1. Non-minimal inflation and SUSY GUTs Nobuchika Okada University of Alabama International Workshop on Grand Unification Yukawa Institute of Theoretical Physics March 15-17, 2012

2. In collaboration with Masato Arai, Shinsuke Kawai, Mansoor Ur Rehman, Qaisar Shafi

3. The Standard Big-Bang Cosmology The success of the Standard Big-Bang Cosmology Hubble expansion Hubble’s law: expansion of the Universe Cosmic Microwave Background (CMB) 2.725K radiation, Planck distribution Big-Bang nucleosynthesis Success in synthesizing light nuclei in the early Universe

4. General theory of relativity Homogeneous & isotropic universe  Friedmann-Robertson-Walker metric (k=0) Einstein equations: Perfect fluid: Expansion law: Continuity equation: w=1/3 : radiation w=0 : matter

5. Brief thermal history of the Universe T Big-bang all particles are in thermal equilibrium ~1 MeV (10^10 K) Big-bang nucleosynthesis ~1 eV Recombination  origin of CMB Equal epoch (radiation density = matter density) ~ 0.1 eV Present ~0.0001 eV decoupling of some particles (example: Dark Matter) Hot & dense thermal state Radiation dominated era Matter dominated era w=1/3 w=0

6. Problems of Big-Bang Cosmology Flatness problem Fine-tuning of density parameter is necessary Horizon problem Observed CMB is isotropic nevertheless two regions have never contacted with each other Origin of density fluctuation need the seed of density fluctuation for the large scale structure formation of the Universe Big-Bang Cosmology: w=1/3 : radiation w=0 : matter Decelerating expansion

7. Basic Idea of Inflationary Universe Suppose the existence of a stage in the early universe with Simple example: de Sitter space Positive cosmological constant (vacuum energy) Expansion law: Continuity equation: ``Inflation’’ Accelerating Expansion

8. Exponential expansion (Inflation) solves flatness problem  spatial curvature flattened horizon problem  small causal region expanded Simple model of inflation  scalar field called ``inflaton’’ Quantum fluctuation of inflaton  origin of primordial density fluctuation

9. Simple inflation model The picture we seek…. Inflation before Big-Bang  Big-bang cosmology Slow-roll inflation A scalar field (inflaton) slowly-rolling down to its potential minimum Slow-roll End of inflation Oscillations & decay 1. Inflation at slow-roll era 2. End of Inflation 3. Coherent oscillations 4. Decays to Standard Model particles 5. Reheating  Big-Bang Cosmology

10. Primordial density fluctuation Slow-roll End of inflation Oscillations & decay During inlaftion era, quantum fluctuation of inflaton is enlarged by inflation Inflaton fluctuation  curvature fluctuation  structure formation, CMB anisotropy Inflaton fluctuation  inflaton potential, initial condition CMB anisotropy  precision measurement by observation

11. CMB Observations: Wilkinson Microwave Anisotropy Probe (WMAP) The observational cosmology is now a precision science!

12. Inflationary Predictions VS. WMAP inflationary scenario Slow-roll parameters Number of e-foldings N > 50-60 is necessary to solve horizon & flatness problem These are very small during inflation End of inflation 

13. Inflationary Predictions VS. WMAP (cont’d) Power spectrum Conditions to fix parameters in inflation model WMAP 7yr e-foldings = 50 -60 Predictions By these conditions, the slow-roll parameters are fixed Spectral index: Tensor-to-scalar ratio:

14. Example models We calculate the slow-roll parameters for each model and find predictions WMAP 7yr contours Model 1: Model 2: N=60 Model 1 Model 2

15. Inflation models with non-minimal gravitational coupling It is generally possible to add the non-minimal gravitational coupling to Einstein-Hilbert action Let us consider the model 2 with the non-minimal coupling In Jordan frame In Einstein frame

16. =const for a large inflaton VEV V

17. Predictions of non-minimal phi^4 model N. O.,Rehman & Shafi Phys. Rev. D 82, 043502 (2010)

18.  Minimal model N. O.,Rehman & Shafi Phys. Rev. D 82, 043502 (2010)

19. Higgs Inflation Replace phi  H Analysis beyond tree-level (RGE improved effective potential) Bezrukov & Shaposhnikov, PLB 659 (2008) 703; JHEP 07 (2009) 089 De Simone, Hertzberg & Wilczek, PLB 678 (2009)1 Barvinsky et al., JCAP 0912 (2009) 003

20. Realization of the non-minimal inflation model in supersymmetric model The Standard Model of elementary particle physics The best theory we know so far in describing elementary particle physics @ E=O(100 GeV) Quarks & leptons Gauge interactions QCD, weak, E&M Higgs  masses of particles

21. However, Experimental results which cannot be explained by the SM ex) neutrino masses & mixings non-baryonic dark matter,… Theoretical problems ex) The gauge hierarchy problem (stability of EW scale) Origin of electroweak symmetry breaking Fermion mass hierarchy, etc. We need to extend the SM, New Physics beyond the SM E ~ 1 TeV or higher

22. New Physics beyond the Standard Model takes place at high energies Remember: inflation occurs at very high energies We need to consider inflation scenario in the context of physics beyond the Standard Model Supersymmetric theory is one of the promising candidate of new physics beyond the Standard Model  Inflation model in the context of SUSY (Supergravity)

23. Minimal Supersymmetric Standard Model (MSSM) SUSY version of SM quark, lepton (1/2) squark, slepton (0) gauge boson (1) gaugino (1/2) Higgs (0) Higgsino (1/2) SM particles Superpartners SUSY Grand Unification is strongly supported by measurement of Standard Model gauge couplings Gauge coupling unification @

24. The Minimal SUSY SU(5) GUT Standard Gauge Interactions are unified into SU(5) GUT gauge interaction All quarks & leptons in the MSSM are unified into 5*+10 Particle contents Higgs fields in the MSSM are included New Higgs field to break SU(5) to the SM

25. Higgs inflation in the minimal SUSY SU(5) GUT Supergravity Lagrangian in superconformal framework Compensating multiplet: Minimal SUSY SU(5) model (Higgs sector) Arai, Kawai & N.O., PRD 84 (2011) 123515

26. We are interested in a special direction of the scalar potential SU(5)  SM

27. *Normalized by reduced Planck scale S is almost constant during inflation

29. Phi^4 inflation model with non-minimal coupling! * This structure has been first pointed out by Ferrara, Kallosh, Linde, Marrani & Van Proeyen (PRD 82 (2010) 045003, PRD 83 (2011) 025008) in the context of Next-to-MSSM

30. Predictions We also examined quantum corrections, but their effects are found to be negligible

31. Extension to other GUT models is possible which includes SU(5) as a subgroup (Example) SO(10) model

32. Another example MSSM + right-handed neutrino (For simplicity, we consider the 1 generation case) Again, we have non-minimal phi^4 inflation Arai, Kawai & N.O. arXiv:1112.239

34. From the seesaw relation by using The CMB data tells

35. Homework Extend the model to a GUT model

36. Summary We study the inflationary scenario in the context of the minimal SUSY SU(5) GUT We have found that the inflation model with non-minimal gravitational coupling is naturally implemented in the minimal SUSYT SU(5) GUT etc. with an appropriate Kahler potential The predicted cosmological parameters are consistent (almost best fit) with WMAP 7yr data In the near future, on-going Planck satellite experiment will provide us with more precise data which can discriminate different inflation models

37. ? Planck satellite experiment is on-going and plans to release the data in 2013 ? ?

38. Planck may tell us M R ?

39. Thank you very much for your attention!