Dark energy, QCD axion, BICEP2, & trans-Planckian decay constant

1. Dark energy, QCD axion, BICEP2, & trans-Planckian decay constant Jihn E. Kim Kyung Hee Univ. & Seoul National Univ. 37th ICHEP, Valencia, Spain, 3-9 July 2014

2. 1. Introduction 2. DE from U(1)deas ps-goldstone boson 3. QCD axion 4. Gravity waves from U(1)depotential 5. Trans-Planckian fquint 6. PQ symmetry breaking below HI

3. 1. Introduction

4. Cosmic pie CC Follows the cold dark matter Responsible for galaxy formation We discuss DE of order 10-47 GeV4 and CDM axion.

5. Axion detection scheme 5/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

6. ★Axion detection is based on the bosonic coherent motion (BCM) can account for CDM. ★Higgs boson is a fundamental scalar. Higgs portal: In the age of fundamental scalars, can these explain both DE and CDM? In the age of GUT scale vacuum energy observed, can these explain all of DE and CDM and inflation-finish? 6/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

7. 2. DE from U(1)deas ps-goldstone boson

8. U(1) breaking potential For gauge symmetry breaking, exactly flat. For global symmetry breaking, ALWAYS a potential is generated: Approximate 8/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

9. Quantum gravity problem ★But quantum gravity effects are known to break global symmetries: the Planck scale wormholes connect observable universe O to the shadow world S. They can take out the global charges from O. ★ We can think of two possibilities of discrete symmetries realized from string compactification, below MP: • The discrete symmetry arises as a part of a gauge symmetry. • [Krauss-Wilczek, PRL 62 (1989) 1211] (ii) The string selection rules directly give the discrete symmetry. [JEK, PRL 111 (2013) 031801] ★ So, we start with discrete gauge symmetries. 9/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

10. Exact and approximate symmetries Vertical, exact sym.: gauged U(1), or string dictated. The global symmetry violating terms. A few low order W’s respected by discrete symmetry defines a global symmetry. 10/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

11. DE magnitude ★There exists a tiny DE of order 10-47 GeV4. ★We propose to relate this DE scale to a pseudo-Goldstone boson mass scale. ★The breaking scale of U(1)de is trans-Planckian, and the intermediate scale PQ symmetry breaking of U(1)de just adds the decay constant only by a tiny amount. 11/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

12. ★The discrete and global symmetries below MP are the consequence of the full W. So, the exact symmetries related to a discrete gauge symmetry or to string compactification are respected by the full W. Considering only W(3), we can consider approximate symmetries too. In particular, the approximate PQ symmetry. ★In string compactification, the bottom-up approach constraints [Lee et al, NPB 850, 1] toward a discrete gauge symmetry need not be considered. They are automatically satisfied with suitable massless singlets. ★For the MSSM interactions supplied by R-parity, one needs to know all the SM singlet spectrum. Z2 needed for a WIMP candidate. 12/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

13. ★Because the Higgs scalar is known to be a fundamental scalar, fundamental SM singlet scalar VEVs at the PQ symmetry breaking scale are considered, The DE potential height is The singlets must couple to Hu Hd : Then, to remove the U(1)de-QCD anomaly , U(1)PQ must be introduced for one linear combination is free of the QCD anomaly. The needed discrete symmetry must be of high order such that some low order W are forbidden. 13/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

14. ★ But, if QCD anomaly coupling to U(1)de is present, then we have the usual QCD axion. ★ U(1)de should not have QCD anomaly. ★ We need one more U(1) such that one linear combination U(1)de does not have the QCD anomaly. We must introduce to global U(1)s, of course approximate: U(1)de and U(1)PQ . ★ We have the scheme to explain both 68% of DE and 28% of CDM via approximate global symmetries. With SUSY, axino may contribute to CDM also. Hilltop inflation 14/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

15. Typical example ★ The height of the potential is highly suppressed and we can obtain 10-47 GeV4 from discrete symmetry Z10R, without the gravity spoil of the global symmetry breaking term. ★ The discrete symmetry Z10R charges are the gauge charges of the mother U(1) gauge symmetry. ★ As a byproduct of the Mexican hat potential, Fig. (b), we also have a model of inflation, the so-called ‘hilltop inflation’. It is a small field inflation, consistent with the recent PLANCK data. Written before BICEP2

16. ★The simplest orbifold is Z(12-I), since there are only 3 fixed points. Note Z(3) has 27 fixed points. The model of [Huh-Kim-Kyae, PRD 80, 115012] has the Higgs with two units of discrete charge. ★For example, the Z10 is a subgroup of one U(1) direction Z10 = (0 0 0 0 0 4 2 0) (0 0 0 0 0 -8, 4, 0)’ (A) ★For the MSSM interactions supplied by R-parity, one needs to know all the SM singlet spectrum. Z2 needed for a WIMP candidate. 16/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

17. ★Some singlets have the even discrete charges. For example, s9 and s13 have Z10 quantum number magnitude 10. ★The VEVs of s9 and s13 break U(1) gauge symmetry direction (A) to Z10 . Even if Higgs doublets obtain VEVs, the resulting discrete group is Z2. From this direction, we can obtain Z10 if d=3 superpotential term contains Z10 =0 terms. We obtain Z10R if d=3 superpotential term does not contain Z10 =0 terms, but contains Z10 =2, 12, 22, etc. terms. For Z10 or Z10R , the d=2 μ Hu Hd term is not allowed. ★In conclusion, it is so simple to obtain the desired ZN or ZnR symmetry if we know all the SM singlets. We presented it in a Z(12-I) model. We find the method very useful for model building. And we can obtain an approximate PQ global symmetry as discussed in[JEK, PRL 111, 031801 (2013)] for the case of S2xS2. . 17/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

18. For DE, the potential is extremely flat; still the DE vacuum looks like contributing to cosmological constant. For QCD axion, the vaucuum already started bosonic coherent motion(BCM) at T1 ≈ 1 GeV.

19. 3. QCD axion

20. Cosmology of axion models 1. BCM: Preskill-Wise-Wilczek, Abbott-Sikivie, Dine-Fischler 2. Axion DW problem: Zel'dovich-Kobzarev-Okun (1975); Vilenkin-Everett (1982); P. Sikivie (1982). 3. N=1 numerical simulation: Florida group (Sikivie-Chang-Hagmann), Cambridge group (Battye-Shellard), ICRR(U. of Tokyo) group (Kawasaki-Hiramatsu-Saikawa-Sekiguchi) 4. Solutions: Works for discrete groups. Lazarides-Shafi, PLB115, 21 (1982), Choi-Kim, PRL55, 2637 (1985), JEK, PLB734, 68 (2014) [arXiv:1405.0221[hep-th]]. 20/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

21. It is very flat if the axion decay constant is large, CP conserving point 10-20 In the evolving universe, at some temperature, say T1, a starts to roll down to end at the CP conserving point sufficiently closely. This analysis constrains the axion decay constant (upper bound) and the initial VEV of a at T1. Still oscillating nEDM was suggested to be measured 20 years ago: Hong-Kim-Sikivie, PRD42, 1847 (1990), Hong-Kim PLB265, 197 (1991), Hong-Kim-Nam-Semertzdis, 1403.1576. Graham et al, 1101.2691, Budker et al, 1306.6089, Sikivie et al, 1310.8545. The axion oscillation is just one example of Bosonic Coherent Motion (BCM). 21/59 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

22. The Lagrangian is invariant under changing θ → θ-2α.But θ becomes dynamical and the θ=a/Fapotential becomes The true vacuum chooses θ=a/Faat 22/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

23. A recent calculation of the cosmic axion density is, 109 GeV < Fa < {1012 GeV ?} Turner (86), Grin et al (07), Giudice-Kolb-Riotto (08), Bae-Huh-K (JCAP 08, [arXiv:0806.0497]): recalculated including the anharmonic term carefully with the new data on light quark masses. It is the basis of using the anthropic argument for a large Fa. Without string radiation Reheating after inflation: Visinelli+Gondolo, Marsh et al. 23/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

24. Many lab. searches were made, and we hope the axion be discovered . BICEP2: Gondolo+Vissinelli, Marsh et al. Only string calculation: JEK, PLB735 (2014) 95 [1405.6175[hep-ph]] Oscillating nEDM was suggested to be measured 20 years ago: Hong-Kim-Sikivie, PRD42, 1847 (1990), Hong-Kim PLB265, 197 (1991). Rate calculation: Hong-Kim-Nam-Semertzidis, arXiv:1403.1576[hep-ph].

25. Only string calculation: JEK, PLB 735 (2014) 95, 1405.6175[hep-ph] 100% axion CDM is ruled out. 25/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

26. The d=4 example is the θ term of Callan-Dashen-Gross and Jackiw-Rebbi. The d=5 examples are Weinberg operator and KN operator(with SUSY). The global symmetry violating terms. A few low order W’s are respected by discrete symmetry.

27. But the dominant breaking is by the QCD anomaly term: 27/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

28. Dominantly by the QCD anomaly term:

29. 4. Gravity waves from U(1)depotential

30. DE magnitude ★There exists a tiny DE of order 10-47 GeV4. ★ What is the form of the U(1)de breaking V? ★We propose to relate this DE scale to a pseudo-Goldstone boson mass scale. ★The breaking scale of U(1)de is trans-Planckian, and the intermediate scale PQ symmetry breaking of U(1)de just adds the decay constant only by a tiny amount. The height is (GUT scale)4 ★It is by closing the green circle of (a): 30/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

31. ★We obtain [0.96, 0.008] New type (chaoton) hybrid inflation 31/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

32. Natural inflation starting at 0 is here. Natural inflation starting at π is here. Freese-Kinney: 1403.5277. 32/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

34. ★One condition to have a large e-folding is the Lyth bound, in our case fDE > 15 MP[D. Lyth, PRL 78 (1997) 1861] ★It is possible if the potential energy density is lower than MP4 .. One method is natural inflation: [Freese-Frieman-Olinto, PRL 65 (1990) 3233]. But, trans-Planckian needed two axions at least: [Kim-Nilles-Peloso, JCAP 01 (2005) 005]

35. 5. Trans-Planckian fquint

36. U(1)de inflation with ‘chaoton’ X, more range. 36/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

37. Kim-Nilles, PLB 730 (2014) 53 [arXiv:1311.0012]. Kim [arXiv:1404.4022].

38. Lyth, 1403.7323 [hep-ph]

39. Trans-Planckian decay constant ★ Fundamental theory suppressed by MP, ★ ZnR example: ZnR quantum number 39/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

40. Trans-Planckian decay constant ★ ψ /MP ≈ 0.01, Φ /MP≈31=103/2 Lyth, 1403.7323 [hep-ph] For Φ104 /Mp100 , we need 10-127 . 40/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

42. 6. PQ symmetry breaking below HI JEK, PLB734, 68 (2014), 1405.0221[hep-th]

43. HI≈1014 GeV imply most probably that the PQ symmetry breaking has occurred after (at the end phase of) inflation. Reheating may go close to HI, maybe suppressed by a factor of 50-100 [Buchmuller et al, 1309.7788]. So, the method of inflating away strings and domain walls of spontaneously broken U(1)PQ is out. The DW number must be one. The horizon size wall(s) is the problem. The domain wall problem: Zeldovich-Kobzarev-Okun (1974); Sikivie (1982). DW number = 1:

44. For the DW number = 2:

45. The Lazarides-Shafi mechanism: Center of nonabelian groups. The Choi-Kim mechanism (PRL55, 2637 (1985)) : Discrete subgroups of U(1)’s or Goldstone boson directions. 46/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

46. Choi-Kim mechanism Choi-Kim, PRL55 (1985) 2637 N1 Flat direction. Max. common divisor of 2 and 3 is NDW= 1. Identification by torus. Identification by torus. N2

47. Model-independent axion with U(1)anom ★ The MI-axion has NDW =1 [Witten, PLB 153, 243 (1985)]. Basically, it is due to the Green-Schwarz condition, with the unit coefficient. It is in 10D and SU(3)-color is in the fundamental of E8 which will become the fundamental of SU(3)-color. For MI axion, we have NDW =1. 47/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

48. U(1)PQ broken at an intermediate scale ★ Three families arise in addition from comp’n with those in the twisted sectors. Then, we have to check all the colored fields, including those from twisted sectors. The necessary condition to have DW number 1 is the U(1)PQ below U(1)anom scale has the coupling with common N ★ This form is necessary to allow a Goldstone boson direction ∂2a=0. Then, we obtain NDW =1by the CK mechanism. 48/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

49. MI-axion: has DW number = 1: [Witten (1985)]. In Z3 orbifold model: [JEK, PLB 207, 434 (1988)]. Actually, Z3 (with 27 fixed points) is not the simplest orbifold model. Z12 is the simplest one (with 3 fixed points). ★ For the Z12 Huh-Kim-Kyae model, we explicitly calculated that N is the same for SU(5)flip , SU(5)’, and SU(2)’: NDW =1 solution. 49/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14

50. 50/55 J E Kim “DE, QCD axion, and trans-Planckian f”, 37th ICHEP, Valencia, 03.07.14