  The primary objective of this work is to investigate the cosmological phase
transitions in the early Universe, with a focus on the electroweak phase
transition in the Standard Model and its extensions. In the Standard Model, the
spontaneously broken electroweak symmetry at zero temperature is restored in
the early Universe due to finite-temperature effects. This phenomenon is
studied using the effective potential at finite temperatures, which determines
the true vacuum state of the theory. Symmetry restoration at high temperatures
is also studied by the finite-temperature field theory introduced to derive the
Feynman rules at finite temperatures using the imaginary-time formalism.
Furthermore, we present the theory of cosmological phase transitions, focusing
on the concepts of thermal tunneling and bubble nucleation. We additionally
discuss the observed baryon asymmetry of the Universe to formulate the
conditions for baryogenesis and describe electroweak baryogenesis. Therefore,
the one-loop effective potential in the Standard Model at finite temperatures
is derived in detail including the ring corrections to study further the
electroweak baryogenesis. Our results indicate that the electroweak phase
transition is not strong enough to explain the observed baryon asymmetry of the
Universe. On the other hand, the real singlet extensions of the Standard Model
describe a strong enough electroweak phase transition and the observed baryon
asymmetry of the Universe. These extensions are also discussed including a
dimension-six operator, which originates from an effective field theory. In
particular, the parameter space of this singlet extension is examined
extensively, while it is restricted by numerous phenomenological constraints,
such as the invisible Higgs decay width.
