E. Komatsu, OBSERVATIONS: COSMOLOGICAL INTERPRETATION, The Astrophysical Journal Supplement Series, vol.180, issue.2, p.330, 2009.
DOI : 10.1088/0067-0049/180/2/330

C. Rovelli and Q. Gravity, Living Rev, Lect. Notes Phys, vol.1, issue.631, p.41, 1998.

J. Grain and A. Barrau, Cosmological Footprints of Loop Quantum Gravity, Physical Review Letters, vol.102, issue.8, p.81301, 2009.
DOI : 10.1103/PhysRevLett.102.081301

URL : https://hal.archives-ouvertes.fr/in2p3-00358636

J. Grain, A. Barrau, and A. Gorecki, Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation, Physical Review D, vol.79, issue.8, p.84015, 2009.
DOI : 10.1103/PhysRevD.79.084015

URL : https://hal.archives-ouvertes.fr/in2p3-00363344

E. J. Copeland, D. J. Mulryne, N. J. Nunes, and M. Shaeri, Superinflation in loop quantum cosmology, Physical Review D, vol.77, issue.2, pp.23510-023508, 2008.
DOI : 10.1103/PhysRevD.77.023510

M. Shimano and T. Harada, Observational constraints of a power spectrum from superinflation in loop quantum cosmology, Physical Review D, vol.80, issue.6, p.63538, 2009.
DOI : 10.1103/PhysRevD.80.063538

A. Ashtekar, T. Pawlowski, and P. Singh, Quantum nature of the big bang: Improved dynamics, Physical Review D, vol.74, issue.8, p.84003, 2006.
DOI : 10.1103/PhysRevD.74.084003

M. Bojowald and G. M. Hossain, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, p.23508, 2008.
DOI : 10.1103/PhysRevD.77.023508

G. Calcagni and G. M. Hossain, Loop Quantum Cosmology and Tensor Perturbations in the Early Universe, Advanced Science Letters, vol.2, issue.2, p.184, 2009.
DOI : 10.1166/asl.2009.1025

E. Komatsu, arXiv:1001.4538v1 [Astrophs, J

M. Bojowald, Inflation from Quantum Geometry, Physical Review Letters, vol.89, issue.26, p.261301, 2002.
DOI : 10.1103/PhysRevLett.89.261301

P. Singh, K. Vandersloot, and G. V. Vereshchagin, Nonsingular bouncing universes in loop quantum cosmology, Physical Review D, vol.74, issue.4, p.43510, 2006.
DOI : 10.1103/PhysRevD.74.043510

J. Mielczarek, Possible observational effects of loop quantum cosmology, Physical Review D, vol.81, issue.6, p.63503, 2010.
DOI : 10.1103/PhysRevD.81.063503

URL : https://hal.archives-ouvertes.fr/in2p3-00466500

D. W. Chiou and K. Liu, Cosmological inflation driven by holonomy corrections of loop quantum cosmology, Physical Review D, vol.81, issue.6, p.63526, 2010.
DOI : 10.1103/PhysRevD.81.063526

M. Bojowald, How Quantum is the Big Bang?, Physical Review Letters, vol.100, issue.22, p.221301, 2008.
DOI : 10.1103/PhysRevLett.100.221301

P. Malkiewicz and W. Piechocki, Energy scale of the Big Bounce, Physical Review D, vol.80, issue.6, p.63506, 2009.
DOI : 10.1103/PhysRevD.80.063506

D. Mulryne and N. Nunes, Constraints on a scale invariant power spectrum from superinflation in loop quantum cosmology, Physical Review D, vol.74, issue.8, p.83507, 2006.
DOI : 10.1103/PhysRevD.74.083507

M. Bojowald and G. M. Hossain, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, p.23508, 2008.
DOI : 10.1103/PhysRevD.77.023508

J. Mielczarek, Tensor power spectrum with holonomy corrections in loop quantum cosmology, Physical Review D, vol.79, issue.12, p.123520, 2009.
DOI : 10.1103/PhysRevD.79.123520

Y. F. Cai, T. T. Qiu, J. Q. Xia, and X. Zhang, Model of inflationary cosmology without singularity, Physical Review D, vol.79, issue.2, p.21303, 2009.
DOI : 10.1103/PhysRevD.79.021303

H. C. Chiang, MEASUREMENT OF COSMIC MICROWAVE BACKGROUND POLARIZATION POWER SPECTRA FROM TWO YEARS OF BICEP DATA, The Astrophysical Journal, vol.711, issue.2, p.1123, 2010.
DOI : 10.1088/0004-637X/711/2/1123

F. T. Falciano, M. Lilley, and P. Peter, Classical bounce: Constraints and consequences, Physical Review D, vol.77, issue.8, p.83513, 2008.
DOI : 10.1103/PhysRevD.77.083513

C. Rovelli, Q. Gravity, and A. Perez, Smolin, arXiv:hep-th/ 0408048v3; T. Thiemann, Lect. Notes Phys, Living Rev. Relativity, vol.1, issue.631, p.41, 1998.

J. Mielczarek, Possible observational effects of loop quantum cosmology, Physical Review D, vol.81, issue.6, p.63503, 2010.
DOI : 10.1103/PhysRevD.81.063503

URL : https://hal.archives-ouvertes.fr/in2p3-00466500

J. Mielczarek, T. Cailleteau, J. Grain, and A. Barrau, Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves, Physical Review D, vol.81, issue.10, p.104049, 2010.
DOI : 10.1103/PhysRevD.81.104049

URL : https://hal.archives-ouvertes.fr/in2p3-00466835

M. Bojowald and G. M. Hossain, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, p.23508, 2008.
DOI : 10.1103/PhysRevD.77.023508

D. Mulryne and N. Nunes, Constraints on a scale invariant power spectrum from superinflation in loop quantum cosmology, Physical Review D, vol.74, issue.8, p.83507, 2006.
DOI : 10.1103/PhysRevD.74.083507

A. Lewis, A. Challinor, and A. Lasenby, Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann???Robertson???Walker Models, The Astrophysical Journal, vol.538, issue.2, p.473, 2000.
DOI : 10.1086/309179

F. T. Falciano, M. Lilley, P. Peter, Y. Piao, B. Feng et al., Classical bounce: Constraints and consequences, Physical Review D, vol.77, issue.8, pp.83513-103520, 2004.
DOI : 10.1103/PhysRevD.77.083513

E. Komatsu, OBSERVATIONS: COSMOLOGICAL INTERPRETATION, The Astrophysical Journal Supplement Series, vol.180, issue.2, p.330, 2009.
DOI : 10.1088/0067-0049/180/2/330

J. Brunneman and T. Thiemann, On (cosmological) singularity avoidance in loop quantum gravity, Classical and Quantum Gravity, vol.23, issue.5, p.1395, 2006.
DOI : 10.1088/0264-9381/23/5/001

M. V. Battisti, A. Marcianò, and C. Rovelli, Triangulated loop quantum cosmology: Bianchi IX universe and inhomogeneous perturbations, Physical Review D, vol.81, issue.6, p.64019, 2010.
DOI : 10.1103/PhysRevD.81.064019

. Grain, Observing the big bounce with tensor modes in the cosmic microwave background: Phenomenology and fundamental loop quantum cosmology parameters, Physical Review D, vol.82, issue.12, pp.123520-123520, 2010.
DOI : 10.1103/PhysRevD.82.123520

URL : https://hal.archives-ouvertes.fr/in2p3-00534185

C. Rovelli, Loop Quantum Gravity, Living Reviews in Relativity, vol.300, issue.12, p.1, 1998.
DOI : 10.1016/0370-2693(93)90356-M

URL : https://hal.archives-ouvertes.fr/hal-00166829

A. Perez, arXiv:gr-qc/0409061v3 Dona P and Speziale S, 2004.

A. Ashtekar, Loop quantum cosmology: an overview, General Relativity and Gravitation, vol.51, issue.4, p.707, 2009.
DOI : 10.1007/s10714-009-0763-4

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Anomaly freedom in perturbative loop quantum gravity, Physical Review D, vol.78, issue.6, p.63547, 2008.
DOI : 10.1103/PhysRevD.78.063547

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity, Physical Review D, vol.79, issue.4, p.43505, 2009.
DOI : 10.1103/PhysRevD.79.043505

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, , 043505 (2009)], Physical Review D, vol.82, issue.10, p.109903, 2010.
DOI : 10.1103/PhysRevD.82.109903

M. Bojowald and G. Hossain, Cosmological vector modes and quantum gravity effects, Classical and Quantum Gravity, vol.24, issue.18, p.4801, 2007.
DOI : 10.1088/0264-9381/24/18/015

M. Bojowald and G. Hossain, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, p.23508, 2008.
DOI : 10.1103/PhysRevD.77.023508

Y. Li and J. Zhu, Application of higher order holonomy corrections to the perturbation theory of cosmology, Classical and Quantum Gravity, vol.28, issue.4, p.45007, 2011.
DOI : 10.1088/0264-9381/28/4/045007

A. Ashtekar and E. Wilson-ewing, Loop quantum cosmology of Bianchi type II models, Physical Review D, vol.80, issue.12, p.123532, 2009.
DOI : 10.1103/PhysRevD.80.123532

W. Nelson and M. Sakellariadou, Lattice refining loop quantum cosmology and the matter Hamiltonian, Physical Review D, vol.76, issue.10, p.104003, 2007.
DOI : 10.1103/PhysRevD.76.104003

W. Nelson and M. Sakellariadou, Lattice-refining loop quantum cosmology and inflation, Physical Review D, vol.76, issue.4, p.44015, 2007.
DOI : 10.1103/PhysRevD.76.044015

A. Corichi and P. Singh, Is loop quantization in cosmology unique?, Physical Review D, vol.78, issue.2, p.24034, 2008.
DOI : 10.1103/PhysRevD.78.024034

M. Sakellariadou, Lattice refinement in loop quantum cosmology, Journal of Physics: Conference Series, vol.189, p.12035, 2009.
DOI : 10.1088/1742-6596/189/1/012035

A. Ashtekar, M. Bojowald, and J. Lewandowski, Mathematical structure of loop quantum cosmology, Advances in Theoretical and Mathematical Physics, vol.7, issue.2, p.233, 2003.
DOI : 10.4310/ATMP.2003.v7.n2.a2

J. Mielczarek, T. Stachowiak, and M. Szydlowski, Exact solutions for a big bounce in loop quantum cosmology, Physical Review D, vol.77, issue.12, p.123506, 2008.
DOI : 10.1103/PhysRevD.77.123506

D. Langlois, Hamiltonian formalism and gauge invariance for linear perturbations in inflation, Classical and Quantum Gravity, vol.11, issue.2, pp.389-407, 1994.
DOI : 10.1088/0264-9381/11/2/011

M. Bojowald and R. Das, Radiation equation of state and loop quantum gravity corrections, Physical Review D, vol.75, issue.12, p.123521, 2007.
DOI : 10.1103/PhysRevD.75.123521

T. J. Battefeld and . Brandenberger, Vector perturbations in a contracting Universe, Physical Review D, vol.70, issue.12, pp.121302-121315, 2004.
DOI : 10.1103/PhysRevD.70.121302

A. Ashtekar and J. Lewandowski, Quantum Grav. 21 R53 Perez A 2004 arXiv:gr-qc/0409061v3 Dona P and Speziale S, 2004.

A. Ashtekar and P. Singh, Loop quantum cosmology: a status report, Classical and Quantum Gravity, vol.28, issue.21, p.213001, 2011.
DOI : 10.1088/0264-9381/28/21/213001

M. Bojowald and G. Hossain, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, p.23508, 2008.
DOI : 10.1103/PhysRevD.77.023508

D. Mulryne and N. Nunes, Constraints on a scale invariant power spectrum from superinflation in loop quantum cosmology, Physical Review D, vol.74, issue.8, p.83507, 2006.
DOI : 10.1103/PhysRevD.74.083507

J. Mielczarek and M. Szydlowski, Relic gravitons as the observable for loop quantum cosmology, Physics Letters B, vol.657, issue.1-3, p.20, 2007.
DOI : 10.1016/j.physletb.2007.10.011

E. J. Copeland, D. J. Mulryne, N. J. Nunes, and M. Shaeri, Superinflation in loop quantum cosmology, Physical Review D, vol.77, issue.2, p.23510, 2008.
DOI : 10.1103/PhysRevD.77.023510

J. Mielczarek, Tensor power spectrum with holonomy corrections in loop quantum cosmology, Physical Review D, vol.79, issue.12, p.123520, 2009.
DOI : 10.1103/PhysRevD.79.123520

E. J. Copeland, D. J. Mulryne, N. J. Nunes, and M. Shaeri, Gravitational wave background from superinflation in loop quantum cosmology, Physical Review D, vol.79, issue.2, p.23508, 2009.
DOI : 10.1103/PhysRevD.79.023508

J. Grain and A. Barrau, Cosmological Footprints of Loop Quantum Gravity, Physical Review Letters, vol.102, issue.8, p.81301, 2009.
DOI : 10.1103/PhysRevLett.102.081301

URL : https://hal.archives-ouvertes.fr/in2p3-00358636

M. Shimano and T. Harada, Observational constraints of a power spectrum from superinflation in loop quantum cosmology, Physical Review D, vol.80, issue.6, p.63538, 2009.
DOI : 10.1103/PhysRevD.80.063538

J. Grain, A. Barrau, and A. Gorecki, Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation, Physical Review D, vol.79, issue.8, p.84015, 2009.
DOI : 10.1103/PhysRevD.79.084015

URL : https://hal.archives-ouvertes.fr/in2p3-00363344

J. Mielczarek, T. Cailleteau, J. Grain, and A. Barrau, Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves, Physical Review D, vol.81, issue.10, p.104049, 2010.
DOI : 10.1103/PhysRevD.81.104049

URL : https://hal.archives-ouvertes.fr/in2p3-00466835

G. Calcagni and G. Hossain, Loop Quantum Cosmology and Tensor Perturbations in the Early Universe, Advanced Science Letters, vol.2, issue.2, p.184, 2009.
DOI : 10.1166/asl.2009.1025

D. Larson, -DERIVED PARAMETERS, The Astrophysical Journal Supplement Series, vol.192, issue.2, p.16, 2011.
DOI : 10.1088/0067-0049/192/2/16

URL : https://hal.archives-ouvertes.fr/hal-00259824

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Anomaly freedom in perturbative loop quantum gravity, Physical Review D, vol.78, issue.6, p.63547, 2008.
DOI : 10.1103/PhysRevD.78.063547

E. Wilson-ewing, Holonomy corrections in the effective equations for scalar mode perturbations in loop quantum cosmology, Classical and Quantum Gravity, vol.29, issue.8, p.85005, 2012.
DOI : 10.1088/0264-9381/29/8/085005

URL : https://hal.archives-ouvertes.fr/hal-00618772

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity, Physical Review D, vol.79, issue.4, p.43505, 2009.
DOI : 10.1103/PhysRevD.79.043505

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, , 043505 (2009)], Physical Review D, vol.82, issue.10, p.109903, 2010.
DOI : 10.1103/PhysRevD.82.109903

J. Mielczarek, T. Cailleteau, A. Barrau, and J. Grain, Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology, Classical and Quantum Gravity, vol.29, issue.8, p.85009, 2012.
DOI : 10.1088/0264-9381/29/8/085009

URL : https://hal.archives-ouvertes.fr/in2p3-00601908

A. Corichi and P. Singh, Is loop quantization in cosmology unique?, Physical Review D, vol.78, issue.2, p.24034, 2008.
DOI : 10.1103/PhysRevD.78.024034

W. Nelson and M. Sakellariadou, Lattice refining loop quantum cosmology and the matter Hamiltonian, Physical Review D, vol.76, issue.10, p.104003, 2007.
DOI : 10.1103/PhysRevD.76.104003

J. B. Hartle and S. W. Hawking, Wave function of the Universe, Physical Review D, vol.28, issue.12, p.2960, 1983.
DOI : 10.1103/PhysRevD.28.2960

A. Ashtekar, T. Pawlowski, and P. Singh, Quantum nature of the big bang: Improved dynamics, Physical Review D, vol.74, issue.8, p.84003, 2006.
DOI : 10.1103/PhysRevD.74.084003

V. F. Mukhanov, H. A. Feldman, and R. Brandenberger, Theory of cosmological perturbations, Physics Reports, vol.215, issue.5-6, pp.203-333, 1992.
DOI : 10.1016/0370-1573(92)90044-Z

M. Bojowald, G. Calcagni, and S. Tsujikawa, Observational Constraints on Loop Quantum Cosmology, Physical Review Letters, vol.107, issue.21, p.211302, 2011.
DOI : 10.1103/PhysRevLett.107.211302

A. Ashtekar and P. Singh, Loop quantum cosmology: a status report, Classical and Quantum Gravity, vol.28, issue.21, p.213001, 2011.
DOI : 10.1088/0264-9381/28/21/213001

M. Bojowald, G. M. Hossain, D. J. Mulryne, and N. J. Nunes, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, pp.23508-083507, 2006.
DOI : 10.1103/PhysRevD.77.023508

T. Shimano and . Harada, Observational constraints of a power spectrum from superinflation in loop quantum cosmology, Physical Review D, vol.80, issue.6, p.63538, 2009.
DOI : 10.1103/PhysRevD.80.063538

J. Goldberg, E. T. Newmann, and C. Rovelli, On Hamiltonian systems with first???class constraints, Journal of Mathematical Physics, vol.32, issue.10, p.2739, 1991.
DOI : 10.1063/1.529065

M. Tanimoto, V. Moncrief, and K. Yasuno, Perturbations of spatially closed Bianchi III spacetimes, Classical and Quantum Gravity, vol.20, issue.9, p.1879, 2003.
DOI : 10.1088/0264-9381/20/9/319

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity, Physical Review D, vol.79, issue.4, p.43505, 2009.
DOI : 10.1103/PhysRevD.79.043505

J. M. Bardeen, Gauge-invariant cosmological perturbations, Physical Review D, vol.22, issue.8, p.1882, 1980.
DOI : 10.1103/PhysRevD.22.1882

V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Theory of cosmological perturbations, Physics Reports, vol.215, issue.5-6, p.203, 1992.
DOI : 10.1016/0370-1573(92)90044-Z

T. Cailleteau, J. Mielczarek, A. Barrau, and J. Grain, Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology, Classical and Quantum Gravity, vol.29, issue.9, p.95010, 2012.
DOI : 10.1088/0264-9381/29/9/095010

URL : https://hal.archives-ouvertes.fr/in2p3-00641523

C. Rovelli, L. Rev, and A. Perez, Smolin, arXiv:hep-th/0408048v3; T. Thiemann, Lect. Notes Phys, Thiemann, Modern Canonical Quantum General Relativity, p.41, 1998.

B. J. Carr, New cosmological constraints on primordial black holes, Physical Review D, vol.81, issue.10, p.104019, 2010.
DOI : 10.1103/PhysRevD.81.104019

I. Agullo, Detailed black hole state counting in loop quantum gravity, Physical Review D, vol.82, issue.8, p.84029, 2010.
DOI : 10.1103/PhysRevD.82.084029

J. Diaz-polo, E. Fernandez-borja, I. Agulló, J. Díaz-polo, and P. P. , Black hole radiation spectrum in loop quantum gravity: isolated horizon framework, Classical and Quantum Gravity, vol.25, issue.10, pp.105007-251301, 2008.
DOI : 10.1088/0264-9381/25/10/105007

. Agullo, black hole entropy in loop quantum gravity, Physical Review D, vol.80, issue.8, p.84006, 2009.
DOI : 10.1103/PhysRevD.80.084006

S. Alexeyev, Black-hole relics in string gravity: last stages of Hawking evaporation, Classical and Quantum Gravity, vol.19, issue.16, p.4431, 2002.
DOI : 10.1088/0264-9381/19/16/314

URL : https://hal.archives-ouvertes.fr/in2p3-00011725

K. Jedamzik and J. C. Niemeyer, Primordial black hole formation during first-order phase transitions, Physical Review D, vol.59, issue.12, p.124014, 1999.
DOI : 10.1103/PhysRevD.59.124014

C. Rovelli, T. Thiemann, R. Gambini, and J. Pullin, Quantum Gravity, First Course in Loop Quantum Gravity, p.41, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01255344

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Anomaly freedom in perturbative loop quantum gravity, Physical Review D, vol.78, issue.6, p.63547, 2008.
DOI : 10.1103/PhysRevD.78.063547

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity, Physical Review D, vol.79, issue.4, p.43505, 2009.
DOI : 10.1103/PhysRevD.79.043505

M. Bojowald and G. M. Hossain, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, p.23508, 2008.
DOI : 10.1103/PhysRevD.77.023508

M. Bojowald, G. Calcagni, and S. Tsujikawa, Observational Constraints on Loop Quantum Cosmology, Physical Review Letters, vol.107, issue.21, p.211302, 2011.
DOI : 10.1103/PhysRevLett.107.211302

J. Mielczarek, Tensor power spectrum with holonomy corrections in loop quantum cosmology, Physical Review D, vol.79, issue.12, p.123520, 2009.
DOI : 10.1103/PhysRevD.79.123520

Y. Li and J. Y. Zhu, Application of higher order holonomy corrections to the perturbation theory of cosmology, Classical and Quantum Gravity, vol.28, issue.4, p.45007, 2011.
DOI : 10.1088/0264-9381/28/4/045007

J. Mielczarek, T. Cailleteau, A. Barrau, and J. Grain, Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology, Classical and Quantum Gravity, vol.29, issue.8, p.85009, 2012.
DOI : 10.1088/0264-9381/29/8/085009

URL : https://hal.archives-ouvertes.fr/in2p3-00601908

T. Cailleteau, J. Mielczarek, A. Barrau, and J. Grain, Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology, Classical and Quantum Gravity, vol.29, issue.9, p.95010, 2012.
DOI : 10.1088/0264-9381/29/9/095010

URL : https://hal.archives-ouvertes.fr/in2p3-00641523

A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, and T. Thiemann, Quantization of diffeomorphism invariant theories of connections with local degrees of freedom, Journal of Mathematical Physics, vol.36, issue.11, p.6456, 1995.
DOI : 10.1063/1.531252

A. Ashtekar, T. Pawlowski, and P. Singh, Quantum nature of the big bang: Improved dynamics, Physical Review D, vol.74, issue.8, p.84003, 2006.
DOI : 10.1103/PhysRevD.74.084003

E. Wilson-ewing, Holonomy corrections in the effective equations for scalar mode perturbations in loop quantum cosmology, Classical and Quantum Gravity, vol.29, issue.8, p.85005, 2012.
DOI : 10.1088/0264-9381/29/8/085005

URL : https://hal.archives-ouvertes.fr/hal-00618772

T. Cailleteau and A. Barrau, Gauge invariance in loop quantum cosmology: Hamilton-Jacobi and Mukhanov-Sasaki equations for scalar perturbations, Physical Review D, vol.85, issue.12, p.123534, 2012.
DOI : 10.1103/PhysRevD.85.123534

URL : https://hal.archives-ouvertes.fr/in2p3-00647301

V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Theory of cosmological perturbations, Physics Reports, vol.215, issue.5-6, p.203, 1992.
DOI : 10.1016/0370-1573(92)90044-Z

D. Langlois, Hamiltonian formalism and gauge invariance for linear perturbations in inflation, Classical and Quantum Gravity, vol.11, issue.2, p.389, 1994.
DOI : 10.1088/0264-9381/11/2/011

V. I. Arnold, Mathematical Methods Of Classical Mechanics, 1989.

J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry : A Basic Exposition of Classical Mechanical Systems, 1994.

D. Lovelock and H. Rund, Tensors, diferential forms and variational principles, 1989.

J. José and E. Saletan, Classical mechanics : a contemporary approach, 1998.

A. Cannas and . Silva, Lectures on Symplectic Geometry, Lecture Notes in Mathematics, vol.1764, 2001.

T. Masson, Géométrie différentielle, groupes et algèbres de Lie, fibrés et connexions

C. Rovelli, Quantum Gravity, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01255344

R. Gambini and J. Pullin, A first course in Loop Quantum Gravity, 2011.
DOI : 10.1093/acprof:oso/9780199590759.001.0001

C. Semay and B. Silvestre-brac, Relativité restreinte. Bases et applications, 2005.

L. H. Ryder, Quantum Field Theory, 1996.
DOI : 10.1017/CBO9780511813900

W. G. Unruh, Notes on black-hole evaporation, Physical Review D, vol.14, issue.4, 1976.
DOI : 10.1103/PhysRevD.14.870

J. Grain, Relativité Générale et champs quantiques : quelques aspects de physique des trous noirs et de cosmologie en gravité de Lovelock, espaces de Sitter et dimensions supplémentaires

S. Carroll, Spacetime and Geometry : Introduction to General Relativity, 2003.

A. Barrau and J. Grain, Relativité Générale, cours et exercices corrigés, p.2011

E. Gourgoulhon, 3+1 formalism and bases of numerical relativity, " gr-qc

C. Kiefer, Quantum gravity: general introduction and recent developments, Annalen der Physik, vol.51, issue.1-2, 2005.
DOI : 10.1002/andp.200510175

S. W. Hawking and R. Penrose, The nature of Space and Time, 1996.

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Anomaly freedom in perturbative loop quantum gravity, Physical Review D, vol.78, issue.6, p.63547, 2008.
DOI : 10.1103/PhysRevD.78.063547

G. Date and G. M. Hossain, Matter in Loop Quantum Gravity, Symmetry, Integrability and Geometry: Methods and Applications, vol.8, p.10, 2012.
DOI : 10.3842/SIGMA.2012.010

C. Rovelli, Loop quantum gravity: the first 25 years, Classical and Quantum Gravity, vol.28, issue.15, p.153002, 2011.
DOI : 10.1088/0264-9381/28/15/153002

URL : https://hal.archives-ouvertes.fr/hal-00723006

A. Perez, Introduction to loop quantum gravity and spin foams, p.409061

A. Ghosh and A. Perez, Black Hole Entropy and Isolated Horizons Thermodynamics, Physical Review Letters, vol.107, issue.24, p.241301, 2011.
DOI : 10.1103/PhysRevLett.107.241301

URL : https://hal.archives-ouvertes.fr/hal-00618578

D. H. Lyth and A. R. Liddle, The Primordial Density Perturbation : Cosmology, Inflation and the Origin of Structure, 2009.
DOI : 10.1017/CBO9780511819209

A. Linde, The Self-Reproducing Inflationary Universe, Scientific American, vol.271, issue.5, 1994.
DOI : 10.1038/scientificamerican1194-48

A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure, 2000.
DOI : 10.1017/CBO9781139175180

D. Langlois, Lectures on inflation and cosmological perturbations, Lect. Notes Phys, vol.800, issue.1, 2010.
DOI : 10.1007/978-3-642-10598-2_1

E. Hubble, A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae, Proceedings of the National Academy of Sciences of the United States of America, 1929.
DOI : 10.1073/pnas.15.3.168

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC522427

G. Gamow, R. A. Alpher, and H. Bethe, The Origin of Chemical Elements, Phys. Rev, vol.73, p.7, 1948.

E. Komatsu, Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations : Cosmological Interpretation, WMAP Collaboration] Astrophys. J, p.18, 2011.
DOI : 10.1088/0067-0049/192/2/18

URL : http://arxiv.org/abs/1001.4538

N. Y. Gnedin and O. Y. Gnedin, Cosmological Neutrino Background Revisited, The Astrophysical Journal, vol.509, issue.1, p.9712199, 1998.
DOI : 10.1086/306469

URL : http://arxiv.org/abs/astro-ph/9712199

C. Rovelli, Statistical mechanics of gravity and the thermodynamical origin of time, Classical and Quantum Gravity, vol.10, issue.8, p.1549, 1993.
DOI : 10.1088/0264-9381/10/8/015

A. Ashtekar, M. Bojowald, and J. Lewandowski, Mathematical structure of loop quantum cosmology, Advances in Theoretical and Mathematical Physics, vol.7, issue.2, 2003.
DOI : 10.4310/ATMP.2003.v7.n2.a2

A. Ashtekar and P. Singh, Loop quantum cosmology: a status report, Classical and Quantum Gravity, vol.28, issue.21, p.213001, 2011.
DOI : 10.1088/0264-9381/28/21/213001

A. Borde, A. H. Guth, and A. Vilenkin, Inflationary Spacetimes Are Incomplete in Past Directions, Physical Review Letters, vol.90, issue.15, p.151301, 2003.
DOI : 10.1103/PhysRevLett.90.151301

T. Cailleteau, A. Cardoso, K. Vandersloot, and D. Wands, Singularities in Loop Quantum Cosmology, Physical Review Letters, vol.101, issue.25, p.251302, 2008.
DOI : 10.1103/PhysRevLett.101.251302

P. Singh and F. Vidotto, Exotic singularities and spatially curved loop quantum cosmology, Physical Review D, vol.83, issue.6, p.64027, 2011.
DOI : 10.1103/PhysRevD.83.064027

URL : https://hal.archives-ouvertes.fr/hal-00549671

A. Ashtekar, Some surprising implications of background independence in canonical quantum gravity, General Relativity and Gravitation, vol.1, issue.9, p.1927, 2009.
DOI : 10.1007/s10714-009-0802-1

T. Thiemann, Quantum spin dynamics (QSD), Classical and Quantum Gravity, vol.15, issue.4, 1998.
DOI : 10.1088/0264-9381/15/4/011

URL : http://arxiv.org/abs/gr-qc/9606089

J. Mielczarek, T. Stachowiak, and M. Szydlowski, Exact solutions for a big bounce in loop quantum cosmology, Physical Review D, vol.77, issue.12, p.123506, 2008.
DOI : 10.1103/PhysRevD.77.123506

M. Bojowald, G. Calcagni, and S. Tsujikawa, Observational test of inflation in loop quantum cosmology, Journal of Cosmology and Astroparticle Physics, vol.2011, issue.11, p.46, 2011.
DOI : 10.1088/1475-7516/2011/11/046

J. Mielczarek, Possible observational effects of loop quantum cosmology, Physical Review D, vol.81, issue.6, p.63503, 2010.
DOI : 10.1103/PhysRevD.81.063503

URL : https://hal.archives-ouvertes.fr/in2p3-00466500

G. Amelino-camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Tests of quantum gravity from observations of gamma-ray bursts, Nature, vol.393, issue.6687, p.763, 1998.
DOI : 10.1038/31647

M. Ackermann, A limit on the variation of the speed of light arising from quantum gravity effects, Fermi GBM/LAT Collaboration] Nature, vol.462, issue.331, 2009.
URL : https://hal.archives-ouvertes.fr/in2p3-00436584

R. Gambini and J. Pullin, Nonstandard optics from quantum space-time, Physical Review D, vol.59, issue.12, p.124021, 1999.
DOI : 10.1103/PhysRevD.59.124021

URL : http://arxiv.org/abs/gr-qc/9809038

R. J. Gleiser and C. N. Kozameh, Astrophysical limits on quantum gravity motivated birefringence, Physical Review D, vol.64, issue.8, p.83007, 2001.
DOI : 10.1103/PhysRevD.64.083007

URL : http://arxiv.org/abs/gr-qc/0102093

P. , P. , and J. Uzan, Cosmologie primordiale, Belin, 2005.

A. Riotto, Inflation and the theory of cosmological perturbations, 210162.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1965.
DOI : 10.1119/1.1972842

R. Parentani, The inflationary paradigm: predictions for CMB, Comptes Rendus Physique, vol.4, issue.8, 2003.
DOI : 10.1016/S1631-0705(03)00100-2

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity, Physical Review D, vol.79, issue.4, p.43505, 2009.
DOI : 10.1103/PhysRevD.79.043505

URL : http://arxiv.org/abs/0811.1572

J. M. Bardeen, P. J. Steinhardt, and M. S. Turner, Spontaneous creation of almost scale-free density perturbations in an inflationary universe, Physical Review D, vol.28, issue.4, p.679, 1983.
DOI : 10.1103/PhysRevD.28.679

V. F. Mukhanov, Quantum Theory of Gauge Invariant Cosmological Perturbations, Zh. Eksp. Teor. Fiz. 94N7, pp.1297-1298, 1988.

M. Sasaki, Large Scale Quantum Fluctuations in the Inflationary Universe, Progress of Theoretical Physics, vol.76, issue.5, p.1036, 1986.
DOI : 10.1143/PTP.76.1036

V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger, Theory of cosmological perturbations, Physics Reports, vol.215, issue.5-6, p.203, 1992.
DOI : 10.1016/0370-1573(92)90044-Z

T. J. Battefeld and R. Brandenberger, Vector perturbations in a contracting Universe, Physical Review D, vol.70, issue.12, p.121302, 2004.
DOI : 10.1103/PhysRevD.70.121302

M. Bojowald and G. M. Hossain, Loop quantum gravity corrections to gravitational wave dispersion, Physical Review D, vol.77, issue.2, p.23508, 2008.
DOI : 10.1103/PhysRevD.77.023508

URL : http://arxiv.org/abs/0709.2365

M. Bojowald and G. M. Hossain, Cosmological vector modes and quantum gravity effects, Classical and Quantum Gravity, vol.24, issue.18, 2007.
DOI : 10.1088/0264-9381/24/18/015

URL : http://arxiv.org/abs/0709.0872

M. Bojowald, G. M. Hossain, M. Kagan, and S. Shankaranarayanan, Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity, Physical Review D, vol.79, issue.4, p.43505, 2009.
DOI : 10.1103/PhysRevD.79.043505

URL : http://arxiv.org/abs/0811.1572

J. M. Pons, D. C. Salisbury, and L. C. Shepley, Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories, Physical Review D, vol.55, issue.2, p.658, 1997.
DOI : 10.1103/PhysRevD.55.658

E. Wilson-ewing, Holonomy corrections in the effective equations for scalar mode perturbations in loop quantum cosmology, Classical and Quantum Gravity, vol.29, issue.8, p.85005, 2012.
DOI : 10.1088/0264-9381/29/8/085005

URL : https://hal.archives-ouvertes.fr/hal-00618772

A. Barrau and J. Grain, Holonomy corrections to the cosmological primordial tensor power spectrum
URL : https://hal.archives-ouvertes.fr/in2p3-00265751

J. Grain and A. Barrau, Cosmological Footprints of Loop Quantum Gravity, Physical Review Letters, vol.102, issue.8, p.81301, 2009.
DOI : 10.1103/PhysRevLett.102.081301

URL : https://hal.archives-ouvertes.fr/in2p3-00358636

J. Grain, A. Barrau, and A. Gorecki, Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation, Physical Review D, vol.79, issue.8, p.84015, 2009.
DOI : 10.1103/PhysRevD.79.084015

URL : https://hal.archives-ouvertes.fr/in2p3-00363344

J. Mielczarek, Tensor power spectrum with holonomy corrections in loop quantum cosmology, Physical Review D, vol.79, issue.12, p.123520, 2009.
DOI : 10.1103/PhysRevD.79.123520

J. Ribassin, E. Huguet, and K. Ganga, Simple fluid models for super-inflation in effective LQC and effects on the CMB B-modes

L. R. Abramo, I. Yasuda, and P. Peter, Nonsingular bounce in modified gravity, Physical Review D, vol.81, issue.2, p.23511, 2010.
DOI : 10.1103/PhysRevD.81.023511

L. Verde, H. Peiris, and R. Jimenez, Considerations in optimizing CMB polarization experiments to constrain inflationary physics, Journal of Cosmology and Astroparticle Physics, vol.2006, issue.01, p.19, 2006.
DOI : 10.1088/1475-7516/2006/01/019

D. Baumann, CMBPol Mission Concept Study : Probing Inflation with CMB Polarization, AIP Conf. Proc. 1141, 2009.

F. Stivoli, J. Grain, S. M. Leach, M. Tristram, C. Baccigalupi et al., Maximum likelihood, parametric component separation and CMB B-mode detection in suborbital experiments, Monthly Notices of the Royal Astronomical Society, vol.408, issue.4, p.231910044756, 2010.
DOI : 10.1111/j.1365-2966.2010.17281.x

URL : https://hal.archives-ouvertes.fr/in2p3-00535987

M. Bojowald and G. M. Paily, Deformed general relativity and effective actions from loop quantum gravity, Physical Review D, vol.86, issue.10
DOI : 10.1103/PhysRevD.86.104018

URL : http://arxiv.org/abs/1112.1899

M. Bojowald, D. Brizuela, H. H. Hernandez, M. J. Koop, and H. A. Morales, High-order quantum back-reaction and quantum cosmology with a positive cosmological constant, Physical Review D, vol.84, issue.4, p.43514, 2011.
DOI : 10.1103/PhysRevD.84.043514