equations for gravitino production
is modified in the brane world cosmology
Const.
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In brane world cosmology
Therefore, we can avoid overproduction of
gravitinos by
independently of the reheating temperature
The gravitino problem can be solved with the
transition temperature low enough
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3.4 Thermal leptogenesis in the brane world
cosmology
N.O Seto, hep-ph/0507279
Leptogenesis is one of the most interesting
scenario for Brayogenesis very
simple related neutrino oscillation physics
In thermal leptogenesis scenario, the condition
for out-of-equilibrium decay of the lightest
right-handed neutrinos leads to the upper bound
on the lightest light neutrino mass
Considering neutrino oscillation data ?
hierarchical light neutrino mass spectrum is
favored
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How is the result altered in brane world
cosmology ?
Out-of-equilibrium decay in brane world cosmology
era
If the out-of-equilibrium decay occurs in brane
world cosmology eara, the upper bound on the
lightest neutrino mass becomes mild!
Thermal leptogenesis can be realized even in
the case of degenerate light neutrino mass
spectrum
For detailed numerical studies, see Bento et al.,
hep-ph/0508213
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4. Summary
There exists a realistic example of the
non-standard cosmology, the RS 2 brane
world cosmology, in which the expansion law is
modified at high temperature but it smoothly
connects to the standard cosmology at low
temperature ltlt transition temperature.
If the transition temperature or
is low enough, the results obtained in the
standard cosmology can be altered
Inflation scenario
gravitiono problem, thermal leptogenesis
(WIMP) dark matter relic density