290 likes | 373 Views
Explore the universe's early stages, transitions, and dynamics shaping gravitational waves. Understand production, detection, and implications of gravitational waves in cosmology. Learn about the possible sources and measurements for detecting gravitational waves.
E N D
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/(8GN) 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
Thomson scattering leads to polarization of the CMB 2003 2009
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
More realistic inflation models : slowroll nT h02 GW ~ V f nT = - (V’/V)2 MPl2 /8 = -T/7S
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/2dt 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 3° (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/dLlensing= 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.