Özet:
This thesis is about getting the most information from the cosmological super nova data about the expansion history of the homogeneous and isotropic universe, with the least possible set of assumptions. To this end, we fit various functions to the lu minosity distance dL(z) and try to reconstruct the scale factor a(t), through the best of those functions, without an assumption of gravity models; hence making this anal ysis model-independent. We find that with the SNe Ia data we can show the current acceleration and past deceleration of the universe. However, to get even better results, we add gamma ray burst data to the dataset at the cost of slightly compromising the model-independent nature of the analysis. With this expanded data set, we can deter mine the redshift of transition from deceleration in the past to current acceleration as zt ≈ 0.55±0.08 for a flat universe (larger for positive spatial curvature, and smaller for negative). In this work, we see that the choice of parametrization heavily affects the results of the analysis. After the assumption of Einstein’s General Relativity, we see that, as in previous work, there is a special redshift value at which the curvature of the universe has no effect on its energy density. Using this redshift value, we manage to put an upper limit on matter density, hence a lower limit on the density of dark energy. If Starobin sky’s gravity model is assumed, we find that from the positive α values (parameter of Starobinsky model) we cannot get anything useful however from a certain negative value we get energy density curve very close to the matter-only curve. Hence, we can find a simple modified-gravity cosmology with no dark energy, but with about twice as much dark matter as the concordance model.
