Özet:
We propose alternative gravitational couplings, fields and design some models to explain some cosmological problems. We investigate a cosmological model in which the Stueckelberg fields describing a massive photon are non-minimally coupled to the scalar curvature in a gauge invariant manner. We present not only a solution that can be considered in the context of the late time acceleration of the universe but also a solution compatible with the inflationary cosmology. The mass mechanism that gains to the vector field in a gauge invariant manner, designed by Stueckelberg, and via coupling to gravitation is used as a first in cosmology and we investigate cosmological effects. While Stueckelberg mechanism is generally used in particle physics , distinct behaviors of the scalar and vector fields together with the real valued mass gained by the Stueckelberg mechanism lead the universe to go through the two different accelerated expansion phases with a decelerated expansion phase between them. On the other hand, in the solutions we present, if the photon mass is null then the universe is either static or exhibits a simple power law expansion due to the vector field potential. In other work in this thesis, we propose a new model of gravity where the Ricci scalar (R) in Einstein-Hilbert action is replaced by an arbitrary function of R and of the norm of energy-momentum tensor i.e., f(R, TμνTμν) in metric formalism. We find that the equation of motion of massive test particles is non-geodesic and these test particles are acted upon by a extra force which is orthogonal to the four-velocity of the particles. We also find the Newtonian limit of the model to calculate the extra acceleration which can affect the perihelion of Mercury. There is a deviation from the general relativistic(GR) result unless the energy density of the fluid is constant. Arranging α parameter gives an opportunity to cure the inconsistency between the observational values for the abundance of light elements and the standard Big Bang Nucleosynthesis results. Even the dust dominated universe undergoes an accelerated expansion without using a cosmological constant in Model II. With this specific choice of f(R, TμνTμν) we get the so-called Cardassian-like expansion in which standard Friedmann equation is modified as H2 = Aρ + Bρn in an ad hoc way in the literature.
