Probing the Extra Dimensions with Gravitational Wave Background of Cosmological Origin

1
Probing the Extra Dimensions with Gravitational
Wave Background of Cosmological Origin

• Dept. of Phys., Theoretical Astrophysics Group,
• University of Tokyo
• Takashi Hiramatsu

2
Introduction

• Gravitational Wave
• Einsteins General Theory of Relativity predicts
  GWs.
• ripples in space-time
• GWs deform an object due to their tidal
  force as
• they pass through it.
• There are several kinds of expected astrophysical
  sources
• Supernovae (the explosion at the end of a
  massive stars
• lifetime)
• Black holes (feeding other objects, ringdown,
  merging)
• Binary stars (e.g. NS/NS, WD/WD, BH/BH)
• etc.

3
Illustration of Gravitational Waves
Binary system (strong gravity source)
Propagating at the light speed
An object placed on the Earth
incredibly small deformation !
This is roughly equivalent to measuring a change
which is the size of an atom in the distance from
the Sun to the Earth.
Deformed by the tidal force of GWs
4

• Considerable effort is devoted to detect GWs.
• Laser Interferometer
  Bar Detector

LIGO _at_ USA
NAUTILUS _at_ Italy
Space Interferometer (LISA) 2012?
5

• Inflation Theory
• The accelerating expansion of the Universe right
  after the Big Bang.

Now(3K)
GWB
CMB
time
LSS(380k years)
Fireball
Inflation ( sec)
During the inflationary epoch, the GWs are
generated as the quantum fluctuation.
Background radiation
To observe the GWB is to obtain the information
about the extremely early universe.
6

• Gravitational Wave Background
• has lots of important information about extremely
• early universe.
• Cosmic strings
• Phase transitions of vacuum
• History of EOS
• in early Universe
• EXTRA DIMENSIONS

?
The image of map of GWB
We cannot obtain them from the ancient light.
7

• Higher dimensional world
• The M-theory or the superstring theory which are
  candidates of the unified theory suggest we live
  in 11 or 10 dimensional spacetime.
• Cosmologists have tried to apply the idea to the
  cosmology brane world cosmology.

Randall-Sundrum model
The gravity can propagate through the whole 5D
spacetime (bulk).
gravity (graviton)
light (photon)
The other matters and fields (EM, baryons) are
confined to the 3D sheet (brane).
3-dimensional brane
8

• The goal of our research is

To make the spectrum of GWB in the brane world
model
Using the GWB, we can confirm if we really live
on brane or not.
9

• The spectrum of GWB in the 4D theory
• We usually use the density parameter of GWB
  instead of
• the amplitude
• The shape of spectrum depends on the history of
  EOS.
• The normalization is mainly restricted by the
  observation of CMB.

Advanced LIGO x 2
LISA
-10
CMB constraint
-14
-18
-14
-10
-6
-2
2
6
10
10

• High energy effects in brane world
• Slower expansion of the early universe
• The amplitude of GWB is decreasing as the
  Universe is expanding. The slow expansion,
  however, keeps the amplitude large.
• Escaping from the brane into the bulk
• The amplitude of GWB on brane decreases
  more rapidly.

0-mode
Kaluza-Klein(KK) mode
brane
11

• The MODIFIED spectrum of GWB (expectation)
• From some experiments, We know the Newtons law
  of gravity is correct on the length scale of
  0.1mm .
• The scale of extra dimension must be less than
  0.1mm
• (corresponding to 0.1mHz).

LISA
Adv. LIGO x 2
-10
?
escaping effect
CMB
-14
-10
-6
-18
-14
-2
2
6
10
12
Basic Equations

• The wave equation of GW

Metric
3D space
time
5D space
Einstein equation
Matter distribution
Curvature of spacetime
Gravity constant
Wave equation
13

• The motion of brane in bulk
• In the RS model, the 5D bulk is bending.
• The moving brane represents our expanding
  Universe.

5D space
14

• Numerical simulation of the GWB
• At the inflationary epoch, the generated KK-modes
  are suppressed, hence there is only the 0-mode at
  initial time.
• At the brane, we have the boundary condition
  derived from the fact that the ordinary matters
  and fields are confined to the brane.

time
Evolution
brane
Initial time
5D space
15
Results

• Wave form in the bulk

5D space
time
16

• Wave form on the brane
• The higher frequency the wave is, the more
  significant difference there is between 4D and 5D
  theory.

Example of high frequency GW
Green 4D Red 5D
time
time
Example of low frequency GW
17

• Spectrum of GWB
• Above the critical frequency which is determined
  from the length scale of bulk, the power of GWB
  is decreasing with increasing the frequency.

1
If the length scale of the extra dimensional
space is 0.1mm, the critical freq. is around
0.1mHz.
0.1
0.1
1
10
18
Conclusion

• Probing the extra dimansions
• GWB is the only probe for the extra dimension.
• We investigate the spectrum of GWB by the
  numerical simulation.
• Unfortunately, in the brane world scenario, the
  spectrum of GWB is decreasing with increasing the
  frequency around the critical frequency.
• At much higher frequency region (e.g. around
  1kHz(LIGO)), however, we have no idea how the GWB
  behaves.