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Tunneling cosmological state and origin of SM Higgs inflation

Tunneling cosmological state and origin of SM Higgs inflation. A.O.Barvinsky Theory Department , Lebedev Physics Institute, Moscow. based on works with A.Yu.Kamenshchik C.Kiefer A.Starobinsky C.Steinwachs. QUARKS - 2010. Introduction.

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Tunneling cosmological state and origin of SM Higgs inflation

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  1. Tunneling cosmological state andorigin of SM Higgs inflation A.O.Barvinsky TheoryDepartment, LebedevPhysicsInstitute, Moscow based on works with A.Yu.Kamenshchik C.Kiefer A.Starobinsky C.Steinwachs QUARKS - 2010

  2. Introduction Problem of quantum initial conditions for inflationary cosmology No-boundary vs tunneling wavefunctions (hyperbolic nature of the Wheeler-DeWitt equation): inflaton other fields Euclidean spacetime Euclidean action of quasi-de Sitter instanton Lorentzian spacetime No-boundary ( + ): probability maximum at the mininmum of the potential vs infrared catastrophe no inflation Tunneling ( - ): probability maximum at the maximum of the potential

  3. Beyond tree level: inflaton probability distribution: contradicts renormalization theory for (- ) Both no-boundary (EQG path integral) and tunneling (WKB approximation) do not have a clear operator interpretation We suggest a unified framework for no-boundary and tunneling states as two different calculational prescriptions for the path integral of themicrocanonical ensemble in quantum cosmology, the tunneling state being consistent with renormalization

  4. Apply it to the Higgs inflation model with a strong non-minimal curvature coupling Higgs doublet CMB for GUT inflation: B. Spokoiny (1984); D.Salopek, J.Bond & J. Bardeen (1989); R. Fakir& W. Unruh (1990); A.Barvinsky & A. Kamenshchik (1994, 1998) F.Bezrukov & M.Shaposhnikov (2008-2009): Standard Model Higgs boson as an inflaton With the Higgs mass in the range 136 GeV < MH < 185 GeV the SM Higgs can drive inflation with the observable CMB spectral index ns¸ 0.94 and a very low T/S ratio r' 0.0004. A.O.B & A.Kamenshchik, C.Kiefer, A.Starobinsky, C.Steinwachs (2008-2009): A.O.B, A.Kamenshchik, C.Kiefer, C.Steinwachs (Phys. Rev. D81 (2010) 043530, arXiv:0911.1408): This model generates initial conditions for the inflationary background in the form of the sharp probability peak in the distribution function of an inflaton for the TUNNELING state of the above type.

  5. Plan Cosmological quantum states revisited microcanonical density matrix no-boundary vs tunneling states New status of the no-boundary state; Hartle-Hawking state as a member of the microcanonical ensemble massless conformal fields vs heavy massive fields Tunneling state for heavy massive fields SM Higgs inflation RG improved effective action inflationary CMB parameters inflaton probability distribution peak – initial conditions for inflation Conclusions

  6. Cosmological quantum states revisited A.O.B., Phys.Rev.Lett. 99, 071301 (2007) Microcanonical density matrix Wheeler-DeWitt equations Canonical (phase-space or ADM) path integral in Lorentzian theory: 3-metric and matter fields -- conjugated momenta constraints lapse and shift functions Range of integration over Lorentzian

  7. Lorentzian path integral = Euclidean Quantum Gravity (EQG) path integral with the imaginary lapse integration contour: Euclidean metric Euclidean action EQG density matrix D.Page (1986) Statistical sum: (thermal) onS3£ S1 including as a limiting (vacuum) case S4

  8. Minisuperspace-quantum matter decomposition: 3-sphere of a unit size Euclidean FRW metric lapse scale factor minisuperspace background quantum “matter” – cosmological perturbations quantum effective action of  on minisuperspace background

  9. Semiclassical expansion and saddle points: No periodic solutions of effective equations with imaginary Euclidean lapse N (Lorentzian spacetime geometry). Saddle points exist for realN (Euclidean geometry): Deformation of the original contour of integration into the complex plane to pass through the saddle point with real N>0 or N<0 gauge equivalent N<0 gauge equivalent N>0

  10. gauge (diffeomorphism) inequivalent!

  11. New status of the no-boundary state • Two cases: • massless conformally coupled quantum fields • 2) heavy massive quantum fields

  12. Massless quantum fields conformally coupledto gravity cosmological constant thermal part conformal anomaly and Casimir energy part coefficient of the Gauss-Bonnet term in the conformal anomaly Free energy (bosonic case): energies of field oscillators on a 3-sphere instanton period in units of conformal time --- inverse temperature

  13. Hartle-Hawking state as a member of the microcanonical ensemble pinching a tubular spacetime density matrix representation of a pure Hartle-Hawking state – vacuum state of zero temperature T~1/:

  14. Transition to statistical sums thermal instantons  = ’ Hartle-Hawking (vacuum) instanton  = ’

  15. Saddle point solutions --- set of periodic (thermal)garland-type instantons with oscillating scale factor ( S1X S3 ) and vacuum Hartle-Hawking instantons ( S4 ) , .... 1- fold, k=1 S4 k- folded garland, k=1,2,3,… bounded range of the cosmological constant new QG scale elimination of the vacuum no-boundary state: # of conformal fields

  16. No-boundary state: heavy massive quantum fields local inverse mass expansion Effective Planck mass (reduced) and cosmological constants Analytic continuation – Lorentzian signature dS geometry: S4 instanton (vacuum): Probability distribution on the ensemble of dS universes: infrared catastrophe no inflation

  17. Tunneling state: heavy massive quantum fields Effective Planck mass (reduced) and cosmological constant S4 (vacuum) instanton: Probability distribution of the ensemble of dS universes: no periodic solutions:

  18. SM Higgs inflation non-minimal curvature coupling inflaton inflaton-graviton sector of SM EW scale Non-minimal coupling constant

  19. RG improved effective action Local gradient expansion: running scale: Running coefficient functions: top quark mass anomalous scaling RG equations:

  20. Anomalous scaling Overall Coleman-Weinberg potential: Anomalous scaling in terms of SU(2),U(1) and top-quark Yukawa constants Determines the running of the ratio /2 – CMB amplitude Determines inflationary CMB parameters

  21. Inflationary CMB parameters end of inflation e-folding # horizon crossing – formation of perturbation of wavelength k related to e-folding # WMAP normalization at amplitude spectral index WMAP+BAO+SN at 2 T/S ratio CMB compatible range of the Higgs mass A.O.B, A.Kamenshchik, C.Kiefer,A.Starobinsky and C.Steinwachs (2008-2009):

  22. Inflaton probability distribution peak Einstein frame potential Probability maximum at the maximum of this potential!

  23. Location of the probability peak – maximum of the Einstein frame potential: RG Quantum scale of inflation from quantum cosmology (A.B.& A.Kamenshchik, Phys.Lett. B332 (1994) 270) ! due to RG Quantum width of the peak:

  24. Conclusions Path integral formulation of the tunneling cosmological state is suggested as a special calculational prescription for the microcanonical statistical sum in cosmology. Within the local gradient expansion it remains consistent with UV renormalization A complete cosmological scenario is obtained in SM Higgs inflation: i) formation of initial conditions for the inflationary background (a sharp probability peak in the inflaton field distribution) and ii) the ongoing generation of the WMAP compatible CMB perturbations on this background. in the Higgs mass range Effect of heavy SM sector and RG running --- small negative anomalous scaling: analogue of asymptotic freedom

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