GRAVITATIONAL WAVES FROM FIRST ORDER PHASE TRANSITIONS

Transcription

1 GRAVITATIONAL WAVES FROM FIRST ORDER PHASE TRANSITIONS Chiara Caprini IPhT, CEA Saclay (France) CC, R. Durrer and X. Siemens, arxiv: CC, R. Durrer and G. Servant, asxiv: CC, R. Durrer and E. Fenu, arxiv: CC, R. Durrer, T. Konstadin and G. Servant, arxiv: CC, R. Durrer and G. Servant, arxiv: CC, R. Durrer and R. Sturani, astro-ph/ CC and R. Durrer, astro-ph/

2 Gravitational waves Once emitted, propagate without interaction: direct probe of physical processes in the early universe first order phase transitions are a source of GW temperature of the phase transition: characteristic frequency strength of the phase transition: characteristic amplitude construction of an analytical model of the GW source in terms of a few free parameters evaluation of the GW signal: amplitude and shape of the spectrum signal potentially interesting for LISA, PTA

3 GW from first order phase transitions universe expands and temperature decreases : PT nature of PT depends on the particle theory model if it is first order it can lead to the production of GW (Hogan 83, Witten 84, Hogan 86...) (Turner et al 92, Kosowsky et al 92, Kosowsky and Turner 93, Kamionkowski et al 94, Kosowsky et al 02, Dolgov et al 02...) EWPT : beyond the standard model (baryogenesis) (Apreda et al 01, Nicolis 04, Grojean et al 05, Huber and Konstandin 08, Kahniashvili et al 09, Kehayias and Profumo 09, Chung and Long 10...) QCDPT : if lepton asymmetry is large (Schwarz and Stuke 09)

4 GW from first order phase transitions potential barrier separates true and false vacua quantum tunneling across the barrier : nucleation of bubbles of true vacuum collisions of bubble walls MHD turbulence in the primordial fluid primordial magnetic fields

5 GW from PT : characteristic frequency GW generation processes related to size of the bubbles towards the end of the PT characteristic wavenumber of causal source of GW : k H (cosmological horizon) k = T g 1 6 Hz 1 GeV dynamics of the source temperature (energy density) of the universe at the source time (standard thermal history)

6 GW from PT : characteristic frequency GW generation processes related to size of the bubbles towards the end of the PT characteristic wavenumber of causal source of GW : k H (cosmological horizon) k = T g 1 6 Hz 1 GeV 100 β 1 R = v b β 1 v b 1 duration of the PT size of bubbles at collision speed of bubble walls

7 GW from PT : characteristic frequency H β 1, H R corresponding to the source characteristic time or scale depending on the source properties: space and time correlations value : (Hogan 83) β H 4 ln mpl T 0.01 EWPT k 100GeV 10 3 Hz LISA QCDPT k 100MeV 10 7 Hz pulsars ( k 10 7 GeV 100 Hz LIGO )

8 GW from PT : scaling of the characteristic amplitude energy density of GWs: δg ij =8πGT ij characteristic time of evolution ρ G β 2 h 8πGT ḣ2 8πG tensor perturbation energy momentum tensor ḣ 8πGT β radiation parameter Ω GW Ω rad H β 2 (Ω s ) 2 DURATION of the source with respect to Hubble time RELATIVE ENERGY DENSITY available in the (radiation-like) source for the GW generation T ρ Ω s

9 GW from PT : scaling of the characteristic amplitude energy density of GWs: δg ij =8πGT ij characteristic time of evolution ρ G β 2 h 8πGT ḣ2 8πG tensor perturbation energy momentum tensor ḣ 8πGT β Ω GW Ω rad H β 2 (Ω s ) for strongly first order PT 10 4 amplitude OK for LISA and future PTA

10 GW from PT : scaling of the characteristic amplitude T ρ Ω s relative energy density in the source bubble collisions : kinetic energy of bubble walls Ω s ρ kin ρ vac + ρ rad MHD turbulence : kinetic energy of chaotic fluid motions and magnetic field energy density (equipartition) Ω s v 2 f b 2 1. from the particle theory model know strength and friction α = ρ vac ρ rad 2. hydrodynamics of bubble growth at late times determine parameters v 3. simple example: Jouguet detonations b, ρ kin,v f α = 1 3,v b =0.87,v f = 1 3 Ω s 0.1

11 Analytical evaluation of the GW spectrum GW power spectrum: Ω GW = ḣijḣij 8πGa 2 ρ c = dk k dω GW dlnk dω GW d ln k k3 tfin dt 1 t in t 1 tfin t in dt 2 t 2 cos[k(t 1 t 2 )] Π(k, t 1,t 2 ) source: anisotropic stress power spectrum at unequal time Π ij (k,t 1 )Π ij(q,t 2 ) = δ(k q)π(k, t 1,t 2 ) analytical model of the stochastic source for bubble collisions and MHD turbulence 1. space correlation structure (at equal times) 2. time correlation structure 3. overall time evolution

12 Spatial correlation of the anisotropic stress bubbles and MHD, causal processes with typical length scale: bubble size flat: spatially uncorrelated, causality slope depending on source power spectrum 0.1 k 4 bubbles k, t1, t characteristic length scale: bubble size R k 11/3 Kolmogorov turbulence k R

13 Temporal correlation of the anisotropic stress BUBBLES : completely coherent different collision events are uncorrelated in time single collision event is coherent : time evolution deterministic Π(k, t 1,t 2 )= Π(k, t 1,t 1 ) Π(k, t 2,t 2 ) GW spectrum becomes the square of the time Fourier transform of the source : peak at the characteristic time of the source k β (β <R 1 ) the source lasts for a short time compared to the Hubble time β H 1

14 Temporal correlation of the anisotropic stress MHD TURBULENCE : decorrelating in time motions decorrelate with eddy turnover time decorrelation time depends on eddy size τ v correlated for t 1 t 2 < 1 k Π(k, t 1,t 2 )={Π(k, t 1,t 1 )Θ[t 1 t 2 ]Θ[1 k(t 1 t 2 )] + t 1 t 2 } no temporal Fourier transform: peak at the spatial correlation scale k R 1 the source lasts for a long time compared to the Hubble time: determined by the decay of the turbulent motions, not very efficient because of low viscosity of the primordial fluid

15 k R Characteristic shape of the GW power spectrum decorrelating source low frequency slope: causality of the source k 3 h 2 d GW dlogk coherent source

16 k R Characteristic shape of the GW power spectrum peak position: k β R = v b /β k R decorrelating source low frequency slope: causality of the source k 3 h 2 d GW dlogk coherent source

17 k R Characteristic shape of the GW power spectrum peak position: k β R = v b /β k R 1 coherent source: feature at k R decorrelating source low frequency slope: causality of the source k 3 h 2 d GW dlogk coherent source

18 k R Characteristic shape of the GW power spectrum peak position: k β R = v b /β k R 1 coherent source: feature at k R 1 high frequency slope: depends on both power spectrum and time correlation of the source decorrelating source low frequency slope: causality of the source k 3 h 2 d GW dlogk coherent source

19 GW spectrum from bubble collisions h 2 d GW dlogk k 3 peak k β k 1 thin wall approximation, no feature at R k Β

20 GW spectrum from MHD turbulence peak k R 1 h 2 d GW dlogk k 3 k 5/3 k 3/2 Kolmogorov or Iroshnikov Kraichnan spectrum k R

21 total GW spectrum for the EWPT Ω s =0.2 T = 100 GeV v b = β H = 10, 100, 1000 LISA h 2 d GW dlogk f Hz

22 total GW spectrum for the QCDPT T = 100 MeV Ω s =0.1 v b = β H =1, 2, 5, 10 Current NANOGrav sensitivity PTA h 2 (f) LISA f [Hz]

23 Conclusions If EWPT is first order: GW generated are interesting for LISA if energy in the bubble walls and turbulent motions is about 20% of radiation energy density lasts for more than one hundredth of Hubble time If QCDPT is first order: GW generated are interesting for PTA2020 if energy in the bubble walls and turbulent motions is about 10% of radiation energy density lasts for more than one tenth of Hubble time Future improvements: connection between phase transition parameters and kinetic energy in bubble walls and turbulence for the bubble case: go beyond thin wall approximation? for the turbulence case: confirm with simulations?