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

2. 1. Introduction 2. DE from U(1) de as ps-goldstone boson 3. QCD axion 4. Gravity waves from U(1) de potential 5. Trans-Planckian f quint 6. PQ symmetry breaking below H I

3. 1. Introduction

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

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

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? J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 6/55

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

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

9. ★ 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. (i)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] ★ We can think of two possibilities of discrete symmetries realized from string compactification, below M P : ★ So, we start with discrete gauge symmetries. Quantum gravity problem J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 9/55

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

11. DE magnitude ★ There exists a tiny DE of order 10 -47 GeV 4. ★ 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. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 11/55

12. ★ The discrete and global symmetries below M P 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. Z 2 needed for a WIMP candidate. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 12/55

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 H u H d : 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. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 13/55

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 J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 14/55

15. ★ The discrete symmetry Z 10R charges are the gauge charges of the mother U(1) gauge symmetry. ★ The height of the potential is highly suppressed and we can obtain 10 -47 GeV 4 from discrete symmetry Z 10R, without the gravity spoil of the global symmetry breaking term. ★ 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. Typical example 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 Z 10 is a subgroup of one U(1) direction Z 10 = (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. Z 2 needed for a WIMP candidate. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 16/55

17. ★ Some singlets have the even discrete charges. For example, s 9 and s 13 have Z 10 quantum number magnitude 10. ★ The VEVs of s 9 and s 13 break U(1) gauge symmetry direction (A) to Z 10. Even if Higgs doublets obtain VEVs, the resulting discrete group is Z 2. From this direction, we can obtain Z 10 if d=3 superpotential term contains Z 10 =0 terms. We obtain Z 10R if d=3 superpotential term does not contain Z 10 =0 terms, but contains Z 10 =2, 12, 22, etc. terms. For Z 10 or Z 10R, the d=2 μ H u H d term is not allowed. ★ In conclusion, it is so simple to obtain the desired Z N or Z nR 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 S 2 xS 2.. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 17/55

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 T 1 ≈ 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]]. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 20/55

21. In the evolving universe, at some temperature, say T 1, 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 T 1. It is very flat if the axion decay constant is large, CP conserving point The axion oscillation is just one example of Bosonic Coherent Motion (BCM). 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. 10 -20 J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 21/59

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

23. A recent calculation of the cosmic axion density is, 10 9 GeV < F a < {10 12 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 F a. Without string radiation Reheating after inflation: Visinelli+Gondolo, Marsh et al. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 23/55

24. Many lab. searches were made, and we hope the axion be discovered. 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]. BICEP2: Gondolo+Vissinelli, Marsh et al.

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

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

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

28. Dominantly by the QCD anomaly term:

29. 4. Gravity waves from U(1) de potential

30. DE magnitude ★ There exists a tiny DE of order 10 -47 GeV 4. ★ 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): ★ What is the form of the U(1) de breaking V? J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 30/55

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

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

34. ★ One condition to have a large e-folding is the Lyth bound, in our case f DE > 15 M P [D. Lyth, PRL 78 (1997) 1861] ★ It is possible if the potential energy density is lower than M P 4.. 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 f quint

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

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 M P, ★ Z nR example: Z nR quantum number J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 39/55

40. Trans-Planckian decay constant ★ ψ /M P ≈ 0.01, Φ /M P ≈31=10 3/2 Lyth, 1403.7323 [hep-ph] For Φ 104 /M p 100, we need 10 -127. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 40/55

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

43. H I ≈10 14 GeV imply most probably that the PQ symmetry breaking has occurred after (at the end phase of) inflation. Reheating may go close to H I, 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. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 46/55

46. Choi-Kim mechanism Flat direction. Max. common divisor of 2 and 3 is N DW = 1. N2N2 N1N1 Identification by torus. Identification by torus. Choi-Kim, PRL55 (1985) 2637

47. For MI axion, we have N DW =1. Model-independent axion with U(1) anom ★ The MI-axion has N DW =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 E 8 which will become the fundamental of SU(3)-color. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 47/55

48. ★ This form is necessary to allow a Goldstone boson direction ∂ 2 a= 0. Then, we obtain N DW =1 by the CK mechanism. 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 J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 48/55

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)’: N DW =1 solution. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 49/55

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

52. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 52/55

53. J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 53/55

54. : JEK, 1405.6175[hep-ph] ★ Furthermore, we can calculate the axion-photon-photon coupling: J E Kim “DE, QCD axion, and trans-Planckian f”, 37 th ICHEP, Valencia, 03.07.14 54/55

55. Conclusion ★ BCM is one possibility of CDM. ★ U(1) de can give anomaly–free pseudo- Goldstone boson for the observed DE, and global symmetry U(1) PQ needed. ★ For CDM, it must live sufficiently long:BSM ★ There is another way for trans-Planckian inflaton. ★ Invisible axion is a CDM candidate. ★ The PQ phase transition after inflation: heterotic string with anomalous U(1) is the solution.