Chapter 2
Phase transitions in the early universe
2.1 Introduction
Elementary particle theory possesses gauge symmetries that are spontaneously
broken by scalar fields belonging to non-trivial representations of the gauge
group when these fields develop non-zero expectation values at the minimum
of the effective potential. In particular, the S U (2) L x U (l)y gauge group of
electroweak theory is spontaneously broken to the U (I )em of electromagnetism
by the electroweak Higgs scalar expectation value. If grand unification to a
group larger than the SU(3)c x SU(2)L x U(1)y of the standard model, e.g.
to SU (5), occurs at some energy scale, then the grand unified gauge group breaks
spontaneously to the standard model gauge group before this gauge group in turn
breaks to the U (I )em gauge group. Things may be more complicated than this,
with a sequence of spontaneous symmetry breakings to subgroups of the original
grand unified group.
As we shall see later in this chapter, finite temperature effects may result
in some other minimum of the effective potential being deeper than the absolute
minimum of the zero-temperature theory. Then, as the universe cools, it may
undergo a series of first- or second-order phase transitions between different
minima of the effective potential. Such transitions will occur at temperatures
corresponding to the scales of energy associated with the various spontaneous
symmetry breakings. In the case of the electroweak phase transition to the phase
with only U (1 )em unbroken, the scale of temperature for the phase transition will
be of order 102-1 oJ Ge V and, in the case of a grand unified phase transition to a
phase with SU(3)c x SU(2)L x U(l)y unbroken, the phase transition will occur
at a temperature closer to the Planck scale, perhaps at about 10 16 Ge V. If the grand
unified theory breaks to SU(3)c x SU(2)L x U(l)y in stages through a sequence
of phase transitions, the additional phase transitions will occur at intermediate
scales.
In later chapters we shall see that these phase transitions can have a profound
effect on the history of the universe through a number of different processes. For
DOl: 10.120119780367806637-2
29
Phase transitions in the early universe
2.1 Introduction
Elementary particle theory possesses gauge symmetries that are spontaneously
broken by scalar fields belonging to non-trivial representations of the gauge
group when these fields develop non-zero expectation values at the minimum
of the effective potential. In particular, the S U (2) L x U (l)y gauge group of
electroweak theory is spontaneously broken to the U (I )em of electromagnetism
by the electroweak Higgs scalar expectation value. If grand unification to a
group larger than the SU(3)c x SU(2)L x U(1)y of the standard model, e.g.
to SU (5), occurs at some energy scale, then the grand unified gauge group breaks
spontaneously to the standard model gauge group before this gauge group in turn
breaks to the U (I )em gauge group. Things may be more complicated than this,
with a sequence of spontaneous symmetry breakings to subgroups of the original
grand unified group.
As we shall see later in this chapter, finite temperature effects may result
in some other minimum of the effective potential being deeper than the absolute
minimum of the zero-temperature theory. Then, as the universe cools, it may
undergo a series of first- or second-order phase transitions between different
minima of the effective potential. Such transitions will occur at temperatures
corresponding to the scales of energy associated with the various spontaneous
symmetry breakings. In the case of the electroweak phase transition to the phase
with only U (1 )em unbroken, the scale of temperature for the phase transition will
be of order 102-1 oJ Ge V and, in the case of a grand unified phase transition to a
phase with SU(3)c x SU(2)L x U(l)y unbroken, the phase transition will occur
at a temperature closer to the Planck scale, perhaps at about 10 16 Ge V. If the grand
unified theory breaks to SU(3)c x SU(2)L x U(l)y in stages through a sequence
of phase transitions, the additional phase transitions will occur at intermediate
scales.
In later chapters we shall see that these phase transitions can have a profound
effect on the history of the universe through a number of different processes. For
DOl: 10.120119780367806637-2
29