Manifestly gauge-invariant general relativistic perturbation theory: I. Foundations

Classical and Quantum Gravity

Volumn 27, Issue 5, 2010, Pages

  Giesel, K ^a   Hofmann, S ^b,c   Thiemann, T ^a,b   Winkler, O ^b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^c NORDITA   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 76749129003     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/27/5/055005     Document Type: Article

References (45)

1. Noh H and Hwang J 2004 Second-order perturbations of the Friedmann world model Phys. Rev. D 69 104011
2. Nakamura K 2003 Gauge invariant variables in two-parameter nonlinear perturbations Prog. Theor. Phys. 110 723
3. Nakamura K 2005 Second-order gauge invariant perturbation theory Prog. Theor. Phys. 113 723
4. Nakamura K 2007 Second-order gauge invariant cosmological perturbation theory Prog. Theor. Phys. 117 723
5. Rovelli C 1998 Loop quantum gravity Living Rev. Rel. 1 1 (arXiv:gr-qc/9710008)
6. Thiemann T 2003 Lectures on loop quantum gravity Lect. Notes Phys. 631 41-135 (arXiv:gr-qc/0210094)
7. Ashtekar A and Lewandowski J 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53 (arXiv:gr-qc/0404018)
8. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
9. Thiemann T 2007 Introduction to Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press)
10. Dirac P A M 1964 Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science, Yeshiva University Press)
11. Mukhanov V, Feldman H and Brandenberger R 1992 Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions Phys. Rep. 215 203-333
12. Ashtekar A and Stachel J (ed) 1991 Conceptual Problems of Quantum Gravity Based on Proceedings of the 1988 Osgood Hill Conference (Basel: Birkhaeuser)
13. Thiemann T 2006 Solving the problem of time in general relativity and cosmology with phantoms and k-essence arXiv:astro-ph/0607380
14. Rovelli C 1991 What is observable in classical and quantum gravity? Class. Quantum Grav. 8 297-316
15. Rovelli C 1991 Quantum reference systems Class. Quantum Grav. 8 317-32
16. Rovelli C 1991 Time in quantum gravity: physics beyond the Schrodinger regime Phys. Rev. D 43 442-56
17. Rovelli C 1990 Quantum mechanics without time: a model Phys. Rev. D 42 2638-46
18. Dittrich B 2007 Partial and complete observables for Hamiltonian constrained systems Gen. Rel. Grav. 39 1891 (arXiv:gr-qc/0411013)
19. Dittrich B 2006 Partial and complete observables for canonical general relativity Class. Quantum Grav. 23 6155-84 (arXiv:gr-qc/0507106)
20. Brown J and Kucha K 1995 Dust as a standard of space and time in canonical quantum gravity Phys. Rev. D 51 5600-5629 (arXiv:gr-qc/9409001)
21. Iftime M and Stachel J 2006 The hole argument for covariant theories Gen. Rel. Grav. 38 1241-52
22. Moncrief V 1974 Gravitational perturbations of spherically symmetric systems: I. The exterior problem Ann. Phys. 88 323
23. Langlois D 1994 Hamiltonian formalism and gauge invariance for linear perturbations in inflation Class. Quantum Grav. 11 389-407
24. Giesel K, Hofmann S, Thiemann T and Winkler O 2007 Manifestly gauge-invariant general relativistic perturbation theory: II. FRW background and first order arXiv:0711.0117 [gr-qc]
25. Thiemann T 2006 Reduced phase space quantization and Dirac observables Class. Quantum Grav. 23 1163-80 (arXiv:gr-qc/0411031)
26. Thiemann T 2007 Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press) (arXiv:gr-qc/0110034)
27. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): I. Conceptual setup Class. Quantum Grav. 24 2465-98 (arXiv:gr-qc/0607099)
28. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): II. Semiclassical analysis Class. Quantum Grav. 24 2499-564 (arXiv:gr-qc/0607100)
29. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory Class. Quantum Grav. 24 2565-88 (arXiv:gr-qc/0607101)
30. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG): IV. Reduced phase space quantisation of loop quantum gravity arXiv:0711.0119 [gr-qc]
31. Dittrich B and Tambornino J 2007 A perturbative approach to Dirac observables and their spacetime algebra Class. Quantum Grav. 24 757 (arXiv:gr-qc/0610060)
32. Dittrich B and Tambornino J 2007 Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology Class. Quantum Grav. 24 4543-86 (arXiv:gr-qc/0702093)
33. Wald R M 1989 General Relativity (Chicago: University of Chicago Press)
34. Sachs R K 1964 Relativity, Groups and Topology ed De Witt B and De Witt C (London: Gordon and Breach) p 523
35. Stewart J M and Walker M 1974 Perturbations of spacetime in general relativity Proc. R. Soc. A 341 49
36. Bruni M, Matarrese S, Mollerach S and Sonego S 1997 Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond Class. Quantum Grav. 14 2585
37. Sonego S and Bruni M 1998 Gauge dependence in the theory of non-linear spacetime perturbations Commun. Math. Phys. 193 209
38. Bruni M and Sonego S 1999 Observables and gauge invariance in the theory of nonlinear spacetime perturbations Class. Quantum Grav. 16 L29
39. Ellis G F R and Bruni M 1989 Covariant and gauge-invariant approach to cosmological density fluctuations Phys. Rev. D 40 1804
40. Bruni M, Dunsby P K S and Ellis G F R 1992 Cosmological perturbations and the physical meaning of gauge-invariant variables Astrophys. J. 395 34
41. Clarkson C 2004 Cosmological density fluctuations and gravity waves: A covariant approach to gauge-invariant nonlinear perturbation theory Phys. Rev. D 70 103524
42. Langlois D and Vernizzi F 2005 Evolution of nonlinear cosmological perturbations Phys. Rev. Lett. 95 091303
43. Henneaux M and Teitelboim C 1982 Quantization of Gauge Systems (Princeton: Princeton University Press)
44. Beig R and Schmidt B G 1982 Einstein's equations near spatial infinity Commun. Math. Phys. 87 65
45. Bartolo N, Matarrese S and Riotto A 2006 The full second-order radiation transfer function for large-scale CMB anisotropies J. Cosmol. Astropart. Phys. JCAP05(2006)010