bose, 2005/12/14, gwdaw10, brownsville sukanta bose washington state university, pullman...
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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
Bose, 2005/12/14, GWDAW10, Brownsville
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).
Bose, 2005/12/14, GWDAW10, Brownsville
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.
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
||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:
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
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
Bose, 2005/12/14, GWDAW10, Brownsville
Brane-world: Experiments
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)]
Bose, 2005/12/14, GWDAW10, Brownsville
Brane-world: Experiments
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)]
Bose, 2005/12/14, GWDAW10, Brownsville
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: