Current experimental goals include (1) testing the Standard Model (SM)
and (2) discovering new physics at the TeV scale, if any. In this talk
we will see some example of how theorists can help on both sides. As
far as goal (1) is concerned, high energy extrapolations of the SM can
provide tests that are complementary to the LHC experiments: for
example, the probable metastability of the SM vacuum may be a problem
during inflation. We will also see how well-motivated new physics can
stabilize such vacuum. Regarding goal (2), naturalness (of the Higgs
mass) could be a useful guide to anticipate new physics at the LHC. We
will discuss a recent definition of naturalness that uses only finite
quantities. This potentially broadens the class of natural theories,
but two challenges have to be addressed: the elimination of the Landau
poles and gravity. The latter will lead us to a possibly sensible and
predictive theory of quantum gravity, whose features and open problems
will be discussed.
