Early Universe Cosmology
Joanne Cohn
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Model Building
Ewan Stewart and I collaborated on a project in
inflationary model building.
Finding particle theory models which produce realistic inflationary scenarios
is an active area of research because it is nontrivial to
consistently combine the conditions of slow roll inflation
(to produce a scale invariant spectrum)
with gravitational effects.
In particular, most inflationary models require field theories with very flat
potentials. Often one can get these very flat potentials in supersymmetric
theories. However, in the context of a supergravity theory, as is appropriate
for a supersymmetric theory where gravity is included, this flatness is
generically ruined. The lack of flatness comes from supergravity
effects which usually give fields a mass of order the Hubble constant,
and makes it difficult for inflation to occur.
Thus one goal of inflationary model building
is to find field theories, or more generally mechanisms,
which guarantee the flatness of the inflaton's potential when
supergravity effects are included.
We use symmetries to produce a flat potential for inflation. However,
instead of putting in a continuous symmetry in order to get inflation
and then breaking the symmetry to get inflation to start and end,
we use
an unbroken discrete symmetry to induce the lowest order continuous
symmetry and thus inflation. Note that not all discrete symmetries will
do this. Also, if the potential is to have special points
where the absolute values of the fields are different, for instance
in order to produce a hybrid exit in a supergravity model, a discrete
nonabelian symmetry is useful. The induced continuous symmetries
allow a flat enough potential for inflation to occur. The
discreteness of the symmetries allows inflation to end via
a hybrid or mutated hybrid mechanism, as neighboring points in field
space can have different potentials because the exact symmetry is
discrete. We have a few examples of
models which guarantee the flatness of the inflaton's potential
using discrete non-abelian gauge symmetries in this way.
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Open Universes
These are currently observationally disfavored, however many of the
tools (related, e.g. to bubble nucleation) may have more general
applicability. These
field theoretic models produce
an open (less than critical matter density) universe.
(A poster on this (1.1Mb) is
here.)
Current observations (e.g. of the
CMB, the cosmic microwave background)
show a large degree of
homogeneity, and have now shown that the universe is
spatially flat.
Most theories producing a homogeneous and isotropic universe rely upon
inflation,
where the scale factor for the
universe accelerates and inhomogeneities are diluted away.
Requiring sufficient inflation to homogenize random initial conditions
also drives the universe to very close to
critical density, making it almost flat. In 1994,
Bucher, Goldhaber and Turok, using earlier work of Gott and
Coleman and de Luccia, proposed a model for an open universe
where a bubble nucleated in the universe after inflation had begun
(and calculated density perturbations).
The interior of the bubble is an open universe.
There is also extensive related work by
Yamamoto, Tanaka and Sasaki.
Bubble nucleation in these models occurs in a vacuum, but
the presence of a curvature scale and the structure of
de Sitter space introduces many subtleties.
Comprehensive calculations of the spectrum for the
coupled gravity and scalar
theories has been done for some cases by
Garriga, Montes, Sasaki and Tanaka.
A recent one field toy model was
proposed by Linde.
Hawking and Turok proposed a controversial mechanism in
early 1998, where the universe tunnels,
but not from a false vacuum. In these models the homogeneity
in the universe comes from the universe taking the most likely
(and hence most symmetric) configuration, as in the Hartle Hawking
formulation of quantum cosmology. Linde has suggested using this
idea but in the context of the tunneling wave function of the universe.
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