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Gravitational waves and cosmology

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

  2. 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

  3. And before? ? gravitons and neutrinos

  4. If gravitons were in thermal equilibrium in the primordial universe  = -1 d/dlogf  g

  5. 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

  6. 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

  7. LF band0.1 mHz - 1 Hz Gravitational wave detection VIRGO

  8. d GW 1 GW = --- -------- , c = 3H0/(8GN) c d logf for =1

  9. 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)

  10. 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

  11. Long wavelength GW produce a redshift on the photons of the CMB Wavelength outside the horizon at LSS Wavelength inside the horizon today

  12. CMB polarisation

  13. Thomson scattering leads to polarization of the CMB 2003 2009

  14. 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

  15. More realistic inflation models : slowroll nT h02 GW ~ V f nT = - (V’/V)2 MPl2 /8 = -T/7S

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

  17. 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

  18. How to measure a stochastic background? Cross correlate ground interferometers Let LISA move around the Sun

  19. 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?

  20. 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

  21. Gravitational dynamics Schwarzchild radius R = 2GM/c2 R in m space interf. 109  ground interf. black hole line 104 100 108 M/M

  22. 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

  23. Inspiral phase (m1 m2)3/5 Key parameter : chirp mass M = (1+z) (z) (m1 + m2)1/5

  24. 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

  25. 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

  26. z = 1 , m1 = 105 M, m1 = 6.105 M 3° (arcminutes) 5% Holz & Hughes dL/dL

  27. 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/

  28. 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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