Noether Symmetries in Theories of Gravity: With Applications to Astrophysics and Cosmology

This volume summarizes the many alternatives and extensions to  Einstein's General Theory of Relativity, and shows how symmetry  principles can be applied to identify physically viable models. The  first part of the book establishes the foundations of classical field  theory, providing an introduction to symmetry groups and the Noether  theorems. A quick overview of general relativity is provided, including  discussion of its successes and shortcomings, then several theories of  gravity are presented and their main features are summarized. In the  second part, the 'Noether Symmetry Approach' is applied to theories of  gravity to identify those which contain symmetries. In the third part of  the book these selected models are tested through comparison with the  latest experiments and observations. This constrains the free parameters  in the selected models to fit the current data, demonstrating a useful  approach that will allow researchers to construct and constrain modified  gravity models for further applications.