8,597 research outputs found
Restoring Time Dependence into Quantum Cosmology
Mini superspace cosmology treats the scale factor , the lapse function
, and an optional dilation field as canonical variables. While
pre-fixing means losing the Hamiltonian constraint, pre-fixing is
serendipitously harmless at this level. This suggests an alternative to the
Hartle-Hawking approach, where the pre-fixed and its derivatives are
treated as explicit functions of time, leaving and a now mandatory
to serve as canonical variables. The naive gauge pre-fix
is clearly forbidden, causing evolution to freeze altogether, so pre-fixing the
scale factor, say , necessarily introduces explicit time dependence
into the Lagrangian. Invoking Dirac's prescription for dealing with
constraints, we construct the corresponding mini superspace time dependent
total Hamiltonian, and calculate the Dirac brackets, characterized by
, which are promoted to commutation relations in the
quantum theory.Comment: Honorable Mentioned essay - Gravity Research Foundation 201
Cosmological Higgs fields
We present a time-dependent solution to the coupled Einstein-Higgs equations
for general Higgs-type potentials in the context of flat FRW cosmological
models. Possible implications are discussed.Comment: 5 pages, no figures. Version to be published in Phys. Rev. Lett.
Changes: references and citations added; introduction partly modified;
expanded discussion of relations between parameters in the Higgs potentia
Topological Defects as Seeds for Eternal Inflation
We investigate the global structure of inflationary universe both by
analytical methods and by computer simulations of stochastic processes in the
early Universe. We show that the global structure of the universe depends
crucially on the mechanism of inflation. In the simplest models of chaotic
inflation the Universe looks like a sea of thermalized phase surrounding
permanently self-reproducing inflationary domains. In the theories where
inflation occurs near a local extremum of the effective potential corresponding
to a metastable state, the Universe looks like de Sitter space surrounding
islands of thermalized phase. A similar picture appears even if the state is unstable but the effective potential has a discrete symmetry . In this case the Universe becomes divided into domains containing
different phases. These domains will be separated from each other by domain
walls. However, unlike ordinary domain walls, these domain walls will inflate,
and their thickness will exponentially grow. In the theories with continuous
symmetries inflation generates exponentially expanding strings and monopoles
surrounded by thermalized phase. Inflating topological defects will be stable,
and they will unceasingly produce new inflating topological defects. This means
that topological defects may play a role of indestructible seeds for eternal
inflation.Comment: 21 pages, 17 figures (not included), Stanford University preprint
SU--ITP--94--
Inflationary cosmology of the extreme cosmic string
Starting with a study of the cosmological solution to the Einstein equations
for the internal spacetime of an extreme supermassive cosmic string kink, and
by evaluating the probability measure for the formation of such a kink in
semiclassical approximation using a minisuperspace with the appropriate
symmetry, we have found a set of arguments in favor of the claim that the
kinked extreme string can actually be regarded as a unbounded chain of pairs of
Planck- sized universes. Once one such universe pairs is created along a
primordial phase transition at the Planck scale, it undergoes an endless
process of continuous self-regeneration driven by chaotic inflation in each of
the universes forming the pair.Comment: 15 pages, RevTex, to appear in Int. J. Mod. Phys.
Inflation and Large Internal Dimensions
We consider some aspects of inflation in models with large internal
dimensions. If inflation occurs on a 3D wall after the stabilization of
internal dimensions in the models with low unification scale (M ~ 1 TeV), the
inflaton field must be extremely light. This problem may disappear In models
with intermediate (M ~10^{11} GeV) to high (M ~ 10^{16} GeV) unification scale.
However, in all of these cases the wall inflation does not provide a complete
solution to the horizon and flatness problems. To solve them, there must be a
stage of inflation in the bulk before the compactification of internal
dimensions.Comment: 4 pages, revtex, minor modification
Inflation with
We discuss various models of inflationary universe with . A
homogeneous universe with may appear due to creation of the
universe "from nothing" in the theories where the effective potential becomes
very steep at large , or in the theories where the inflaton field
nonminimally couples to gravity. Inflation with generally requires
intermediate first order phase transition with the bubble formation, and with a
second stage of inflation inside the bubble. It is possible to realize this
scenario in the context of a theory of one scalar field, but typically it
requires artificially bent effective potentials and/or nonminimal kinetic
terms. It is much easier to obtain an open universe in the models involving two
scalar fields. However, these models have their own specific problems. We
propose three different models of this type which can describe an open
homogeneous inflationary universe.Comment: 29 pages, LaTeX, parameters of one of the models are slightly
modifie
STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY
In Brans-Dicke theory the Universe becomes divided after inflation into many
exponentially large domains with different values of the effective
gravitational constant. Such a process can be described by diffusion equations
for the probability of finding a certain value of the inflaton and dilaton
fields in a physical volume of the Universe. For a typical chaotic inflation
potential, the solutions for the probability distribution never become
stationary but grow forever towards larger values of the fields. We show here
that a non-minimal conformal coupling of the inflaton to the curvature scalar,
as well as radiative corrections to the effective potential, may provide a
dynamical cutoff and generate stationary solutions. We also analyze the
possibility of large nonperturbative jumps of the fluctuating inflaton scalar
field, which was recently revealed in the context of the Einstein theory. We
find that in the Brans--Dicke theory the amplitude of such jumps is strongly
suppressed.Comment: 19 pages, LaTe
Dynamics of Gravitating Magnetic Monopoles
According to previous work on magnetic monopoles, static regular solutions
are nonexistent if the vacuum expectation value of the Higgs field is
larger than a critical value , which is of the order of the
Planck mass. In order to understand the properties of monopoles for
, we investigate their dynamics numerically. If is
large enough (), a monopole expands exponentially and a
wormhole structure appears around it, regardless of coupling constants and
initial configuration. If is around , there are three
types of solutions, depending on coupling constants and initial configuration:
a monopole either expands as stated above, collapses into a black hole, or
comes to take a stable configuration.Comment: 11 pages, revtex, postscript figures; results for various initial
conditions are added; to appear in Phys. Rev.
From the Big Bang Theory to the Theory of a Stationary Universe
We consider chaotic inflation in the theories with the effective potentials
phi^n and e^{\alpha\phi}. In such theories inflationary domains containing
sufficiently large and homogeneous scalar field \phi permanently produce new
inflationary domains of a similar type. We show that under certain conditions
this process of the self-reproduction of the Universe can be described by a
stationary distribution of probability, which means that the fraction of the
physical volume of the Universe in a state with given properties (with given
values of fields, with a given density of matter, etc.) does not depend on
time, both at the stage of inflation and after it. This represents a strong
deviation of inflationary cosmology from the standard Big Bang paradigm. We
compare our approach with other approaches to quantum cosmology, and illustrate
some of the general conclusions mentioned above with the results of a computer
simulation of stochastic processes in the inflationary Universe.Comment: No changes to the file, but original figures are included. They
substantially help to understand this paper, as well as eternal inflation in
general, and what is now called the "multiverse" and the "string theory
landscape." High quality figures can be found at
http://www.stanford.edu/~alinde/LLMbigfigs
Features of deSitter Vacua in M-Theory
We compute the masses of all moduli in the unstable deSitter vacua arising in
the toy model of cosmological M-theory flux compactifications on the G2
holonomy manifolds of [1]. The slow-roll parameters in the tachyonic directions
are shown to be too large to be useful for conventional models of inflation.
However, it appears that we can find fast roll regimes which could, under
certain conditions, account for the current dark energy driven accelerated
expansion of the universe.Comment: 14 pages, 1 figur
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