Higgs particle and cosmology

The Standard Model of particle physics and gravity may describe the physical processes in our Universe from the present day to the very early stages of its expansion related to the Big Bang and cosmological inflation. We give a pedagogical introduction to the role of the Higgs boson in the early Universe, starting from the late times and moving toward the earlier moments of the Universe's evolution. Several topics will be covered. We will discuss the physical reactions in the early universe and see that they are fast enough to describe the Standard Model phenomena in the framework of equilibrium quantum field theory at finite temperatures. We will consider the possibility of having an electroweak phase transition at the temperatures of the order of the Fermi scale and discuss the rate of the baryon and lepton number non-conservation at high temperatures. We will describe Higgs inflation and the transfer of energy from the Higgs field to Standard Model particles, leading to the Big Bang. The discussion will be done in the framework of the Standard Model, with a few remarks at the end concerning its extensions.