During the past two decades, cosmologists turned to particle physics in order
to explore the physics of the very early Universe. The main link between the
physics of the smallest and largest structures in the Universe is the idea of
spontaneous symmetry breaking, familiar from condensed matter physics.
Implementing this mechanism into cosmology leads to the interesting possibility
that phase transitions related to the breaking of symmetries in high energy
particle physics took place during the early history of the Universe. These
cosmological phase transitions may help us understand many of the challenges
faced by the standard hot Big Bang model of cosmology, while offering a unique
window into the very early Universe and the physics of high energy particle
interactions.Comment: 31 pages, LaTeX, 10 figures, 8 provided (7 EPS + 1 PS). Uses
psfig.tex. Invited article for ``Contemporary Physics'