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

URL : http://arxiv.org/pdf/1108.0893

M. Bojowald, Loop quantum cosmology, Living Rev. Rel, vol.11, issue.4, 2008.

K. Banerjee, G. Calcagni, and M. Martín-benito, Introduction to Loop Quantum Cosmology, Symmetry, Integrability and Geometry: Methods and Applications, vol.016, issue.8, 2012.
DOI : 10.3842/SIGMA.2012.016

URL : http://www.emis.de/journals/SIGMA/2012/016/sigma12-016.pdf

E. Wilson-ewing, Testing loop quantum cosmology, Comptes Rendus Physique, vol.18, issue.3-4, 2017.
DOI : 10.1016/j.crhy.2017.02.004

URL : http://arxiv.org/pdf/1612.04551

D. Battefeld and P. Peter, A critical review of classical bouncing cosmologies, Physics Reports, vol.571, pp.1-66, 2015.
DOI : 10.1016/j.physrep.2014.12.004

R. Brandenberger and P. Peter, Bouncing Cosmologies: Progress and Problems, Foundations of Physics, vol.65, issue.4, pp.797-850, 2017.
DOI : 10.1103/PhysRevD.65.126003

URL : https://hal.archives-ouvertes.fr/hal-01472863

M. Ostrogradsky, Mémoires sur leséquationsleséquations différentielles, relatives auprobì eme des isopérimètres, Mem. Acad. St. Petersbourg VI, vol.4, pp.385-517, 1850.

R. P. Woodard, Ostrogradsky's theorem on Hamiltonian instability, Scholarpedia, vol.10, issue.8, 2015.
DOI : 10.4249/scholarpedia.32243

URL : https://doi.org/10.4249/scholarpedia.32243

G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, International Journal of Theoretical Physics, vol.29, issue.4, pp.363-384, 1974.
DOI : 10.1007/BF03016051

C. Deffayet, X. Gao, D. A. Steer, and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev, pp.84-064039, 2011.
DOI : 10.1103/physrevd.84.064039

URL : http://arxiv.org/pdf/1103.3260

J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, Healthy theories beyond Horndeski, Phys. Rev. Lett, vol.114, 2015.
URL : https://hal.archives-ouvertes.fr/cea-01073587

J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, Exploring gravitational theories beyond Horndeski, Journal of Cosmology and Astroparticle Physics, vol.2015, issue.02, p.15021408, 1952.
DOI : 10.1088/1475-7516/2015/02/018

URL : https://hal.archives-ouvertes.fr/cea-01073383

D. Langlois and K. Noui, Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability, Journal of Cosmology and Astroparticle Physics, vol.2016, issue.02, p.1602, 2016.
DOI : 10.1088/1475-7516/2016/02/034

URL : https://hal.archives-ouvertes.fr/hal-01554319

D. Langlois and K. Noui, Hamiltonian analysis of higher derivative scalar-tensor theories, Journal of Cosmology and Astroparticle Physics, vol.2016, issue.07, p.1607, 2016.
DOI : 10.1088/1475-7516/2016/07/016

URL : https://hal.archives-ouvertes.fr/hal-01553968

M. Crisostomi, M. Hull, K. Koyama, and G. Tasinato, Horndeski: beyond, or not beyond?, Journal of Cosmology and Astroparticle Physics, vol.2016, issue.03, p.1603, 2016.
DOI : 10.1088/1475-7516/2016/03/038

URL : http://iopscience.iop.org/article/10.1088/1475-7516/2016/03/038/pdf

M. Crisostomi, K. Koyama, and G. Tasinato, Extended scalar-tensor theories of gravity, Journal of Cosmology and Astroparticle Physics, vol.2016, issue.04, p.1604, 2016.
DOI : 10.1088/1475-7516/2016/04/044

URL : http://iopscience.iop.org/article/10.1088/1475-7516/2016/04/044/pdf

J. B. Achour, D. Langlois, and K. Noui, Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations, Phys. Rev, pp.93-2016
URL : https://hal.archives-ouvertes.fr/hal-01554099

J. B. Achour, M. Crisostomi, K. Koyama, D. Langlois, K. Noui et al., Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order, Journal of High Energy Physics, vol.94, issue.12, p.12, 2016.
DOI : 10.1088/1475-7516/2015/08/054

URL : https://link.springer.com/content/pdf/10.1007%2FJHEP12%282016%29100.pdf

A. H. Chamseddine and V. Mukhanov, Mimetic dark matter, Journal of High Energy Physics, vol.2013, issue.11, 2013.
DOI : 10.1007/JHEP11(2013)135

A. H. Chamseddine and V. Mukhanov, Resolving cosmological singularities, Journal of Cosmology and Astroparticle Physics, vol.2017, issue.03, p.1703, 2017.
DOI : 10.1088/1475-7516/2017/03/009

URL : https://hal.archives-ouvertes.fr/hal-01554788

A. Ijjas, J. Ripley, and P. J. Steinhardt, NEC violation in mimetic cosmology revisited, Physics Letters B, vol.760, pp.132-138, 2016.
DOI : 10.1016/j.physletb.2016.06.052

URL : https://doi.org/10.1016/j.physletb.2016.06.052

A. Ijjas and P. J. Steinhardt, Classically Stable Nonsingular Cosmological Bounces, Physical Review Letters, vol.117, issue.12, 2016.
DOI : 10.1103/PhysRevD.94.043511

URL : http://arxiv.org/pdf/1606.08880

A. Ijjas and P. J. Steinhardt, Fully stable cosmological solutions with a non-singular classical bounce, Physics Letters B, vol.764, pp.289-294, 2017.
DOI : 10.1016/j.physletb.2016.11.047

URL : https://doi.org/10.1016/j.physletb.2016.11.047

G. Date and S. Sengupta, Effective actions from loop quantum cosmology: correspondence with higher curvature gravity, Classical and Quantum Gravity, vol.26, issue.10, 2009.
DOI : 10.1088/0264-9381/26/10/105002

URL : http://arxiv.org/pdf/0811.4023

R. C. Helling, Higher curvature counter terms cause the bounce in loop cosmology

H. Motohashi, K. Noui, T. Suyama, M. Yamaguchi, and D. Langlois, Healthy degenerate theories with higher derivatives, Journal of Cosmology and Astroparticle Physics, vol.2016, issue.07, pp.1607-1640, 2016.
DOI : 10.1088/1475-7516/2016/07/033

URL : https://hal.archives-ouvertes.fr/hal-01554346

R. Klein and D. Roest, Exorcising the Ostrogradsky ghost in coupled systems, Journal of High Energy Physics, vol.82, issue.7, p.7, 2016.
DOI : 10.1007/JHEP04(2013)032

C. De-rham and A. Matas, Ostrogradsky in theories with multiple fields, Journal of Cosmology and Astroparticle Physics, vol.2016, issue.06, pp.1606-1647, 2016.
DOI : 10.1088/1475-7516/2016/06/041

M. Crisostomi, R. Klein, and D. Roest, Higher derivative field theories: degeneracy conditions and classes, Journal of High Energy Physics, vol.733, issue.6, p.1706, 2017.
DOI : 10.1103/PhysRevD.90.024050

URL : https://doi.org/10.1007/jhep06(2017)124

F. Arroja, N. Bartolo, P. Karmakar, and S. Matarrese, The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier, pp.1509-051, 2015.

J. Kluson, Canonical analysis of inhomogeneous Dark Energy Model and theory of limiting curvature, Journal of High Energy Physics, vol.10, issue.3, 2017.
DOI : 10.4249/scholarpedia.32243

N. Deruelle and J. Rua, Disformal transformations, veiled General Relativity and Mimetic Gravity, Journal of Cosmology and Astroparticle Physics, vol.2014, issue.09, p.1409, 2014.
DOI : 10.1088/1475-7516/2014/09/002

URL : http://arxiv.org/pdf/1407.0825

J. F. Barbero and G. , Real Ashtekar variables for Lorentzian signature space-times, Physical Review D, vol.49, issue.10, pp.51-5507, 1995.
DOI : 10.1103/PhysRevD.49.6935

S. Holst, Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action, Physical Review D, vol.11, issue.10, pp.5966-5969, 1996.
DOI : 10.1088/0264-9381/11/5/003

URL : http://arxiv.org/pdf/gr-qc/9511026

T. Thiemann, Modern canonical quantum general relativity, 2008.
DOI : 10.1017/CBO9780511755682

A. Ashtekar, T. Paw, and P. Singh, Quantum nature of the big bang: Improved dynamics, Physical Review D, vol.71, issue.8, 2006.
DOI : 10.1088/1475-7516/2005/09/012

V. Taveras, Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field, Phys. Rev, vol.78, issue.064072, 2008.

C. Rovelli and E. Wilson-ewing, Why are the effective equations of loop quantum cosmology so accurate?, Physical Review D, vol.90, issue.2, pp.90-2014
DOI : 10.1088/0264-9381/29/21/215013

URL : https://hal.archives-ouvertes.fr/hal-01111680

G. J. Olmo and P. Singh, Covariant effective action for loop quantum cosmology ?? la Palatini, Journal of Cosmology and Astroparticle Physics, vol.2009, issue.01, 2009.
DOI : 10.1088/1475-7516/2009/01/030

URL : http://arxiv.org/pdf/0806.2783

A. Ashtekar, T. Paw-lowski, P. Singh, K. Vandersloot, L. Szulc et al., Loop quantum cosmology of k=1 FRW models 024035, arXiv:gr-qc/0612104, Phys. Rev. Closed FRW model in Loop Quantum Cosmology Class. Quant. Grav, vol.75, issue.24, pp.2621-2636, 2007.

K. Vandersloot, Loop quantum cosmology and the k = -1 RW model, Phys. Rev, vol.arXiv, p.75, 2007.

A. Ashtekar and E. Wilson-ewing, Loop quantum cosmology of Bianchi type II models, Physical Review D, vol.7, issue.12, 2009.
DOI : 10.1088/0264-9381/25/19/195006

E. Wilson-ewing, Loop quantum cosmology of Bianchi type??IX models, Physical Review D, vol.5, issue.4, p.82, 2010.
DOI : 10.1088/0264-9381/27/13/135020

A. Corichi and A. Karami, Loop quantum cosmology of k=1 FRW: A tale of two bounces, Phys. Rev, vol.84, issue.044003, 2011.

P. Singh and E. Wilson-ewing, Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology, Classical and Quantum Gravity, vol.31, issue.3, p.35010, 2014.
DOI : 10.1088/0264-9381/31/3/035010

URL : http://arxiv.org/pdf/1310.6728

D. Chiou and K. Vandersloot, The Behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology, Phys. Rev, pp.76-084015, 2007.

A. Ashtekar and E. Wilson-ewing, Loop quantum cosmology of Bianchi I models, Phys. Rev, vol.79, issue.083535, 2009.
DOI : 10.1103/physrevd.79.083535

URL : http://arxiv.org/pdf/0903.3397

B. Gupt and P. Singh, Quantum gravitational Kasner transitions in Bianchi-I spacetime, Physical Review D, vol.14, issue.2, pp.86-2012
DOI : 10.1103/PhysRevD.82.104038

Y. Cai and E. Wilson-ewing, Non-singular bounce scenarios in loop quantum cosmology and the effective field description, Journal of Cosmology and Astroparticle Physics, vol.2014, issue.03, pp.1403-1429, 2014.
DOI : 10.1088/1475-7516/2014/03/026

A. H. Chamseddine and V. Mukhanov, Nonsingular black hole, The European Physical Journal C, vol.15, issue.03, 2017.
DOI : 10.1103/PhysRevD.15.2738

URL : https://hal.archives-ouvertes.fr/hal-01554795

C. Rovelli and F. Vidotto, Planck stars, International Journal of Modern Physics D, vol.49, issue.12, pp.23-2014
DOI : 10.1086/186670

URL : https://hal.archives-ouvertes.fr/hal-00957704

D. Lorenzo, C. Pacilio, C. Rovelli, and S. Speziale, On the effective metric of a Planck star, General Relativity and Gravitation, vol.216, issue.4, 2015.
DOI : 10.1063/1.4756964

URL : https://hal.archives-ouvertes.fr/hal-01114686

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. H. Chamseddine, A. Connes, and V. Mukhanov, Quanta of Geometry: Noncommutative Aspects, Physical Review Letters, vol.44, issue.9, p.91302, 2015.
DOI : 10.1088/1475-7516/2014/01/023

N. Bodendorfer, A. Schäfer, and J. Schliemann, Canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity, Physical Review D, vol.97, issue.8
DOI : 10.1088/1361-6382/aa8f2f