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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

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

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)

= ---------

aT*4

h02 GW

radiation energy

at transition

Nicolis

gr-qc/0303084

f in mHz

turbulence

bubble collision

fturb/fcoll~ 0.65 ut/vb

redshift on the photons of the CMB

Wavelength outside the horizon at LSS

Wavelength inside the horizon today

Vacuum fluctuations : de Sitter inflation (constant vacuum energy)

h02GW =10-13(feq/f) 2(H/10-4MPl)2

h02GW =10-13 (H/10-4MPl)2

Fluctuations reenter horizon during matter era radiation era

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?

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

Schwarzchild radius

R = 2GM/c2

R in m

space interf.

109

ground interf.

black hole line

104

100

108

M/M

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

(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/2dt

M(z)5/3 f(t)2/3

h(t) = F (angles) cos (t)

dL

Luminosity distance

(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

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/dLlensing= 1-1/

- 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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