Executive Summary : | Ever since the discovery of the expansion of the universe from the observation of recessional velocity of distant galaxies by Edwin Hubble the field of cosmology has experienced a lot of developments. The observations on cosmic microwave background (CMB) enable us to look into the past history of the universe along with constraining the constituents of the universe. The research in the field of cosmology got a great boost after the discovery of late time cosmic acceleration from type Ia supernova (SNIa) observations in 1998. After that we have many important observations like WMAP, HST, Planck, BOSS etc. which gave us precise data. Availability of the observational data led us to a great era of research in cosmology. While some observations can be explained with the standard model of cosmology namely the ΛCDM model there are still some unexplained observations. Even though the most suitable model for the late time acceleration or namely dark energy is the standard ΛCDM model there are some issues like fine-tuning problem associated with this model. So we need to look for more suitable models or we may also have to modify the gravity sector. Very recently it has been reported that there exist significant (4σ to 6σ) amount of discrepancy arising between the CMB observation and the local measurements of cosmological parameters like present value of the Hubble parameter. These anomalies put the standard ΛCDM model in question and points us towards finding more suitable models which can alleviate these anomalies in different measurements. So, in this project we are going to look for such models. While building some cosmological model we not only have to alleviate the current discrepancies but also have to satisfy the well established cosmological constraints coming from different observations. At the same time we will also give predictions for the models for the forthcoming observations like Euclid. |