Selected topics in scalar-tensor theories and beyond
  Scalar fields have played an important role in the development of the
fundamental theories of physics as well as in other branches of physics such as
gravitation and cosmology. For a long time these escaped detection until 2012
year when the Higgs boson was observed for the first time. Since then
alternatives to the general theory of relativity like the Brans-Dicke theory,
scalar-tensor theories of gravity and their higher derivative generalizations
-- collectively known as Horndeski theories -- have acquired renewed interest.
In the present review we discuss on several selected topics regarding these
theories, mainly from the theoretical perspective but with due mention of the
observational aspect. Among the topics covered in this review we pay special
attention to the following: 1) the asymptotic dynamics of cosmological models
based in the Brans-Dicke, scalar-tensor and Horndeski theories, 2) inflationary
models, extended quintessence and the Galileons, with emphasis in causality and
stability issues, 3) the chameleon and Vainshtein screening mechanisms that may
allow the elusive scalar field to evade the tight observational constraints
implied by the solar system experiments, 4) the conformal frames conundrum with
a brief discussion on the disformal transformations and 5) the role of Weyl
symmetry and scale invariance in the gravitation theories. The review is aimed
at specialists as well as at non-specialists in the subject, including
postgraduate students.
