Constraints on the Early Universe and Dark Energy from Big Bang Nucleosynthesis

This thesis explores two main mysteries of modern cosmology. I explore possible solutions for the unsolved cosmic lithium problem. Secondly I explore many properties of various old and new dark energy models. Big bang nucleosynthesis (BBN) has been used as a powerful tool to constrain models of cosmology due to it's precise calculation of light element abundances. However the tool itself has a glaring problem. It's calculation of the amount of Lithium is completely wrong. In this thesis , I have shown that the nuclear reaction rates at BBN would be different from the standard calculation. This would alter all the final light element abundance and thus I have shown that all the BBN calculations performed till today is wrong. This completely shatters a pillar of cosmology that has been steady for almost half a century. In the second part of my thesis I constrain the free parameters of many dark energy models by modeling the evolution of dark energy density from a time before BBN till present time. The allowed values of dark energy density today and during BBN can be used to constrain dark energy models.