Hunting modifications of gravity: from the lab to cosmology via compact
  objects
  Modifications of gravity have been considered to model the primordial
inflation and the late-time cosmic acceleration. Provided that modified gravity
models do not suffer from theoretical instabilities, they must be confronted
with observations, not only at the cosmological scales, but also with the local
tests of gravity, in the lab and in the Solar System, as well as at the
astrophysical scales. Considering in particular sub-classes of the Horndeski
gravity, we study their observational predictions at different scales. In order
to pass the local tests of gravity while allowing for long-range interactions
in cosmology, Horndeski gravity exhibits screening mechanisms, among them the
chameleon. The chameleon screening mechanism has been tested recently using
atom interferometry in a vacuum chamber. Numerical simulations are provided in
this thesis in order to refine the analytical predictions. At the astrophysical
scale, Horndeski gravity predicts a variation of the gravitational coupling
inside compact stars. Focusing on Higgs inflation, we discuss to what extent
the Higgs vacuum expectation value varies inside stars and conclude whether the
effect is detectable in gravitational and nuclear physics. Finally, the
covariant Galileon model exhibits non-linearities in the scalar field kinetic
term such that it might pass the local tests of gravity thanks to the
Vainshtein screening mechanism. We discuss if a sub-class of the covariant
Galileon theory dubbed the Fab Four model leads to a viable inflationary phase
and provide combined analysis with neutron stars and Solar System observables.
