Cosmological Models with Symmetric Teleparallel Gravity and its Extension

This thesis investigates late-time cosmic acceleration using modified gravity theories with a focus on $f(Q)$ gravity, as an alternative to the $\Lambda$CDM model. The standard cosmological model attributes the acceleration to a cosmological constant, but it faces issues like the unexplained nature of dark matter and dark energy and discrepancies with certain observations. Modified gravity including $f(Q)$ gravity, offers a potential solution by incorporating dynamic dark energy or changes to gravitational interactions, avoiding the need for a constant cosmological term. Also, thesis evaluates the viability of $f(Q)$ gravity by analyzing observational data from Type Ia Supernovae, Hubble parameter measurements and other cosmological datasets. Using statistical tools like Markov Chain Monte Carlo (MCMC) analysis, this work constrains the parameters of $f(Q)$ gravity and compares it to the $\Lambda$CDM model.....