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

This volume summarizes the many modified theories of gravity and shows how to select physically viable models using symmetry principles.

Francesco Bajardi (Author), Salvatore Capozziello (Author)

9781009208741, Cambridge University Press

Hardback, published 24 November 2022

475 pages
25.1 x 17.4 x 2.9 cm, 0.92 kg

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.

Preface
Acknowledgements
Amalie Emmy Noether: a life for mathematics
Notation
Acronyms
Part I. Preliminaries: 1. The concept of symmetry
2. The two Noether theorems
3. Applications of the Noether first theorem to fields and particles
4. Theories of gravity: an overview
Part II. The Noether Symmetry Approach: 5. From the Noether theorem to the Noether symmetry approach
6. The extensions of GR, TEGR and STEGR
7. Higher-order extensions with the Gauss–Bonnet invariant
8. Extensions with higher derivatives or R and T
9. Scalar-tensor theories of gravity
10. Non-local gravity
11. Noether symmetries in Bianchi universes
12. The Noether approach in spherical symmetry
Part III. Applications: 13. Applications to solar system, stars and our galaxy
14. Applications to galaxies
15. Applications to cosmology
16. Applications to quantum cosmology
17. Strings, swampland, renormalizability and viability
Epilogue
Appendices
References
Index.

Subject Areas: Mathematical physics [PHU], Physics [PH], Mathematics & science [P]