Diluting the inflationary axion fluctuation by stronger QCD in the early Universe

Transcription

1 Diluting the infltionry xion fluctution by stronger QCD in the erly Universe K. Choi, E. J. Chun, S. H. Im, KSJ rxiv: Kwng Sik JEONG Pusn Ntionl University CosKASI Drk Mtter Workshop June 2015

2 Outline Strong CP problem in the SM Axion drk mtter mu-trnsition nd stronger QCD in the erly Universe Diluting infltionry xion fluctutions Summry

3 1. SM

4 1. SM (1/3) The Stndrd Model of prticle physics Bsed on quntum field theory (specil reltivity + quntum mech.) Guge sector: SU(3) c SU(2) L U(1) Y guge bosons Mtter sector - qurks nd leptons - 3 fmily: only mss difference Sclr sector: Higgs field - determines the vcuum structure of the SM L (kinetic terms) (guge int's) (Yukw int's)

5 1. SM (2/3) Some fetures of the SM Accidentl globl symmetries t the renormlizble level - U(1) B nd U(1) L - Explins why protons re stble, nd why neutrinos re light. Flvor violtion only through chrged-current wek int s Flvor violtion only through chrged-current wek int s - Explins why FCNC effects re suppressed s experimentlly mesured

6 1. SM (3/3) SM: very successful t energy scles below TeV, BUT Nturlness problems - Origin of EWSB: why <H> 0, nd why <H>~100 GeV << M Pl? - Origin of flvor structure - Strong CP problem Drk mtter, Drk energy Bryon symmetry in the Universe Neutrino msses Why 3 guge interctions? Grnd unifiction? Cosmic infltion Quntum grvity, Requires new physics beyond the SM!

7 2. Axion solution to the strong CP problem

8 2. Strong CP problem (1/5) CP violtion in the SM C: chrge conjugtion (q -q) P: prity conversion (x -x) CP violtion if the Lgrngin involves complex coupling which cnnot be rotted wy by ny field redefinition. e.g. Yukw couplings in the SM

9 2. Strong CP problem (2/5) CP violtion in the SM CP violtion in the EW sector - CKM mtrix: ti qurk mixing ii mtrix ti in ssocition iti with wek int s Unitry tr to obtin mss eigensttes from m u,d =y u,d <H> One CP violting phse: δ CKM = 1.20±0.3 - PMNS mtrix: lepton mixing mtrix (mssive neutrinos) One CP phse: δcp the vlue is not well-known yet CP violtion in strong interctions - One CP violting phse relted with topologicl structure of QCD, nomly, nd instntons.

10 2. Strong CP problem (3/5) CP violtion in the electrowek nd strong interctions QCD LSM yqhqq GG 2 8 CP violtions CKM rg( y ) 1 q rg det( y ) QCD q 10 Experimentl bound on the neutron EDM n p d n Strong CP problem n mm u d e cm ( m m ) m u d s Strong CP problem: Why does QCD (lmost) preserve CP? Need some physicl explntion!

11 2. Strong CP problem (4/5) Axion solution to the strong CP problem Peccei nd Quinn 1977 Introduce NG boson ssocited with spontneously broken U(1) PQ symmetry which is nomlous under QCD the xion couples to gluons through f GG f : xion decy constnt ~ (PQ symmetry breking scle) QCD instntons explicitly brek PQ generting xion potentil QCD instntons explicitly brek PQ, generting xion potentil fter QCD phse trnsition t Λ QCD ~ 400 MeV.

12 2. Strong CP problem (5/5) Axion solution to the strong CP problem Axion potentil V( ) V 4 1 cos QCD f clssicl 0 f QCD instntons explicitly brek PQ, generting xion potentil. θ is dynmiclly cncelled, nd thus QCD becomes CP conserving: 0 f

13 3. Axion drk mtter

14 3. Axion DM (1/3) Axion properties determined by f ~ (PQ breking scle) - xion mss: m -xion couplings to SM xion-nucleon interction g NN GeV xion-photon interctionn g 2 12 QCD 6 10 GeV 510 ev f f f 10 GeV 10 GeV f To void the strophysicl constrints (xion emission from neutron strs, nd supernove), f GeV The xion is stble on cosmologicl time scle, nd so cn explin the drk mtter of the Universe.

15 3. Axion DM (2/3) Axion drk mtter The xion necessrily contributes to cold drk mtter if it solves the strong CP problem. - Axions re produced by coherent oscilltions of misligned xion field when H becomes comprble to the xion mss, nd behve like non-reltivistic prticles. V ( ) 2 f 1.7mis GeV DM H m H m ( T) f (xion direction) θ mis: initil mislignment ngle of the xion

16 3. Axion DM (3/3) PQ extension of the SM PQ extension nturlly explins why the strong interction does not brek CP, nd provides good drk mtter cndidte. KSVZ models (hdronic xion model): PQ chrged hevy qurks DFSZ models: PQ chrged Higgs biliner H u H d

17 4. Cosmologicl constrints on xion drk mtter

18 4. Constrints (1/2) Possible scenrios depending on when PQ phse trnsition occurs 1. PQ symmetry breking occurs fter infltion - Need N DW =1 (number of degenerte vcu) to void overclosure of the Universe severe constrint n on xion models - Mny ptches with different xion initil vlue: <θ 2 ini>=π 2 /3 - Axions re produced d minly by collpsing string-wll system (N DW =1) + from coherent oscilltions. domin-wll (disc-like object surrounded by string): unstble 10 DM f (2 4) 10 GeV Numericl simultion - Hirmtsu, Kwski, Sikw, Sekiguchi, 2012 V

19 4. Constrints (2/3) 2. No PQ restortion during infltion nd therefter There is no domin-wll problem. Axion cquires quntum um fluctutions u δθ during infltion. Axenides et l 1983, Turner et l 1985, - They do not ffect the totl energy density during the primordil infltion. - They turn into isocurvture density perturbtions t the QCD phse trnsition. CMB observtion T T 5 10, T K

20 4. Constrints (3/3) 2. No PQ restortion during infltion nd therefter Single-field infltion genertes dibtic perturbtions: no perturbtions in reltive number densities of different species i ( x) ( x) consistent with the observtions Isocurvture constrint on the xion DM T T 5 iso DM mis 6 Or high enough reheting temperture Axion density: θ mis (>>δθ) uniform throughout the whole observble Universe DM f( t0) 1.7mis 1 lrge f requires smll GeV mis

21 5. Axion drk mtter in the scenrio with no PQ restortion

22 5. Axion DM with no PQ restortion (1/4) Questions Wht is the mechnism stbilizing the xion decy constnt? DM f( t0) mis GeV Cn we suppress xion isocurvture perturbtions? T T 5 iso DM mis 6 - Axion fluctution: ( t ) I Ht ( I ) 2 f ( t ) I Plnck results: (tensor-to-sclr rtio) < 0.1 H(t I ) < GeV

23 5. Axion DM with no PQ restortion (2/4) Questions Cn we suppress xion isocurvture perturbtions? - Evolution of the xion fluctution ti from t I to t QCD : Ht ( I ) ( t QCD ) ( t I ) 2 f ( t ) where γ 1. -f (t I ) >> f (t 0 ) for θ mis =O(1) nd δθ 1 I Vlidity of n effective theory: f < M Pl Wek grvity conjecture: grvittionl interction is Arkni-Hmed, Motl, Nicolis, Vf, 2007 the wekest force γ<1 cn be importnt. 1 GG O 1 f M GG 2 8 Pl

24 5. Axion DM with no PQ restortion (3/4) Scenrio relizing f (t I ) >> f (t 0 ) Supersymmetric xion models generting xion scles through competition between supersymmetric higher dim superpotentil term nd SUSY breking effects f ( t ) m M 0 SUSY f ( t ) H( t ) M Pl I I Pl intermedite xion scle t present, while Hubble-induced lrge xion scle during infltion. This type of xion models cn be successfully embedded into string theory, where we cn explin why globl PQ symmetry is well protected from quntum grvity effects. K. Choi, KSJ, M. S. Seo, 2014

25 5. Axion DM with no PQ restortion (4/4) Scenrios relizing f (t I ) >> f (t 0 ) Isocurvture constrint f( t0) msusy 12 DM Ht ( I ) 10 GeV GeV 1TeV An observble tensor-to-sclr rtio ( ) in CMB cn be comptible with the xion drk mtter Ω =Ω DM, if the xion fluctution experiences mild suppression.

26 6. Diluting infltionry xion fluctution by stronger QCD

27 6. Dilution mechnism (1/6) We propose simple wy suppressing δθ through its cosmologicl evolution. Axions scles fixed by competition between supersymmetric higher dim superpotentil nd SUSY breking effects mu-trnsition: Higgs mu-term genertion through W X M 2 Pl H H J.E. Kim nd H. P. Nilles, 1984 Therml effects mke PQ-chrged X evolve s u d V T T m SUSY X t t X t t m M ( ) 0, ( ) SUSY Pl ( t t ) 0, ( t t ) m SUSY 0 X

28 6. Dilution mechnism (2/6) With the mu-trnsition, the wek scle cn experience unusul evolution becuse the H u H d flt direction (φ) hs mss m c H m SUSY Before the mu-trnsition (μ=0), negtive c φ nd ξ φ led to f ( t ) ( t ) H( t ) M I I I Pl f ( t t t ) ( t t t ) m M I I SUSY Pl - After the mu-trnsition, μ=m SUSY nd m 2 φ>0φ H ( t ) O(100GeV) ud, 0 f ( t ) X ( t ) m M 0 0 SUSY Pl

29 6. Dilution mechnism (3/6) Stronger QCD Lrge wek-scle before the mu-trnsition results in stronger QCD becuse the qurks become hevier: 10 5 (gluino mss before mu-trnsition), (tnβ t present) GeV QCD v GeV m f 2 QCD The xion obtins lrge mss for lrge Λ QCD!

30 6. Dilution mechnism (4/6) Suppression of δθ The xion experiences dmped oscilltion for m (t) > H(t). Note: The xion mss is highly suppressed by therml effects for T >> Λ QCD The xion fluctution is diluted s I SUSY 3/2 Ht ( ) m Ht ( I ) 2 f( ti) QCD 2 f( ti) if the xion mss is lrger thn H before the mu-trnsition: n: 1 2 f QCD V 0 m 0.4MeV H t 0.2MeV 12, ( ) GeV 20TeV 1TeV 10 GeV Vcuum energy density V 0 ~ m SUSY2 f (t 0 ) 2 drives therml infltion. Lyth nd Stewrt, 1995

31 6. Dilution mechnism (5/6) Upper bound on the infltionry Hubble scle consistent with Upper bound on the infltionry Hubble scle consistent with the xion drk mtter Ω =Ω DM :

32 6. Dilution mechnism (6/6) Axion relic bundnce The minimum of the xion potentil induced by the stronger QCD is generlly different from the minimum of the xion potentil t present. t ( ) t ( 0 ) mis O(1) f ( t ) f ( t ) 0 Combined with n intermedite xion scle t present, it leds to Ω =Ω DM in nturl wy.

33 7. Models implementing the suppression mechnism

34 7. Models (1/4) Simple exmple Superpotentil W c (MSSM Yukw) Y X HH XY M M M HH LH u d u d u Pl Pl Pl PQ chrged X nd Y re responsible for mu-trnsition: - Y obtins therml mss from the λ interction, nd is fixed t the origin until T drops below bout m SUSY. - X is lso trpped t the origin during this period becuse it hs vnishing tdpole. therml infltion: diluting wy unwnted relics (moduli, grvitino,..) 1 number of e-foldings: N ln( MPl / msusy ) 4

35 7. Models (2/4) Before the mu-trnsition, κ 3 term stbilizes the H u H d nd LH u flt directions. After the mu-trnsition, the mu-term mkes the flt directions non-tchyonic, nd consequently H u nd H d re stbilized ner the wek scle while L is fixed t the origin. X nd Y re fixed by κ 2 term. Axion mislignment ngle is generlly of O(1) becuse - the minimum of the xion potentil induced by stronger QCD is determined by the phse of κ 3 A 3. - the minimum t present is determined by the phse of Bμ. Axion cn nturlly ccount for the observed DM bundnce.

36 7. Models (3/4) The model cn successfully relize the desired cosmologicl evolution of 3 relevnt scles for m SUSY between 1-10 TeV: the xion scle, the wek scle, nd the QCD scle. Axion scle Ht ( I ) f ( t ) f ( t0), f ( t0 ) msusym m I Pl SUSY Wek scle vt ( t ) f( tt ), vt ( ) O(100GeV) Stronger QCD before the mu-trnsition ( t ) (20-30) TeV, ( t ) 400 MeV QCD QCD 0 0

37 7. Models (4/4) Interesting issues (work in progress) To complete our scheme, we need lte-time bryogenesis. - The simple model offers n elegnt mechnism to generte bryon symmetry through the rolling flt direction LHu: Affleck-Dine leptogenesis

38 8. Summry

39 8. Summry The QCD xion nturlly solves the strong CP problem, nd contributes to drk mtter of the Universe. Well-motivted drk mtter cndidte! We hve exmined how to suppress xion isocurvture perturbtions while producing the right mount of xion DM in nturl mnner. -Axion scles re induced by SUSY breking. - Intermedite phse trnsition to generte Higgs mu-term leds to stronger QCD, providing further suppression of xion isocurvture perturbtions. Thnk you!

40 Bckup

41 Infltion Infltion cn explin the initil conditions required for the Universe to evolve to its current stte in the Big Bng theory. genertes density perturbtions tht give rise to the cosmic structures. Slow-roll infltion Importnt observbles re the spectrl index nd tensor-to-sclr rtio: V inflton n s V V 1 2 3, V V At V r 8 A V s 2 2

42 No PQ restortion during infltion nd therefter - Single-field infltion genertes dibtic perturbtions: no perturbtions in the reltive number densities of different Or high enough reheting temperture species i ( x ) ( x) consistent with the observtions T T 5 10, T K - Axion fluctutions re produced during infltion, but do not ffect the totl energy density.

43 No PQ restortion during infltion nd therefter - Axion fluctutions turn into isocurvture density perturbtions t QCD phse trnsition, nd there ppers non-gussinity. T T iso DM ( x ) ( x) Axenides, Brndenberger, Turner, 1983; Seckel, Turner 1985; Linde 1985; Fox, Pierce, Thoms 2004, The xion is DM cndidte with isocurvture perturbtions, nd so is constrined from the observed CMB spectrum.