  In this thesis, we aim to investigate the mechanisms underlying the genesis
of magnetic fields in the Universe and explore their potential in addressing
the matter-antimatter asymmetry. We construct consistent models that generate
the helical magnetic field consistent with observations. We also develop an
effective field theory approach to magnetogenesis, where the choice of EFT
parameters describes the magnetogenesis scenario in the early Universe, and
different choices of parameters correspond to different models. Our EFT
explicitly shows that generating primordial magnetic fields requires two
necessary conditions: conformal invariance breaking and causal propagation.
Furthermore, we establish that the presence of a strong magnetic field near
compact objects, such as neutron stars, aids in understanding the phenomenon of
Fast radio bursts through the conversion of gravitational waves to
electromagnetic waves in the background of a strong transverse magnetic field.
