The Mathematical Theory Of Cosmic Strings - M. Anderson
The existence of cosmic strings was first proposed in 1976 by Tom Kibble, who
drew on the theory of line vortices in superconductors to predict the formation
of similar structures in the Universe at large as it expanded and cooled during
the early phases of the Big Bang. The critical assumption is that the strong and
electroweak forces were first isolated by a symmetry-breaking phase transition
which converted the energy of the Higgs field into the masses of fermions and
vector bosons. Under certain conditions, it is possible that some of the Higgs
field energy remained in thin tubes which stretched across the early Universe.
These are cosmic strings.
The masses and dimensions of cosmic strings are largely determined by the
energy scale at which the relevant phase transition occurred. The grand unification
(GUT) energy scale is at present estimated to be about 1015 GeV, which indicates
that the GUT phase transition took place some 10−37–10−35 s after the Big Bang,
when the temperature of the Universe was of the order of 1028 K. The thickness of
a cosmic string is typically comparable to the Compton wavelength of a particle
with GUT mass or about 10−29 cm. This distance is so much smaller than the
length scales important to astrophysics and cosmology that cosmic strings are
usually idealized to have zero thickness.
The mass per unit length of such a string, conventionally denoted µ,is
proportional to the square of the energy scale, and in the GUT case has a value
of about 1021 gcm−1. There is no restriction on the length of a cosmic string,
although in the simplest theories a string can have no free ends and so must
either be infinite or form a closed loop. A GUT string long enough to cross
the observable Universe would have a mass within the horizon of about 1016 M ,
which is no greater than the mass of a large cluster of galaxies.
Interest in cosmic strings intensified in 1980–81, when Yakov Zel’dovich
and Alexander Vilenkin independently showed that the density perturbations
generated in the protogalactic medium by GUT strings would have been large
enough to account for the formation of galaxies. Galaxy formation was then (and
remains now) one of the most vexing unsolved problems facing cosmologists. The
extreme isotropy of the microwave background indicates that the early Universe
was very smooth. Yet structure has somehow developed on all scales from
the planets to clusters and superclusters of galaxies. Such structure cannot be adequately explained by random fluctuations in the density of the protogalactic
medium unless additional ad hoc assumptions about the process of galaxy
formation are made.
- Hardcover: 380 pages
- Publisher: Taylor & Francis; 1st edition (November 2002)
- Language: English
- ISBN-10: 0750301600
- ISBN-13: 978-0750301602
The existence of cosmic strings was first proposed in 1976 by Tom Kibble, who
drew on the theory of line vortices in superconductors to predict the formation
of similar structures in the Universe at large as it expanded and cooled during
the early phases of the Big Bang. The critical assumption is that the strong and
electroweak forces were first isolated by a symmetry-breaking phase transition
which converted the energy of the Higgs field into the masses of fermions and
vector bosons. Under certain conditions, it is possible that some of the Higgs
field energy remained in thin tubes which stretched across the early Universe.
These are cosmic strings.
The masses and dimensions of cosmic strings are largely determined by the
energy scale at which the relevant phase transition occurred. The grand unification
(GUT) energy scale is at present estimated to be about 1015 GeV, which indicates
that the GUT phase transition took place some 10−37–10−35 s after the Big Bang,
when the temperature of the Universe was of the order of 1028 K. The thickness of
a cosmic string is typically comparable to the Compton wavelength of a particle
with GUT mass or about 10−29 cm. This distance is so much smaller than the
length scales important to astrophysics and cosmology that cosmic strings are
usually idealized to have zero thickness.
The mass per unit length of such a string, conventionally denoted µ,is
proportional to the square of the energy scale, and in the GUT case has a value
of about 1021 gcm−1. There is no restriction on the length of a cosmic string,
although in the simplest theories a string can have no free ends and so must
either be infinite or form a closed loop. A GUT string long enough to cross
the observable Universe would have a mass within the horizon of about 1016 M ,
which is no greater than the mass of a large cluster of galaxies.
Interest in cosmic strings intensified in 1980–81, when Yakov Zel’dovich
and Alexander Vilenkin independently showed that the density perturbations
generated in the protogalactic medium by GUT strings would have been large
enough to account for the formation of galaxies. Galaxy formation was then (and
remains now) one of the most vexing unsolved problems facing cosmologists. The
extreme isotropy of the microwave background indicates that the early Universe
was very smooth. Yet structure has somehow developed on all scales from
the planets to clusters and superclusters of galaxies. Such structure cannot be adequately explained by random fluctuations in the density of the protogalactic
medium unless additional ad hoc assumptions about the process of galaxy
formation are made.
