Under the assumption that General Relativity (GR) correctly describes the
phenomenology of our Universe, astronomical observations provide compelling
evidence that (1) the dynamics of cosmic structure is dominated by dark matter
(DM), an exotic matter mostly made of hypothetical elementary particles, and
(2) the expansion of the Universe is currently accelerating because of the
presence of a positive cosmological constant Lambda. The DM particles have not
yet been detected and there is no theoretical justification for the tiny
positive Lambda implied by observations. Therefore, over the last decade, the
search for extended or alternative theories of gravity has flourished.Comment: Invited review to appear in the Proceedings of the 1st AFI symposium
"From the Vacuum to the Universe", Innsbruck, Austria, October 2007, to be
published by the Innsbruck University Press, ed. by S.D. Bass, F. Schallhart
and B. Tasse