Aspects of accelerating universe and the de Sitter spacetime

The observation of type Ia supernova and cosmic microwave background radiation (CMBR) anisotropy strongly suggest that our universe is undergoing an accelerated expansion. Furthermore these observations also suggest that the total energy of our universe consists of only 5% visible matter, 25% dark matter and remaining 70% energy is dark energy. One of the leading candidates for dark energy is a cosmological constant. If that is the case, then cosmological constant will be the dominant term in the expression of the total energy budget of the universe now and in future. That is because the matter energy density will be reduced due to expansion of universe but the energy density of cosmological constant will remain the same. In other words our universe will become nearly de Sitter universe in future. Therefore to understand our universe, it is important to study different aspects of the de Sitter universe. In this thesis, we aim to study several aspects of the de Sitter universe like its geometrical structure, particle horizon and Gibbons-Hawking radiation. By exploring the origin of such radiation we aim to understand certain aspects of quantum gravity in particular that of loop quantum gravity.