Unit:
Department of PhysicsLibrary of the School of Science
Dissertation committee:
Παναγιώτης Σταυρινός, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Θεοχάρης Αποστολάτος, Καθηγητής, Τμήμα Φυσικής, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Θεοδόσιος Χριστοδουλάκης, Καθηγητής, Τμήμα Φυσικής, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Νεκτάριος Βλαχάκης, Καθηγητής, Τμήμα Φυσικής, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Εμμανουήλ Σαριδάκης, Κύριος Ερευνητής, Εθνικό Αστεροσκοπείο Αθηνών
Κωνσταντίνος Αναγνωστόπουλος, Αναπληρωτής Καθηγητής, Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών, Εθνικό Μετσόβιο Πολυτεχνείο
Γεώργιος Παππάς, Επίκουρος Καθηγητής, Τμήμα Φυσικής, Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης
Original Title:
Γενικευμένες Γεωμετρικές Δομές σε Τροποποιημένες Θεωρίες Βαρύτητας
Translated title:
Generalized Geometric Structures in Modified Gravity Theories
Summary:
The aim of the present dissertation, is the study of cosmological models, which are based on generalized geometric structures of spacetime, especially on Finsler and Finsler-like Geometries. These theories are part of the so called anisotropic field theories. Finsler geometry is a natural generalization of Riemannian geometry, in which all geometric objects depend, besides the position, from a direction or velocity argument as well. Finsler geometry is useful in the study of gravity, as it embeds local anisotropy as an intrinsic property of spacetime, it describes systems which spontaneously violate Lorentz symmetry, it provides information on the motion of mass and it allows the direct calculation of the metric tensor from the Lagrangian of the system. Firstly, we develop the basic concepts of the differential geometry of manifolts, we study the main elements of Riemann geometry and Finsler geometry and we describe the most important points of the general theory of relativity, gravity and cosmology in a Riemannian space. Subsequently, we apply the above to Finsler - Randers cosmology, where matter moves in spacetime, under the simultaneous influence of a gravitational and an electromagnetic field. Finally, we investigate the phenomenon of cosmological Bounce, that is the transition of the universe from a contracting to an expanding phase in a continuous way. Specifically, after a detailed analysis of the notion and the conditions of cosmological Bounce, we examine the possibility of Bounce realization, in various modified gravity models, which are based on Finsler and Finsler-like geometries. In particular, we investigate the conditions which must be satisfied for a Bounce creation, in General Very Special Relativity, in Finsler - Randers spacetime, in generalized Finsler-like gravity on the tangent bundle, as in a scalar - tensor theory on the fiber bundle.
Main subject category:
Science
Keywords:
Modified Gravity, Local Anisotropy, Finsler Geometry, Generalized Friedmann Equations, Cosmological Bounce.
