Quantum Cosmology: Effective Theory

Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge of specific properties of quantum states, it remained difficult to make testable predictions. For quantum cosmology to be part of empirical science, it must allow for a systematic framework in which corrections to well-tested classical equations can be derived, with any ambiguities and ignorance sufficiently parameterized. As in particle and condensed-matter physics, a successful viewpoint is one of effective theories, adapted to specific issues one encounters in quantum cosmology. This review presents such an effective framework of quantum cosmology, taking into account, among other things, space-time structures, covariance, the problem of time and the anomaly issue.

Note:

75 pages, 3 figures, Invited Topical Review

98.80.Qc
04.60.P
04.60.K
03.65.Sq
quantum cosmology: loop space
quantum gravity
minisuperspace
covariance
anomaly
quantum geometry

References(149)

Figures(4)

[1]

General relativity as an effective field theory: The leading quantum corrections

John F. Donoghue
(
- Massachusetts U., Amherst
)

- Phys.Rev.D 50 (1994) 3874-3888
•
e-Print:
- gr-qc/9405057
•
DOI:
- 10.1103/PhysRevD.50.3874

[2]

Quantum gravity in everyday life: General relativity as an effective field theory

C.P. Burgess
(
- McGill U.
)

- Living Rev.Rel. 7 (2004) 5-56
•
e-Print:
- gr-qc/0311082
•
DOI:
- 10.12942/lrr-2004-5

[3]

Quantum Cosmology: Fundamentals, [to appear]

M. Bojowald
,
C. Kiefer

[4]

Quantum Cosmology: A Fundamental Theory of the Universe New York, 2011

M. Bojowald

[5]

Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity, Cambridge University Press, Cambridge, 2010

M. Bojowald

[6]

Gauge-invariant perturbation theory for trans-Planckian inflation

S. Shankaranarayanan
(
- ICTP, Trieste
)
,
Musongela Lubo
(
- ICTP, Trieste
)

- Phys.Rev.D 72 (2005) 123513
•
e-Print:
- hep-th/0507086
•
DOI:
- 10.1103/PhysRevD.72.123513

[7]

Gauge Invariant Cosmological Perturbations

James M. Bardeen
(
- Princeton, Inst. Advanced Study
)

- Phys.Rev.D 22 (1980) 1882-1905,
- Also in *Abbott, L.F. (ed.), Pi, S.Y. (ed.): Inflationary cosmology*, 202-225, and in *Kolb, E.W. (ed.), Turner, M.S. (ed.): The Early universe* 563-586
•
DOI:
- 10.1103/PhysRevD.22.1882

[8]

Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions

Viatcheslav F. Mukhanov
(
- Brown U. and
- Moscow, INR
)
,
H.A. Feldman
(
- Canadian Inst. Theor. Astrophys.
)
,
Robert H. Brandenberger
(
- Brown U.
)

- Phys.Rept. 215 (1992) 203-333
•
DOI:
- 10.1016/0370-1573(92)90044-Z

[9]

Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

- Phys.Rev.D 55 (1997) 658-668
•
e-Print:
- gr-qc/9612037
•
DOI:
- 10.1103/PhysRevD.55.658

[10]

The Theory of gravitation in Hamiltonian form

Paul A.M. Dirac
(
- Cambridge U.
)

- Proc.Roy.Soc.Lond.A 246 (1958) 333-343
•
DOI:
- 10.1098/rspa.1958.0142

[11]

Anomaly freedom in perturbative loop quantum gravity

Martin Bojowald
(
- Penn State U.
)
,
Golam Mortuza Hossain
(
- Penn State U.
)
,
Mikhail Kagan
(
- Penn State U.
)
,
S. Shankaranarayanan
(
- Portsmouth U., ICG
)

- Phys.Rev.D 78 (2008) 063547
•
e-Print:
- 0806.3929
•
DOI:
- 10.1103/PhysRevD.78.063547

[12]

Introduction to doubly special relativity

Jerzy Kowalski-Glikman
(
- Wroclaw U.
)

- Lect.Notes Phys. 669 (2005) 131-159,
•
e-Print:
- hep-th/0405273
•
DOI:
- 10.1007/11377306_5

[13]

Lorentz invariance with an invariant energy scale

Joao Magueijo
(
- Imperial Coll., London
)
,
Lee Smolin
(
)

- Phys.Rev.Lett. 88 (2002) 190403
•
e-Print:
- hep-th/0112090
•
DOI:
- 10.1103/PhysRevLett.88.190403

[14]

Gravity's rainbow

Joao Magueijo
(
- Imperial Coll., London
)
,
Lee Smolin
(
- Perimeter Inst. Theor. Phys. and
- Waterloo U.
)

- Class.Quant.Grav. 21 (2004) 1725-1736
•
e-Print:
- gr-qc/0305055
•
DOI:
- 10.1088/0264-9381/21/7/001

[15]

Holonomy Corrections in the Effective Equations for Scalar Mode Perturbations in Loop Quantum Cosmology

Edward Wilson-Ewing
(
- Marseille, CPT
)

- Class.Quant.Grav. 29 (2012) 085005
•
e-Print:
- 1108.6265
•
DOI:
- 10.1088/0264-9381/29/8/085005

[16]

Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations

- Phys.Rev.D 78 (2008) 083516
•
e-Print:
- 0804.1098
•
DOI:
- 10.1103/PhysRevD.78.083516

[17]

Quantization of a Friedmann Universe Filled with a Scalar Field

W.F. Blyth
(
- King's Coll. London
)
,
C.J. Isham
(
- King's Coll. London
)

- Phys.Rev.D 11 (1975) 768-778
•
DOI:
- 10.1103/PhysRevD.11.768

[18]

The Flat FRW model in LQC: The Self-adjointness

Wojciech Kaminski
(
- Warsaw U. and
- Penn State U.
)
,
Jerzy Lewandowski
(
- Warsaw U. and
- Penn State U.
)

- Class.Quant.Grav. 25 (2008) 035001
•
e-Print:
- 0709.3120
•
DOI:
- 10.1088/0264-9381/25/3/035001

[19]

The LQC evolution operator of FRW universe with positive cosmological constant

Wojciech Kaminski
(
- Warsaw U.
)
,
Tomasz Pawlowski
(
- Madrid, Inst. Estructura Materia and
- Warsaw U.
)

- Phys.Rev.D 81 (2010) 024014
•
e-Print:
- 0912.0162
•
DOI:
- 10.1103/PhysRevD.81.024014

[20]

Physical time and other conceptual issues of QG on the example of LQC

Wojciech Kaminski
(
- Warsaw U.
)
,
Jerzy Lewandowski
(
- Warsaw U.
)
,
Tomasz Pawlowski
(
- Madrid, Inst. Estructura Materia and
- Warsaw U. and
- Warsaw, CFT and
- Penn State U.
)

- Class.Quant.Grav. 26 (2009) 035012
•
e-Print:
- 0809.2590
•
DOI:
- 10.1088/0264-9381/26/3/035012

[21]

Time and interpretations of quantum gravity, In G. Kunstatter, D. E. Vincent, and J. G. Williams (eds.) Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, Singapore, 1992

K.V. KuchaVr

[22]

Canonical Quantum Gravity and the Question of Time, In J. Ehlers and H. Friedrich (eds.) Canonical Gravity: From Classical to Quantum, pages 150-169 -Verlag, Berlin, Heidelberg, 1994

C.J. Isham

[23]

The Problem of Time in Quantum Gravity

Edward Anderson
(
- Cambridge U., DAMTP and
- Madrid U.
)

e-Print:
- 1009.2157

[24]

Reduced phase space approach to Kasner universe and the problem of time in quantum theory

Przemyslaw Malkiewicz
(
- Penn State U. and
- Warsaw, Inst. Nucl. Studies
)

- Class.Quant.Grav. 29 (2012) 075008
•
e-Print:
- 1105.6030
•
DOI:
- 10.1088/0264-9381/29/7/075008

[25]

High-order quantum back-reaction and quantum cosmology with a positive cosmological constant

Martin Bojowald
(
- Penn State U.
)
,
David Brizuela
(
- Penn State U.
)
,
Hector H. Hernandez
(
- Autonoma U., Chihuahua
)
,
Michael J. Koop
(
- Penn State U.
)
,
Hugo A. Morales-Tecotl
(
- Mexico City U., Iztapalapa
)

- Phys.Rev.D 84 (2011) 043514
•
e-Print:
- 1011.3022
•
DOI:
- 10.1103/PhysRevD.84.043514

1-25 of 149
1
2
3
4
5
6
25 / page