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Creation from Nothing Revisited: Landscape from Cosmological Bootstrap

Creation from Nothing Revisited: Landscape from Cosmological Bootstrap. A.O.Barvinsky Theory Department , Lebedev Physics Institute, Moscow and A.Yu.Kamenshchik Landau Institute for Theoretical Physics , Moscow and Dipartimento di Fisica and INFN , Bologna , Italy. Introduction.

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Creation from Nothing Revisited: Landscape from Cosmological Bootstrap

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  1. Creation from Nothing Revisited: Landscape from Cosmological Bootstrap A.O.Barvinsky TheoryDepartment, LebedevPhysicsInstitute, Moscow and A.Yu.Kamenshchik Landau Institute for Theoretical Physics, Moscow and DipartimentodiFisicaandINFN, Bologna, Italy

  2. Introduction Motivation: search for selection rule restricting landscape of stringy vacua quantum cosmology and Euclidean quantum gravity Euclidean spacetime Lorentzian spacetime Infrared catastrophe: Cosmology debate: no-boundary vs tunneling Wheeler-DeWitt equation

  3. Outline Density matrix vs pure state in Euclidean quantum gravity Back reaction of hot (radiation-like) quantum matter Conformal anomaly and ghost-avoidance renormalization Effective (modified Friedmann) and bootstrap equations Elimination of infrared catastrophe of small  Bounded cosmological landscape of instanton garlands Shrinking stringy landscape?

  4. From pure state to statistical ensemble – density matrix: instanton bridge mediates density matrix correlations

  5. Density matrix of pure Hartle-Hawking state Main effect: back reaction of quantum matter destroys HH instanton by radiation that prevents half-instantons from closure and maintains thermal nature of physical state

  6. Calculation of partition function – toroidal instanton with periodically identified Euclidean time Bootstrap: back reaction of radiation supports instanton background on top of which this radiation exists Bounded cosmological landscape Boundedness of on-shell gravitational action in Euclidean QG Infinite sequence of 1-parameter families of garland-type instantons saturating max – sound link between gravitational tunneling and renormalization theory

  7. Effectofradiation

  8. Density matrix effective action: integration over periodic fields on a torus

  9. Back reaction: nature of approximation minisuperspace background quantum “matter” – cosmological perturbations nature of approximation

  10. Conformal anomaly and ghosts Conformally invariant quantum matter Conformal transform to static Einstein universe conformal time Weyl tensor Euler density ghosts (BAD!) Coefficient of conformal anomaly

  11. Finite ghost-avoidance renormalization: Euler density coefficient in conformal anomaly For low spins: scalar Weyl spinor vector (e-m field) zeta-functional and point-separation regularizations

  12. Effective action on static Einstein instanton vacuum energy free energy ghost avoidance renormalization coefficient of in anomaly modified vacuum energy Important universality Euler density coefficient in anomaly

  13. Effective Friedmann and bootstrap equations lapse function conformal time § – turning points of solutions: Total effective action classical anomaly vacuum energy thermal nonlocality (polylocality) breezing of instanton in -direction

  14. Effective equation (via variation of N() or a()) anomaly contribution “radiation” term Bootstrap equation On-shell action: thermal part geometric part !

  15. Effect of anomaly and bootstrap: beginning of landscape The same two turning points provided

  16. Elimination of infrared catastrophe bootstrap bootstrap

  17. One-parameter family of instantons Upper (hyperbolic) boundary: static Einstein Universe with hot equilibrium gas of temperature

  18. Instanton garlands k- folded garland, k=2,3,…

  19. k-folded conformal time k=2 garland

  20. sequence of garlands no additivity in k ! Increasingly long 0» log k2, increasingly static and more and more cold garlands saturating upper bound of landscape Consequence of universality relation between vacuum energies and conformal anomaly – sound link of renormalization theory and Euclidean quantum gravity Final bounds of landscape for scalar and vector matter:

  21. Conclusions: some like it hot Bounded cosmological landscape: Lorentzian evolution, expansion, radiation dilution, inflation, usual structure formation scenario : <min ruled out by =+1 boundedness of on-shell gravitational action in infrared domain of Euclidean gravity – nonlocal effect of anomaly and nonlocal bootstrap Beyond conformal quantum matter? Instantons are nearly static. Universality relation can be broken: C0<B/2 – sequence of garlands becomes hot; B>C0>B/2 -- sequence of garlands is truncated; C0>B – infrared catastrophe develops Normalizability of partition function – sum over instantons. Measure and prefactors. Semiclassical validity – scaling behavior with N – number of fields: 1/N-expansion Climbing up phenomenology energy scale and higher spins, B>>1: Shrinking stringy landscape?

  22. This is how cosmological landscape comes out of Nothing, if some like it hot

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