Nobuchika Okada (KEK) Brane World Cosmolo gies IX Workshop on High Energy Physics Phen omenology 03 January – 14 Janua ry, 2006 Institute of Physics, Sachivalaya Mar g, Bhubaneswar
Jan 16, 2016
Nobuchika Okada (KEK)
Brane World Cosmologies
IX Workshop on High Energy Physics Phenomenology
03 January – 14 January, 2006
Institute of Physics, Sachivalaya Marg, Bhubaneswar
1. Introduction
Robertson-Walker metric:
Einstein equation:
with
The Standard Big Bang Cosmology
Friedmann eq.
For radiation:
Time
Temp.
high
low
Inflation?
Reheating most of the particles are in thermal equilibrium
Big Bang Nucleosynthesis
Equal epoch
Matter dominated era
Radiation dominated era
Thermal history of the universe
decoupling from thermal plasma
production from thermal plasma
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)
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
``3-brane’’
2. Brane world cosmology
Randall-Sundrum model (static solution)
Randall & Sundrum, PRL 83 (1999) 3370;PRL 83 (1999) 4699
5th dim. is compactified
on
Solving Einstein’s equations with cosmological constants in bulk
on branesMetric ansatz
4 dimensional Poincare invariance
Others = 0
IF satisfied
Solution consistent with the orbifold Z2 symmetry:
4-dim. effective Planck scale
Solution:
Free parameters:
: 5D Planck scale
: AdS curvature
: Warp factor
with a constraint
Graviton KK mode
KK mode decomposition
Mode equation
(volcano potential)
KK mode configuration
localize around y=0 brane
localize around y=pi brane
Graviton KK mode mass
KK mode configuration
We live here
Which brane are we living on?
Two cases: 1) IR brane at y=pi (RS 1)
2) UV brane at y=0 (RS 2)
(1) ``RS 1’’ model
Warp down of the scale solution to hierarchy problem
with
Strong interactions among KK gravitons and SM particles
SM
(2) ``RS 2’’ model
Weak interactions among KK gravitons and SM particles
SM
Alternative to compactification
Even in the limit , we can reproduce 4D gravity correctly
Newton potential for continuum KK mode
4D gravity
Brane world cosmology
Original RS model static solution
We want a realistic cosmological solution
Shiromizu et al., PRD 62, 024012 (2000)
Binetury et al., PLB 477, 285 (2000)
Langlois, PTP Suppl. 148, 181 (2003),
references therein
Metric ansatz:
Einstein equation:
with the junction conditions
Assume stabilization of the 5th dimension
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
where
Cosmological constraint: BBN constraint
Not to spoil the success of BBN
at
* We take C=0 for simplicity
Modified Freedmann equation in Brane World Cosmology
Brane World Cosmology era
Standard Cosmology era
Radiation dominated era:
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.
Standard cosmology is recovered at low temperature!
``transition temperature’’
Time
Temp.
high
low
Inflation?
Reheating most of the particles are in thermal equilibrium
Big Bang Nucleosynthesis
Equal epoch
Matter dominated era
Radiation dominated era
Thermal history of the brane universe
decoupling from thermal plasma
production from thermal plasma
Non
-sta
nda
rdSt
anda
rd
Model independent BBN cosmological constraint
3-1: Chaotic inflation on the brane
3. Brane world cosmological effects
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
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
3-2: thermal relic density of dark matter NO & Seto, PRD 70, 083531, 2004
After WMAP results
Dark energy: 73%
Dark matter: 23%
Baryon: 4%
The flat universe dominated by unknown energy densities
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
Boltzmann equation:
: average of annihilation cross section
Relic abundance of the dark matter
Example:
In the limit
The standard case:
Brane world case:
Enhancement of the relic density in the brane world cosmology
Application: neutralino dark matter in minimal SUGRA model
WMAP data
Lahanas & Nanopoulos,
PLB 568 (2003) 55
Very narrow allowed region!
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))
Allowed region shrinks and eventually disappears as M5 decreases
Nihei, NO & Seto, PRD 71, 063535 (2005)
Standard Cosmology
Region shrinks
WMAP 2 sigma
Allowed region appears by the enhancement
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
Model: AMSB + universal soft scalar mass @ GUT scale
Standard Cosmology
Nihei, N.O. & Seto, hep-ph/0509231
Rough estimation gives
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
The Boltzmann equation relevant to the gravitino production process
For
Kawasaki & Moroi,
PTP 93, 879 (1995)
Kawasaki, Kohri & Moroi,
Astro-ph/0402249
is problematic
in inflation scenario
thermal leptogenesis scenario
Gravitino problem
Kawasaki, Kohri & Moroi,
astro-ph/0402249
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.
Therefore, we can avoid overproduction of gravitinos by
independently of the reheating temperature
In brane world cosmology
The gravitino problem can be solved
with the transition temperature low enough
3.4 Thermal leptogenesis in the brane world cosmology N.O & Seto, hep-ph/0507279
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
Leptogenesis is one of the most interesting scenario for Brayogenesis
very simple & related neutrino oscillation physics
Considering neutrino oscillation data
hierarchical light neutrino mass spectrum is favored
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
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 << 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