Gravitational%20waves%20and%20cosmology

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Gravitational waves and cosmology

• P. Binétruy
• APC, Paris

6th Rencontres du Vietnam Hanoi, August 2006
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At t 400 000 yrs, the Universe becomes
transparent photons no longer interact with
matter
Looking back to the primordial Universe
BIG BANG
Cosmological background T 3 K - 270 C
WMAP satellite
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And before?
?
gravitons and neutrinos
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If gravitons were in thermal equilibrium in the
primordial universe
? ?-1 d?/dlogf
?
g
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When do graviton decouple?
T5
Interaction rate
? GN2 T5 ----
MPl4
T2
Expansion rate
H ----
(radiation dominated era)
MPl
T3
?
---- ----
H
MPl3
Gravitons decouple at the Planck era fossile
radiation
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But gravitons could be produced after the Planck
era.
Gravitons of frequency f produced at temperature
T are observed at a redshifted frequency
1/6
f 1.65 10-7 Hz --- ( ----- ) ( ---- )
1
T
g
?
1GeV
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At production ? ? H-1 (or f H/ ?)
Horizon length
Wavelength
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Gravitational wave detection
VIRGO
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d ?GW
1
?GW --- --------
, ?c 3H0/(8?GN)
?c
d logf
for ?1
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Electroweak phase transition
If the transition is first order, nucleation of
true vacuum bubbles inside the false vacuum
Collision of bubbles ? production of
gravitational waves
Pros and cons for a 1st order EW phase transition

• in the Standard Model, requires mh lt 72 GeV
  (ruled out)
• in the MSSM, requires a light stop (less and
  less probable)
• possible to recover a strong 1st order
  transition by including ?6 terms
• in SM potential
• needed to account for baryogenesis at the
  electroweak scale (? out
• of equilibrium dynamics)

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Efalse vac
? ---------
aT4
h02 ?GW
radiation energy at transition
Nicolis gr-qc/0303084
f in mHz
turbulence
bubble collision
fturb/fcoll 0.65 ut/vb
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Long wavelength GW produce a redshift on the
photons of the CMB
Wavelength outside the horizon at LSS
Wavelength inside the horizon today
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CMB polarisation
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Thomson scattering leads to polarization of the
CMB
2003
2009
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Vacuum fluctuations de Sitter inflation
(constant vacuum energy)
h02 ?GW 10-13 (H/10-4MPl)2
h02 ?GW 10-13(feq/f) 2(H/10-4MPl)2
Fluctuations reenter horizon during matter era
radiation era
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More realistic inflation models slowroll
nT
h02 ?GW V f
nT - (V/V)2 MPl2 /8? -T/7S
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String-motivated scenarios e.g. pre-big-bang
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Cosmic strings
Presence of cusps enhances the production of
gravitational waves
Damour-Vilenkin
log h
LIGO
stochastic GW background
log 50 GN?
zlt1
zgt1 (MD)
zgt1 (RD)
Loops radiate at
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How to measure a stochastic background?
Cross correlate ground interferometers
Let LISA move around the Sun
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2. Dark energy in search of standard candles

• Supernovae of type Ia

magnitude versus redshift
mB 5 log(H0dL) M - 5 log H0 25

• Gamma ray bursts

• Coalescence of black holes the ultimate
  standard candle?

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Gravitational dynamics
f (?G?)1/2
R in m
f 10-4 Hz
space interf.
109
?
f 1 Hz
ground interf.
f 104 Hz
104
100
108
M/M?
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Gravitational dynamics
Schwarzchild radius R 2GM/c2
R in m
space interf.
109
?
ground interf.
black hole line
104
100
108
M/M?
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Gravitational dynamics
Supermassive BH mergers
R in m
space interf.
109
?
chirp line
coalesc. in 1 yr
ground interf.
black hole line
104
100
108
M/M?
NS-NS coalescence
after B. Schutz
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(No Transcript)
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Inspiral phase
(m1 m2)3/5
Key parameter chirp mass M
(1z)
(z)
(m1 m2)1/5
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Inspiral phase
(m1 m2)3/5
Key parameter chirp mass M
(1z)
(z)
(m1 m2)1/5
Amplitude of the gravitational wave
frequency f(t) d?/2?dt
M(z)5/3 f(t)2/3
h(t) F
(angles) cos ?(t)
dL
Luminosity distance
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Inspiral phase
(m1 m2)3/5
Key parameter chirp mass M
(1z)
(z)
(m1 m2)1/5
Amplitude of the gravitational wave
M(z)5/3 f(t)2/3
h(t) F
(angles) cos ?(t)
dL
Luminosity distance
poorly known in the case of LISA
10 arcmin
1 Hz
??
SNR
fGW
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z 1 , m1 105 M?, m1 6.105 M?
3
?? (arcminutes)
5
Holz Hughes
?dL/dL
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Using the electromagnetic counterpart
Allows both a measure of the direction and of the
redshift
0.5
Holz and Hughes
?dL/dL
But limited by weak gravitational lensing!
?dL/dL?lensing 1-1/??
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Conclusions

• LISA will provide complentary ways to identify
  the geometry
• of the Universe.

• regarding a stochastic background of primordial
  gravitational
• waves, no detection in the standard inflation
  scenarios, but many
• alternatives lead to possible signals within
  reach of advanced
• ground interferometers or LISA.