Quantum Cosmology From Three Different Perspectives

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Quantum Cosmology From Three Different
Perspectives

• Giampiero Esposito, INFN, Naples MG11
  Conference, Berlin, 23-29 July 2006, COT5 Session

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I Familiar formulation via functional integrals
(Misner 57, Hawking 79)
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Hartle-Hawking quantum state (Phys. Rev. D28,
2960 (1983)).

• Quantum state of the Universe an Euclidean
  functional integral over compact four-geometries
  matching the boundary data on the final surface,
  while the initial three-surface shrinks to a
  point (hence called no boundary proposal).

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II Renormalization-group approach

• If the scale-dependent effective action Gamma
  equals the classical action at the UV cut-off
  scale K, one uses the RG equation to evaluate
  Gamma(k) for all k less than K, and then sends k
  to 0 and K to infinity. The continuum limit as K
  tends to infinity should exist after ren.
  finitely many param. in the action, and is taken
  at a non-Gaussian fixed point of the RG-flow.

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New paths a new ultraviolet fixed point
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Figure caption (from Lauscher-Reuter in
HEP-TH/0511260)

• Part of theory space of the Einstein-Hilbert
  truncation with its Renormalization Group flow.
  The arrows point in the direction of decreasing
  values of k. The flow is dominated by a
  non-Gaussian fixed point in the first quadrant
  and a trivial one at the origin.

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Cosmological applications

• Lagrangian and Hamiltonian form of pure gravity
  with variable G and Lambda, in
• A. Bonanno, G. Esposito, C. Rubano, Class.
  Quantum Grav. 21, 5005 (2004). Cf. earlier
  analysis of RG-improved equations for
  self-interacting scalar fields coupled to
  gravity, by A. Bonanno, G. Esposito, C. Rubano,
  Gen. Rel. Grav. 35, 1899 (2003).

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Power-law inflation for pure gravity

• A. Bonanno, G. Esposito, C. Rubano, Class.
  Quantum Grav. 21, 5005 (2004) Int. J. Mod. Phys.
  A 20, 2358 (2005).

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An accelerating Universe without dark energy

• Main assumption existence of an infrared fixed
  point. By linearization of the RG-flow we
  evaluate the critical exponents and find how the
  fixed point is approached. We obtain a smooth
  transition between FLRW cosmology and the
  observed accelerated expansion.
• A. Bonanno, G. Esposito, C. Rubano, P.
  Scudellaro, Class. Quantum Grav. 23, 3103 (2006).

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III Perturbative quantum cosmology
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Singularity avoidance at one loop?

• For pure gravity, one-loop quantum cosmology in
  the limit of small three-geometry describes a
  vanishing probability of reaching the singularity
  at the origin (of the Euclidean 4-ball) only with
  diff-invariant boundary conditions, which are a
  particular case of the previous scheme. All other
  sets of boundary conditions lead instead to a
  divergent one-loop wave function!

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Peculiar property of the 4-ball?

• We stress we do not require a vanishing one-loop
  wave function. We rather find it, on the
  Euclidean 4-ball, as a consequence of
  diff-invariant boundary conditions.
• Peculiar cancellations occur on the Euclidean
  4-ball, and the spectral (also called
  generalized) zeta function remains regular at the
  origin, despite the lack of strong ellipticity.

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One-loop recent bibliography

• G. Esposito, G. Fucci, A.Yu. Kamenshchik, K.
  Kirsten, Class. Quantum Grav. 22, 957 (2005)
  JHEP 0509063 (2005) J. Phys. A 39, 6317 (2006).
• G. Esposito, A.Yu. Kamenshchik, G. Pollifrone,
  Euclidean Quantum Gravity on Manifolds with
  Boundary, Kluwer, Fundam. Theor. Phys. 85
  (1997).

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IV Towards brane-world quantum cosmology
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Braneworld effective action
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Key open problem

• Does braneworld quantum cosmology preserve
  singularity avoidance at one-loop level?
• A.O. Barvinsky, HEP-TH/0504205 A.O. Barvinsky,
  D.V. Nesterov, Phys. Rev. D73, 066012 (2006).