Hubble tension in the context of cosmological scalar field models

This thesis delves into the issue of Hubble tension that is the discrepancy between different types of measurements of the expansion rate of the universe at present (i.e. Hubble constant H0). Various techniques can be employed to measure H0. There are two types of measurements, namely, direct and indirect measurements for measurement of H0. Direct measurements involve determining the recession velocities of galaxies or supernovae at relatively small cosmological distances, so this type of measurements are direct local measurements. On the other hand, indirect measurements encompass both local methods, such as utilizing the Tully-Fisher relation, and non-local approaches, including cosmic microwave background (CMB) measurements and baryon acoustic oscillation (BAO) measurements of large-scale structures (LSS). The most precise local measurements are achieved through supernovae calibrated by Cepheid variable star measurements, while CMB measurements provide the most precise non-local measurements. However, even when considering measurement errors, there is a significant discrepancy between supernovae and CMB measurements. This is known as the Hubble tension. A milder discrepancy is also observed between local direct measurements and BAO measurements. Many different potential sources of this tension and many different models are proposed to resolve this tension. This thesis focuses on the subset of the proposed models that employ scalar fields in the context of general relativity. The primary objective is to provide a comprehensive understanding of the fundamental ideas underlying these models and emphasize their theoretical aspects