Research Projects

General relativity, one of the most successful physical theories ever proposed, was born as a result of the fruitful interaction between physics, represented by the equivalence principle, and the deformation of the Minkowski metric, and mathematics, represented by the differential geometric theory of the Riemann spaces, introduced, and initially developed by B. Riemann (1867). In Riemannian geometry the properties of the space-time are described via a metric tensor g_μν, and an affine connection Γ_μν^λ, which in turn is determined by the metric tensor [A. Einstein (1915, 1916), D. Hilbert (1915)]. General relativity did have a tremendous impact on the development of physics, astrophysics, and cosmology [Ø Gron, S. Hervik (2007)]. The recent measurements by the Planck satellite of the temperature fluctuations of the Cosmic Microwave Background Radiation [Y. Akrami et al., Planck 2018 results (2020), N. Aghanim et al., Planck 2018 results (2020)], as well as the observations of the distant supernovae [A.G. Riess (2019)] have confirmed that the Universe is in a state of accelerating expansion, and that its matter content consists of only 5% baryonic matter, while 95% of matter–energy resides in two mysterious components, called dark energy and dark matter, respectively. The dark components model [A. Joyce, B. Jain, J. Khoury, M. Trodden (2015), A. Joyce, L. Lombriser, F. Schmidt (2016), A.N. Tawfik, E.A. El Dahab (2019), N. Frusciante, L. Perenon (2020), A. Arbey, F. Mahmoudi (2021)] assumes that the Universe is filled with two (still mysterious) components, dark energy, and dark matter, respectively, components for which many proposals have been advanced. On the other hand, one possibility of expansion of the universe can be justified by modified theory of gravity. The presence of a late-time cosmic acceleration of the Universe can be indeed be explained by f(R) gravity (Carroll et al. 2004; Sotiriou and Faraoni 2010). Nojiri and Odintsov (2007) have reviewed various modified gravities like F(T), F(Q), F(R,T), F(Q,T) etc. To conclude, in this research proposal we will introduce a systematic investigation of the application of the Finsler geometry with modify theories of gravitation, and we will try to prove its theoretical consistency. This approach will also motivate and encourage the study of further extensions of the F(R,T), F(Q,T) F(R,G) type family of theories in a Finsler space as an n-dimensional point space. We will try to show that the presented approach predicts de Sitter type expansions of the Universe, and thus it may represent a geometric alternative to dark energy. Hence this study offers some basic theoretical tools for the in-depth investigation of the geometric aspects of gravity, and of its cosmological implications.