Noether Symmetries in Theories of Gravity

Francesco Bajardi is a Researcher at Scuola Superiore Meridionale in Napoli. His primary areas of research are general relativity, theoretical cosmology and theories of gravity. He graduated at the University of Palermo and obtained his Ph.D. at the Università di Napoli 'Federico II'. Salvatore Capozziello is a Full Professor in Astronomy and Astrophysics at the Università di Napoli 'Federico II', and former President of the Italian Society for General Relativity and Gravitation. His primary areas of research are general relativity, cosmology and relativistic astrophysics. He has authored more than 600 scientific publications with more than 34,000 citations.

• 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.