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Quantum Cosmology From Three Different Perspectives

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Giampiero Esposito, INFN, Naples; MG11 Conference, Berlin, 23-29 July 2006, COT5 ... A. Bonanno, G. Esposito, C. Rubano, P. Scudellaro, ... G. Esposito, A.Yu. ... – PowerPoint PPT presentation

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Title: Quantum Cosmology From Three Different Perspectives


1
Quantum Cosmology From Three Different
Perspectives
  • Giampiero Esposito, INFN, Naples MG11
    Conference, Berlin, 23-29 July 2006, COT5 Session

2
I Familiar formulation via functional integrals
(Misner 57, Hawking 79)
3
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).

4
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.

5
New paths a new ultraviolet fixed point
6
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.

7
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).

8
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).

9
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).

10
III Perturbative quantum cosmology
11
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!

12
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.

13
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).

14
IV Towards brane-world quantum cosmology
15
Braneworld effective action
16
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).
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