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Abstract The topic of the thesis is the studying accelerated expansion phenomenon of the universe that confronts theoretical models of cosmology. This thesis is organized as follows: In chapter one, we have presented an introduction of principles of modern cosmology science starting from the Einstein model of the static universe by introducing cosmological constant into his equations in 1917 and Friedmann’s modifications to Einstein’s equations in 1922 to conform this phenomenon which was discovered by Hubble in 1929. After that observation of Supernova type, Ia through Rises et al. in 1998 and Perlmutter et al. in 1999 confirmed the universe has acceleration. Late cosmic acceleration source has been labelled as “dark energy”. We presented challenges that face the Big Bang Model and inflation as a solution to the problem of initial conditions. We introduced theoretical models that explain the accelerated expansion of universe such as modified gravity models as Einstein’s general relativity modification and dark energy models. We focused on Quintessence model as a type of scalar field dark energy models. Quintessence model has recently succeeded in explaining the acceleration of the expansion of the universe by possessing an equation of state fit with the latest observations. |