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Scope
Our
understanding of the Universe at astrophysical scales and its
fundamental laws is rapidly growing, thanks to many advances in
observational astrophysics and cosmology. These insights enable us to
refine predictions of General Relativity (GR) theory, the concordance
model of cosmology (Lambda-CDM), and the Standard Model (SM) of
particle physics and their extensions.

Concerning
the astrophysics and the physics of black hole (BH), probing the
Universe with gravitational waves (GW), by using ground-based and
space-based GW detectors, will open a new window of observation in
astronomy which should be extremely powerful, with possibly new types
of sources and richness of discoveries. The detailed study of the
coalescence of compact binary systems is likely to be the "bread and
butter" of GW detectors. In the case of neutron star coalescences, one
expects a wealth of information concerning their masses and probably
the equation of state of nuclear matter inside neutron stars. They
might be the basic mechanism for production of short gamma ray bursts
(GRB); and their observations should open a New Multi-messenger
astronomy. The coalescence of supermassive BH binaries, when galaxies
collide, is expected to be observed at cosmological distances. Among
other issues, measurements of BH spin and accurate tests of the basic
no-hair theorem for BH in GR will be performed.
Moreover,
improvements also take place in testing GR and the equivalence
principle (EP), and the inverse square-law of gravity by using
high-precision experiments: e.g., torsion balance experiments and the
Lunar laser ranging for testing the EP, observations in the Solar
system which are compared and fitted by the best planetary ephemerides
for constraining the parametrized-post-Newtonian (PPN) parameters, ….
Space missions, such as Microscope and STE-Quest, will test further the
EP, as well as atomic clocks in space (ACES experiment), which measure
accurately the gravitational redshift.

In
cosmology, the concordance model Lambda-CDM, based on
Friedmann-Lemaître-Robertson-Walker (FLRW) universe, associates a
cosmological constant and Cold Dark Matter (CDM) as the main component
of massive gravitational sources, completed with a primordial inflation
era, and stands for the state-of-the-art model. Parameters of this
model are obtained by fitting jointly several types of data, which has
permitted to transform cosmology into a high-precision science. This
approach has known a remarkable success in explaining and predicting
diverse observations corresponding to the Universe at its largest
scales. However, it addresses the question of the nature of the
fundamental constituents of the Universe. Although the
cosmological constant, viewed as a fundamental constant of nature, is
the simplest interpretation, the attempts at explaining it as being a
vacuum energy have failed. High redshift surveys enable us to check
possible alternatives, named dark energy (DE) or sometimes
"quintessence". Moreover, CDM accounts for non-baryonic weakly
interacting massive particles, while there is no SM candidate.
Faced with these issues, one has to improve or study alternatives to
the standard model of cosmology, notably with new insights on the
nature of the DE, in which gravity is modified by the presence of new
fundamental fields, or even more drastically, by interpreting dark
matter using the possibility that GR may no longer be correct in a
certain regime. This last proposal goes under the name of MOND, and
attempts at solving difficulties of the standard cosmological model at
explaining the extremely fine-tuned distribution of dark matter at
galactic scales. Additional improvements for the understanding of the
dynamics at large scale will be provided with inhomogeneous cosmology,
which takes into account the irregularities in the distribution of
gravitational sources.
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