Evolution of dark matter candidate axions in the early universe

Solving the problem U(1)A with instantons in a non-trivial QCD vacuum introduced a problem in QCD known as the 'strong CP problem'. The spherical U(1)PQ symmetry proposed by Peccei and Quinn provides a solution to this problem. This symmetry solves the strong CP problem by incorporating the axion field, a light pseudoscalar Nambu-Goldstone boson. In this thesis, we will review the axion models and calculate the mass and potential for the axion. Next, we'll examine the formation and evolution of axion in the early universe and its supposed function as dark matter. The formation and production of axions in the early universe can occur in two different ways. Thermal generation or nonthermal generation, known as misalignment mechanism or decaying of topological defects. In this thesis, we will talk about the role of the axion particle in cosmology and examine the production of axions in the early universe in different cosmology scenarios.