L Breaking: (Dark) Matter & Gravitational Waves

Transcription

1 Cosmological B L Breaking: (Dark) Matter & Gravitational Waves Wilfried Buchmüller DESY, Hamburg with Valerie Domcke, Kai Schmitz & Kohei Kamada ; , 2.45, GGI, Florence, June 203

2 I. B L breaking, inflation & dark matter Light neutrino masses can be explained by mixing with Majorana neutrinos with GUT scale masses from B L breaking (seesaw mechanism) Decays of heavy Majorana neutrinos natural source of baryon asymmetry (leptogenesis; thermal (Fukugita, Yanagida 86) or nonthermal (Lazarides, Shafi 9) ) In supersymmetric models with spontaneous B L breaking, natural connection with inflation (Copeland et al 94; Dvali, Shafi, Schaefer 94;...) LSP (gravitino, higgsino,...) natural candidate for dark matter Consistent picture of inflation, baryogenesis and dark matter? Possible direct test: gravitational waves

3 Leptogenesis and gravitinos: for thermal leptogenesis and typical superparticle masses, thermal production yields observed amount of DM, Gh 2 TR 0 GeV 2 m g = C, C 0.5 ; GeV TeV m G DM h 2 0. is natural value; but why T R T L? Starting point simple observation: heavy neutrino decay width 0 N = m 8 M v EW 2 3 GeV, em 0.0 ev, M GeV. yields reheating temperature (for decaying gas of heavy neutrinos) T R 0.2 q 0 N M P GeV, wanted for gravitino DM. Intriguing hint or misleading coincidence? 2

4 II. Spontaneous B L breaking and false vacuum decay Supersymmetric SM with right-handed neutrinos, W M = h u ij i j H u + h d ij5 i j H d + h ij5 i n c jh u + h n i n c in c is, in SU(5) notation: =(q, u c,e c ), 5 =(d c,l); electroweak symmetry breaking, hh u,d i/v EW, and B L breaking, W B L = p 2 v 2 B L 2S S 2, hs,2 i = v B L / p 2 yields heavy neutrino masses. Lagrangian is determined by low energy physics: quark, lepton, neutrino masses etc, but it contains all ingredients wanted in cosmology: inflation, leptogenesis, dark matter,..., all related! 3

5 Parameters of B L breaking sector: m = p m 2 m 3 = 3 2 ev, M M 2,3 ' m S, em =(m D m D) /M, v B L. Spontaneous symmetry breaking: consider Abelian Higgs model in unitary gauge (! massive vector multiplet, no Wess-Zumino gauge!), S,2 = p 2 S 0 exp(±it ), V = Z + i 2g (T T ). Inflaton field : slow motion (quantum corrections), changes mass of waterfall field S, rapid change after critical point where m S =0; basic mechanism of hybrid inflation. Shift around time-dependent background, s 0 = p 2 ( 0 +i ), with v(t) = p 2 h 02 (t, ~x)i /2 ; masses of fluctuations: ~x 0! p 2v(t)+ 4

6 m 2 = 2 (3v2 (t) v 2 B L), m 2 = 2 (v2 B L + v 2 (t)), m 2 = v 2 (t), m 2 = v 2 (t), m 2 Z =8g 2 v 2 (t), M 2 i =(h n i ) 2 v 2 (t) ; time-dependent masses of B neutrinos, all supermultiplets! L Higgs, inflaton, vector boson, heavy 5

7 Constraints from cosmic strings and inflation: upper bound on string tension (Planck Collaboration 3) Gµ < 3.2 7, µ =2 B( )v 2 B L, with = /(8 g 2 ) and B( )=2.4[ln(2/ )] constraint from CMB (cf. Nakayama et al ), yields for < 2 ; further 3 5 GeV. v B L. 7 5 GeV, 4. p.. Final choice for range of parameters (analysis within FN flavour model): v B L =5 5 GeV, 5 ev apple em apple ev, 9 GeV apple M apple 3 2 GeV. (range of em : uncertainty of O() parameters) 6

8 Tachyonic Preheating Hybrid inflation ends at critical value c of inflaton field by rapid growth of fluctuations of B L Higgs field S 0 ( spinodal decomposition ): φ(t) (Tanh) <φ 2 (t)> /2 /v (Lattice) n B (x0) (Tanh) n B (x0) (Lattice) Bosons: Lattice Tanh Fermions: Lattice Tanh 0. <φ 2 (t)> /2 /v, nb(t) Occupation number: n k e e time: mt e k/m in addition, particles which couple to S 0 are produced by rapid increase of waterfall field (Garcia-Bellido, Morales 02); no coherent oscillations! 7

9 Decay of false vacuum produces long wave-length -modes, true vacuum reached at time t PH (even faster decay with inflaton dynamics), h 0 2 i =2vB 2 L, t PH ' 32 2 t=t PH 2m ln. Initial state: nonrelativistic gas of -bosons, N 2,3, Ñ 2,3, A, Ã, C (contained in superfield Z),... ; energy fractions ( = m X /m S, 0 = vb 4 L /4): B / 0 ' 2 3 g s f(,.3), F / 0 '.5 3 g s f(, 0.8). Time evolution: rapid N 2,3, Ñ 2,3, A, Ã, C decays, yields initial radiation, thermal N s and gravitinos; decays produce nonthermal N s; N decays produce most of radiation and baryon asymmetry; details of evolution described by Boltzmann equations. 8

10 Reheating Process Major work: solve network of Boltzmann equations for all (super)particles; treat nonthermal and thermal contributions di erently, varying equation of state; result: detailed time resolved description of reheating process, prediction of baryon asymmetry and gravitino density (possibly dark matter). Illustrative example for parameter choice M =5.4 GeV, em =4.0 2 ev, m eg = 0 GeV, m g =TeV; Gµ =2.0 7 fixes (within FN flavour model) all other masses, CP asymmetries etc. Note: emergence of temperature plateau at intermediate times; final result: B ' ' nt B, eg h 2 ' 0., i.e., dynamical realization of original conjecture. 9

11 Thermal and nonthermal number densities Inverse temperature M ê T R 45 s+y+f N nt +N é nt abs NHaL N eq B - L G é 30 N th +N é th N 2,3 +N é 2,3 25 i f a RH a RH a RH Scale factor a Comoving number densites of thermal and nonthermla N 0 s,..., B L, gravitinos and radiation as functions of scale factor a.

12 Time evolution of temperature: intermediate plateau 2 - Inverse temperature M ê T i f a RH a RH a RH Scale factor a Gravitino abundance can be understood from standard formula and e ective reheating temperature (determined by neutrino masses).

13 III. Gravitinos & Dark Matter Thermal production of gravitinos is origin of DM; depending on pattern of SUSY breaking, gravitino DM or higgsino/wino DM. Mass spectrum of superparticles motivated large Higgs mass measured at the LHC, m LSP m squark,slepton m eg. LSP is typically pure wino or higgsino (bino disfavoured, overproduction in thermal freeze-out), almost mass degenerate with chargino. Thermal abundance of wino ( ew) or higgsino ( e h) LSP significant for masses above TeV, well approximated by (Arkani-Hamed et al 06; Hisano et al 07, Cirelli et al 07) m 2 th ew, e h ew, e h h2 = c ew, e h, c ew =0.04, c eh TeV =0., Heavy gravitinos ( TeV... 3 TeV) consistent with BBN, eg ' 24 2

14 ( TeV/m eg ) 3 sec. Total higgsino/wino abundance ew, e h h 2 = e G ew, e h h2 + th ew, e h h2, G e LSP h 2 = m LSP eg h 2 ' m LSP m eg 0 GeV T RH (M, em ) GeV, with reheating temperature determined by neutino masses (takes reheating process into account), /4 5/4 T RH '.3 em M GeV 0.04 ev. GeV Requirement of LSP dark matter, i.e. LSP h 2 = DM h 2 ' 0., yields upper bound on the reheating temperature, T RH < 4.2 GeV; lower bound on T RH from successfull leptogenesis (depends on em ). 3

15 3000 WLSP > Wobs DM D é He -4 é Wwé > Wobs DM é w é G Whé > Wobs DM é h é -2-0 For each reheating temperature, i.e. pair (M, m e ), lower bound on gravitino mass (taken from Kawasaki et al 08) (left panel). Requirement of higgsino/wino dark matter puts upper bound on LSP mass, dependent on m e, reheating temperature (right panel); more stringent for higgsino mass, since freeze-out contribution larger. E.g., m = 0.05 ev implies meh < 900 GeV, mge & TeV. 4

16 IV. Gravitational Waves Relic gravitational waves are window to very early universe; contributions from inflation, preheating and cosmic strings (Rubakov et al 82; Garcia-Bellido and Figueroa 07; Vilenkin 8; Hindmarsh et al 2); cosmological B L breaking: prediction of GW spectrum with all contributions! Perturbations in flat FRW background, ds 2 = a 2 ( )( µ + h µ )dx µ dx, hµ = h µ 2 µ h, determined by linearized Einstein equations, h 00 µ (x, )+2 a0 a h 0 µ (x, ) r 2 x h µ (x, ) = 6 GT µ (x, ). Spectrum of GW background, GW (k, ) = GW (k, ln k, 5

17 Z d ln GW (k, ln k = 32 G Dḣij (x, ) ḣij (x, )E ; use initial conditions for super-horizon modes from inflation, calculate correlation function of stress energy tensor. Contribution from inflation (primordial spectrum, transfer function; Nakayama et al 08): cf. GW (k, ) = = 2 t 2 k 2 a 2 0 H2 0 2 t 2 r g k g 0 T 2 k ( ) g 0,s g k,s 8! 4/3 >< 2 (k eq/k) 2, k 0 k k eq, k eq k k RH >: 2 C3 RH (k RH/k) 2 k RH k k PH 6

18 with boundary frequences (f = k/(2 a 0 )), h f 0 = Hz, 0.70 f eq =.57 7 m h 2 Hz, 0.4 f RH =4.25 TRH Hz 7, GeV /6 2/3 /3 f PH =.99 4 v B L TRH Hz GeV 7. GeV Contribution from preheating (cf. Dufaux et al 07): GW (k PH ) h 2 ' c PH (R PH H PH ) 2 a PH a r h 2 g RH RH g 0 g 0,s g RH,s 4/3, 7

19 with characteristic scalar and vector scales R (s) PH =( vb L c ) /3, R (v) PH mz =2 p 2 gv B L. Contribution from cosmic strings (Abelian Higgs): GW (k) ' 6 2F r vb M Pl L 4 r h 2 8 < : (k eq /k) 2, k 0 k k eq, k eq k k RH (k RH /k) 2, k RH k constant F r recently determined in numerical simulation (cf. Figueroa, Hindmarsh, Urrestilla 2). Result similar to contribution from inflation, but very di erent normalization! 8

20 - D cosmic strings f PH HsL W GW h 2-20 HvL f PH preheating inflation - 25 f 0 f eq f RH f PH f@hzd 9

21 Are macroscopically long cosmic strings Nambu-Goto strings? Energy loss of string network by massive radiation or gravitational waves? GW radiation from NG strings, radiated by loops of length l(t, t i )= t i Gµ(t t i ); rate for amplitude h and frequency f (cf. Kuroyanagi et al 2), d 2 R dzdh (f, h, z) ' 3 m 2 4( + z)( + Gµ)h 2 t 4 (z) dv (z) dz ( m); can be approximately integrated analytically over z and h; results di ers qualitatively from Abelian-Higgs prediction; five orders of magnitude di erence in normalization! Truth somewhere inbetween? 20

22 Abelian-Higgs Strings vs. Nambu-Goto Strings - D a = - 6 a = - 2 W GW h 2 - Nambu-Goto - 5 Abelian- Higgs f@hzd 2

23 Observational Prospects - D W GW h HL H2L H9L AH cosmic strings H8L H7L H6L H5L H3L H4L NG cosmic strings inflation preheating f@hzd 22

24 Summary and Outlook Decay of false vacuum of unbroken B-L symmetry leads to consistent picture of inflation, baryogenesis and dark matter (everything from heavy neutrino decays) Prediction: relations between neutrino and superparticle masses for gravitino or higgsino/wino dark matter Possible direct test: detection of relic gravitational wave background, may provide determination of reheating temperature 23

25 (Non)thermal leptogenesis in M m plane é,m L hbhm vb-l = GeV hb < hobs B obs hnt B > hb obs hth B > hb th hnt B = hb Inflation & strings m - 0 Upper bound on M from inflation; lower bound from baryogenesis 24

26 Gravitino Dark Matter vs. leptogenesis such that WGé h2 = mgé = TeV 2 hb < hobs B 5 50 vb-l = GeV obs hnt B > hb m - 0 Gravitino mass range: GeV < mge < 700 GeV; heavy neutrino mass < range: 2 GeV < M 2 GeV (more stringent than inflation) 25