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