Kozmolojide skaler alan potensiyelleri

In this thesis we describe how to construct a scalar field potential V(phi) in a five-dimensional cosmological model with non-zero curvature for the three-dimensional spatial part, where we use the scale factor a(t) for observed space and the additional scale factor b(t) for the extra dimension. We want to verify whether or not scalar field potentials arise which are ruled out in the case of the effective four-dimensional observed universe. Explicit expressions for the scalar field potential V(phi) and the scalar field phi in terms of cosmic time are derived for both non-interacting and interacting scalar fields. A standard method in cosmology is to obtain the scale factor a(t) by solving Einstein's equations or modifications thereof. We, however, find the form of the potential and scalar field for non-interacting scalar fields using a given scale factor a(t) and b(t) by employing such a method of reverse engineering. One of the interesting results reached in this context is, in the case of de Sitter type expansion for the observed space, that there is a room for a universe with k=-1 for a certain contracting-type evolution of the extra dimension which was not possible in the context of effective four-dimensional model. There is also the possibility of getting a cosmological constant term in the potential which depends also on the size of the extra dimension. For the case of power-law-type expansion of observed space and for stabilized extra dimension, we get an exponential type potential which vanishes if the observed space evolves like non-relativistic matter, namely a(t) ~ t^(2/3). This reminds us that these kind of models should further be investigated to get information about which kind of scalar field potentials can lead to which type of evolutions in these extra dimensional models. With this thesis, the main concern is to investigate the implications of an extra dimension on the scalar field potential, V(phi), for the inflation phase because, it seems reasonable to take into account extra spatial dimensions for the early universe. Despite our focus on inflation, the method explained here is capable of finding other scalar field potentials in quintessence models, thus giving us a way of grasping effects of scalar field potentials in the late acceleration phase. But we have to stress that this toy-model approximation only equips us with a basic understanding of the shape of the potential under the consideration of an extra dimension, without going into details about the fundamental theory behind V(phi).