The new century has brought two fundamental advances in astrophysics that are
the discoveries of the accelerated expansion of the Universe with type Ia
supernovae, as well as of the flatness of the Universe with the analysis of the
angular fluctuations of the cosmic microwave background. These two discoveries,
together with old results on the internal kinematics of structures and new
results on the statistics of the large-scale distribution and kinematics of
galaxies and weak gravitational lensing effects on galaxy shapes have enabled
cosmologists to converge towards a concordance model, called ΛCDM, which
describes with surprising success the large-scale properties of the Universe.
However, the ΛCDM Universe is mainly built upon two entities of which we do not
know the physical nature: dark matter and dark energy. Moreover, there seems to
be significant discrepancies with several smaller-scale observations: in
particular, in comparison to observational data, structures arising in very
large N-body simulations of the ΛCDM Universe appear to be too cuspy in their
centres and contain too many sub-structures. These difficulties have generated a
lot of interest in theories that modify the behaviour of gravity on large scales,
e.g. MOND is able to explain with remarkable success the majority of
observational constraints on mass profiles, without recourse to any dark matter.
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