1. Dark energy and QCD axion from approximate U(1) de & U(1) PQ JEK, Phys. Rev. Lett. 111 (2013) 031801; JEK, Phys. Lett. B726 (2013) 450; JEK+H. P. Nilles, Phys. Lett. B730 (2014) 53 ; JEK, JKPS 64 (2014)795 [arXiv:1311.4545[hep-ph] ]. Jihn E. Kim Kyung Hee Univ. & Seoul National Univ. KASI, 16 April 2014

2. Sure, data needs more crayons! Or, color generating computer! All colors are constructed with three fundamental ones! (She may be a theorist)

3. 1. Introduction 2. Axions and the strong CP problem 3. QCD axion from discrete symmetries 4. Dark energy from U(1) de

4. 1. Introduction

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

6. A rough sketch of WIMP masses and cross sections. [Baer-Choi-Kim- Roszkowski, Soon appearing [arXiv:1404.xxxx]] J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 6/40

7. ★ Because DE is a property of potential energy, bosonic coherent motion (BCM) can account for it. BCM such as axion also accounts for CDM. ★ Higgs boson is a fundamental scalar. In the age of fundamental scalars, can these explain both DE and CDM? Higgs portal: The Higgs fields know the fundamental scalars contributing to CDM and DE. THEN, GLOBAL SYMMETRIES, AS FOR THE AXION, IS BETTER TO BE CONSIDERED. In the age of GUT scale vacuum energy observed, can these explain all of DE and CDM and inflation-finish? J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 7/40

8. ★ 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 “Dark energy and QCD axion”, KASI, 16 April 2014 8/40

9. 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 “Dark energy and QCD axion”, KASI, 16 April 2014 9/40

10. 2. Axions and Strong CP

11. The strongly interacting θ(Gluon) μν (Gluon-dual) μν term gives a nEDM. Neutron EDM is measured very accurately. d n th = (1.2-14.5)x10 -16 θe cm d n exp = 2.9 x10 -26 e cm, Baker et al (2006) Strong CP “Why is nEDM so small?” is the strong CP problem. J E Kim “Dark energy and QCD axion”, KASI, 16 April y 2014 1140

12. For gauge symmetry breaking, exactly flat. For global symmetry breaking, a potential is generated: Approximate J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 12/40

13. 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 “Dark energy and QCD axion”, KASI, 16 April 2014 13/40

14. 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 “Dark energy and QCD axion”, KASI, 16 April 2014 14/40

15. 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 All these three figures, Baer-Choi-Kim-Roszkowski, “Nonthermal DM”, to appear. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 15/40

16. L. Rosenberg and G. Rybka in front of the ADMX apparatus. Science 343, 552, 1 November 2013. CAPP at KAIST(Y. Semertzdis) will do for a larger axion mass and more. Xe tank at XMASS before completing filling water 30 October 2013.

17. Science Vol. 343, 552 (2013): 1 November 2013, Focus Solve technical problem in theory of strong nuclear force Explain dark matter Bounce off atomic nuclei Turn into photons in strong magnetic field Solve more than one problem; allow for decisive test. Follow naturally from supersymmetry; provide many models and multiple avenues of detection Year invented 1977 by Lee-Weinberg; SUSY WIMP 1983 Gold. 1979 invisible axion 1982 CDM

18. Many lab. searches were made, and we hope the axion be discovered. Graham et al, 1101.2691, Budker et al, 1306.6089, Sikivie et al, 1310.8545. Oscillating nEDM was suggested to be measured 20 years ago: Hong-Kim- Sikivie, PRD42, 1847 (1990), Hong-Kim PLB265, 197 (1991), Hong-Kim- Nam-Semertzidis, arXiv:1403.1576[hep-ph]. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 18/40

19. KSVZ axion: The Peccei-Quinn symmetry by renormalizable couplings to heavy quarks. Here, Higgs doublets are neutral under PQ. If they are not neutral, then it is not necessary to introduce heavy quarks [DFSZ axion]. In any case, the axion is the phase of the SM singlet S, if the VEV of S is much above the electroweak scale. Because F a can be in the intermediate scale, axions can live up to now (m<24 eV) and constitute DM of the Universe. Why are we restricted to renormalizable interactions only at the EW scale? Definition of a global symmetry can be non- renormalizable terms also: DFSZ. Kim-Nilles term J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 19/40

20. The axion is created at T=F a, but the universe  ( )does not roll until 3H=m a (T=0.92 GeV [Bae-Huh-Kim]). From then on, the classical field starts to oscillate. harmonic oscillator motion: m a 2 F a 2 = energy density = m a x number density = like CDM. See, Bae-Huh-Kim, arXiv:0806.0497 [JCAP09 (2009) 005], Figure will be given with correct coefficients and new data Baer-Choi-Kim-Roszkowski, “Nonthermal DM”, to appear. 10 9 GeV < F a <10 12 GeV, J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 20/40

21. 3. QCD axion from discrete symmetries

22. S 2 (L) x S 2 (R) symmetric fermion masses can arise from The fermion mass matrix will be The first step for the solution of the μ-problem. [JEK, arXiv:1303.1822]. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 22/40

23. [JEK, PRL111, 031801 arXiv:1303.1822].

24. In string theory, matter fields are from E 8 x E 8 representations. Not from B MN. Kim-Nilles μ-term arises from Where do X and X–bar belong? Anyway, B MN fields: decay constant is very large F>10 16 GeV [Choi-Kim (1984), Svrcek-Witten(2006)] Probably, in matter reps. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 24/40

25. How can we break S 2 (L) x S 2 (R) symmetry ? Spontaneously by The massless (0) fields, and superheavy (G) fields J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 25/40

26. This defines the PQ charges of X and H. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 26/40

27. ★ Quantum gravity effects occurring at the Planck scale connect the observable universe O to the shadow world S via the Planck size wormholes. The discrete symmetry is a part of a gauge symmetry. How did we succeed? J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 27/40

28. 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. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 28/40

29. The PQ breaking diagram is J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 29/40

30. But the dominant breaking is by the QCD anomaly term: J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 30/40

31. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 31/40

32. 4. Dark energy from U(1) de

33. 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 “Dark energy and QCD axion”, KASI, 16 April 2014 33/40

34. ★ 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 “Dark energy and QCD axion”, KASI, 16 April 2014 34/40

35. ★ 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 “Dark energy and QCD axion”, KASI, 16 April 2014 35/40

36. ★ A related comment is on the dilatonic symmetry: The dilatonic symmetry is spontaneously broken at the Planck scale. So, the dilaton is created without potential. It appears in the exponent. How do we raise the height of the dilaton potential? Another VEV such as and cannot render a potential for the dilaton. Maybe a confining force can do it. So, dilaton may have a severe problem accounting the scale of DE. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 36/40

37. ★ 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 “Dark energy and QCD axion”, KASI, 16 April 2014 37/40

38. ★ 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 J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 38/40

39. ★ 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 “Dark energy and QCD axion”, KASI, 16 April 2014 39/40

40. ★ 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 “Dark energy and QCD axion”, KASI, 16 April 2014 40/40

41. 5. Gravity waves from U(1) de

42. 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 “Dark energy and QCD axion”, KASI, 16 April 2014 42/40

43. ★ We obtain [0.96, 0.008] New type (chaoton) hybrid inflation J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 43/40

44. Natural inflation starting at π is here. Freese-Kinney: 1403.5277. Natural inflation starting at 0 is here. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 44/40

45. ★ 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] J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 45/40

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

47. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 49/40

48. J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 48/40 U(1) de inflation with ‘chaoton’ X, more range.

49. Conclusion ★ BCM is one possibility of CDM. ★ Global symmetry U(1) PQ needed. ★ For CDM, it must live sufficiently long. ★ Invisible axion is a CDM candidate. ★ Higgs portal, or anomaly portal always give U(1) PQ –gluon-gluon anomaly. ★ U(1) de can give anomaly–free pseudo- Goldstone boson for the observed DE.

50. City of Daejeon, Yusung Prefecture KAIST Campus Head Q Campus 3 km Center for Axion and Precision Physics: Yannis Semertzidis Center for Underground Physics: Young Duk Kim Center for Theoretical Physics of the Universe(hep-ph, -th, nucl-th, astro-ph[CO]): Kiwoon Choi