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Gravitational waves and cosmology. P. Binétruy APC, Paris. 6th Rencontres du Vietnam Hanoi, August 2006. 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

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Gravitational waves and cosmology

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Gravitational waves and cosmology

P. Binétruy

APC, Paris

6th Rencontres du Vietnam

Hanoi, August 2006


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


And before?

?

gravitons and neutrinos


If gravitons were in thermal equilibrium in the primordial universe

 = -1 d/dlogf

g


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


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

100

At production * =  H*-1 (or f* = H*/ )

Horizon length

Wavelength


LF band0.1 mHz - 1 Hz

Gravitational wave detection

VIRGO


d GW

1

GW = --- --------

, c = 3H0/(8GN)

c

d logf

for =1


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 < 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)


Efalse vac

 = ---------

aT*4

h02 GW

radiation energy

at transition

Nicolis

gr-qc/0303084

f in mHz

turbulence

bubble collision

fturb/fcoll~ 0.65 ut/vb


Long wavelength GW produce a

redshift on the photons of the CMB

Wavelength outside the horizon at LSS

Wavelength inside the horizon today


CMB polarisation


Thomson scattering leads to polarization of the CMB

2003

2009


Vacuum fluctuations : de Sitter inflation (constant vacuum energy)

h02GW =10-13(feq/f) 2(H/10-4MPl)2

h02GW =10-13 (H/10-4MPl)2

Fluctuations reenter horizon during matter era radiation era


More realistic inflation models : slowroll

nT

h02 GW ~ V f

nT = - (V’/V)2 MPl2 /8 = -T/7S


String-motivated scenarios: e.g. pre-big-bang


Cosmic strings

Presence of cusps enhances the production of gravitational waves

Damour-Vilenkin

log h

LIGO

stochastic GW

background

log 50 GN

Loops radiate at

z>1 (MD)

z>1 (RD)

z<1


How to measure a stochastic background?

Cross correlate

ground interferometers

Let LISA move around the Sun


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?


Gravitational dynamics

f ~ (G)1/2

R in m

f = 10-4 Hz

space interf.

109

f = 1Hz

ground interf.

f = 104 Hz

104

100

108

M/M


Gravitational dynamics

Schwarzchild radius

R = 2GM/c2

R in m

space interf.

109

ground interf.

black hole line

104

100

108

M/M


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


Inspiral phase

(m1 m2)3/5

Key parameter : chirp mass M =

(1+z)

(z)

(m1 + m2)1/5


Inspiral phase

(m1 m2)3/5

Key parameter : chirp mass M =

(1+z)

(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


Inspiral phase

(m1 m2)3/5

Key parameter : chirp mass M =

(1+z)

(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


z = 1 , m1 = 105 M, m1 = 6.105 M

(arcminutes)

5%

Holz & Hughes

dL/dL


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/


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.


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