Bose, 2005/12/14, GWDAW10, Brownsville Sukanta Bose Washington State University, Pullman Acknowledgements: Roy Maartens, U. Portsmouth, Aaron Rogan, Yuri.

Bose, 2005/12/14, GWDAW10, Brownsville

Sukanta Bose

Washington State University, Pullman

Acknowledgements:

Roy Maartens, U. Portsmouth,

Aaron Rogan, Yuri Gusev, Wash. State

NSF-PHY-0239735

Probing extra dimensions with gravitational wave observations


Literature

• R. Maartens, “Brane-world gravity,” Living Rev.Rel.7, 7 (2004) [gr-qc/0312059].

• D. Langlois et al., “Gravitational waves from inflation on the brane,” Phys. Lett B489, 259 (2000).

• V. Sahni et al., “Relic gravity waves from brane-world inflation,” Phys. Rev. D65, 023518 (2001).

• S. Seahra et al. “Detecting extra dimensions with gravity-wave spectroscopy,” Phys. Rev. Lett. 94, 121302 (2005).


The brane-world scenario

Basic idea: The universe has extra dimensions, but only gravity can propagate in the bulk space-time

We live on a 3+1 brane and do not “feel” the other sub-millimeter dimension

Such space-times arise as solutions in super-string theories, but need not be limited to them

Might be experimentally constrained / falsified.


Brane-world: Old paradoxes & new physics

Hierarchy problem: Running coupling constants: Gravity is weak owing to a faster than fall off at short length scales. Unification may occur at closer than 10TeV.

Black hole hairs: The gravitational degrees of freedom in the bulk leave an imprint on the brane as a non-local tensor field. This field can encode information about the astrophysical source that forms a black hole

2/1 r


Brane-world: Experiments

Particle accelerators:» Proton-proton smash-ups are being

studied at Fermilab (574 GeV); 10TeV accessible to the LHC, which is under construction

» Black hole evaporation: A non-negligible probability for the production of black hole pairs in such smash-ups exists and can be detected from excess photon emissions.

The Large Hadron Collider


Brane-world: Experiments (contd.)

1. Table-tops: Testing the law of gravity at sub-millimeter scales. Places the bound:

2. Indirect: Hawking luminosity is considerably enhanced:

Existence of BH X-ray binaries then =>

? e 11 /

2r

rF

[Hoyle et al., Phys.Rev.Lett. (2001)]

mm1.0

yr, mm 1

103

sun

2life BH

M

M

mm01.0 (meters) 10 -4 10 -6 10

-410

1

410

910


Solutions for GW detections: The black-string

Chamblin et al., Phys.Rev.D61 (2000)]

branes. twoebetween th separation

theis Also, ./21 where

,

:issolution string"black " 5D Its

radius. curvature theis where

,6

:isdeSitter -Anti 5Dfor Eq.Einstein The

222212/2

2

2

drGMf

dydrdrffdteds

gG

y

Our brane Shadow brane

Large Black hole

Small Black hole 0y

dy


Allowed Black String Configurations

d appears as a massless field and effective theory is Brans-Dicke-like:

Unstable solutions

Permissible configurations

Sca

lar-

tens

or

limit

- 10

- 0

- 5

|

10|

5|

15|

20

,104

11.5 4

/2

de

.0.1

yinstabilit GF the

Also, .5~/at

occurswhich

/

deGM

d

log SunM/M

/ ,separation brane d


GW Modes in Braneworld

The Kaluza-Kline tower of massive modes in flat space:

./ where

,0

,0

232

42

Lnm

hm

h

n

nD

t

Dt

0n

] of [units GMt

4

8

||log 00

The BH QNM

signal (m=0) in GR


Black string: Quasi-Normal Modes

Massive modes in Anti-deSitter:[Seahra et al., Phys.Rev.Lett. (2005)]

0 and

where

),(

: and in ofty separabili Using

4

:AdS 5DIn

1/

1

2/22

2222

ndn

n

knitn

knitnn

nnn

y

bJeb

m

eAeAt

ytyth

yth

hhehkh

1n

2n

3n

] of [units GMt

n


Total QNM waveform-I

A time-series of a superposition of the first 9 modes for d / l = 6. Fractional energy in n=0 is over 99%. For a black hole – black string collision:

] of [units GMt

||log n


||log n

] of [units GMt

Total QNM waveform-II

A time-series of a superposition of the first 9 modes for d / l = 20. Fractional energy in n=0 is over 2e-13%. For a black string – black string collision:


Black string QNMs in ground-based detectors

Massive modes, with n=1,…,13 (with increasingfrequencies) for a single brane separation, d=2.2,and l=0.1mm

-2510

-2210

-1410

10 310


Black string: QNM frequencies (n=1) vs d/l

[Hoyle et al., Phys.Rev.Lett. (2001)]

The frequency of a mode (here n=1) decreases with increasing brane separation d.

-2310

-1410

310310

0 andmm1.0/

:are Hz)(in

sfrequencie mode The

1

/9.26

n

dnn

bJ

eb

f


Detecting black string QNMs

1. Matched filtering well suited as detection strategy. The massive waveform frequencies are dependent on d and l, but independent of black string/black hole mass

2. The mode frequencies and amplitudes (sans the “fine structure”) well understood and robust

3. Clearly, if there were a GR QNM trigger (m=0), a follow up search for the massive waveforms must be implemented

4. However, since it is also possible that the massive modes dominate the massless one, they must be searched for independently anyway.

5. A slow fall-off suggests that when looking up to sufficiently far distances, these waveforms may form a stochastic background [Clarkson & Maartens (2005)]. Once this background is modeled, it should be possible to fold it into the LSC search pipeline


GW Predictions:Stochastic GW background

Current prediction for the SGWB spectra:

[Sahni et al., Phys.Rev.D65 (2001)]

10

RDkinRD

0

MDRD0

MD

2

0

10 where

, ~

, ~

, ~

N

N

N

N

r

r

hh

m

The best COBE-normalized transitions are for the “exponential” potential, at:

cm04.0 cm,102 kin18

RD - 10-16

- 10-11

- 10-4

- 100

|

0|

10|

20

|10

|0

|10

(cm)log

(Hz) log f


Future work

1. Construct template banks based on values of parameters d and l

2. Account for differences between arrival times of different modes based on different initial conditions and dispersion

3. Properties of the 3 other polarizations remain to be studied

4. The stochastic GW background remains to be calculated more carefully to account for coupling of the massless modes with the massive modes



1. Table-tops: Testing the law of gravity at sub-millimeter scales.

2. Particle accelerators:» Proton-proton smashups are being studied

at Fermilab (574 GeV); 10TeV accessible to the LHC under construct.

» Black hole evaporation: A non-negligible probability for the production of black hole pairs in such smashups exists and can be detected from excess photon emissions.

3. Gravitational-wave experiments: Tell-tale deviations in the spectra of:» Black hole ringdowns

GR

Black hole ringdown spectra

[Seahra et al. Phys.Rev.Lett (2005)]



Table-tops: Testing the law of gravity at sub-millimeter scales.

Particle accelerators:» Proton-proton smashups are being studied

at Fermilab (574 GeV); 10TeV accessible to the LHC under construct.

» Black hole evaporation: A non-negligible probability for the production of black hole pairs in such smashups exists and can be detected from excess photon emissions.

Gravitational-wave experiments: Tell-tale deviations in the spectra of both:

» Black hole ringdowns» Cosmic graviton background

Grav. wave energy density

[Ichika, Nakamura (2004), Bose, Phys.Rev.D (2005); Rogan, Bose, Class.Quant.Grav.(2004)]


Interferometric ObservatoriesPresent & Future


The Sensitivities:LISA vs LIGO


Why Quantize Gravity?

||

84

Tc

GG

Since we have a theoretical framework that unifies the other 3 fundamental forces. » Gravity is the weakest of those forces:

1/(10 trillion trillion trillion) weaker than E!

» Allowing for extra dimensions makes it probable that all forces unify at as for electroweak.

m 10 19

Since matter is quantized:

Bose, 2005/12/14, GWDAW10, Brownsville Sukanta Bose Washington State University, Pullman Acknowledgements: Roy Maartens, U. Portsmouth, Aaron Rogan, Yuri.

Documents