Alternative theories of gravity and applications

This thesis deals with some applications of alternative theories of relativistic gravity. We study in particular the two-body problem in a purely scalar theory of gravity and the associated emission of gravitational waves. We derive many analytical and numerical results regarding this non trivial dynamics. We also study in detail the Modified Newtonian Dynamics (MOND) paradigm that may account for the rotation curves of spiral galaxies by means of a rather simple modification of gravitational laws in ultra-weak fields, instead of invoking a large amount of (Cold) Dark Matter. This thesis notably deals with the issue of formulating such a relativistic theory, that must differ from General Relativity since it cannot reduce to Newton's law in the nonrelativistic and weak-field limit. We present some alternative models that may be relevant and put forward some new models of MOND. We analyse them carefully and pay attention to both experimental and theoretical constraints, including in particular the issues of stability, causality, locality, and naturalness. Such constraints impose to change significantly the MOND phenomenology if the MOND effects are produced by a k-essence scalar field. We also account for the Pioneer anomaly within a class of generalized scalar-tensor models, and finally show how to explain the local galactic escape speed without invoking Dark Matter. (author)