11,293 research outputs found
Measure Problem for Eternal and Non-Eternal Inflation
We study various probability measures for eternal inflation by applying their
regularization prescriptions to models where inflation is not eternal. For
simplicity we work with a toy model describing inflation that can interpolate
between eternal and non-eternal inflation by continuous variation of a
parameter. We investigate whether the predictions of four different measures
(proper time, scale factor cutoff, stationary and causal {diamond}) change
continuously with the change of this parameter. We will show that {only} for
the stationary measure the predictions change continuously. For the proper-time
and the scale factor cutoff, the predictions are strongly discontinuous. For
the causal diamond measure, the predictions are continuous only if the stage of
the slow-roll inflation is sufficiently long.Comment: 9 pages, 4 figure
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
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--
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
Towards a gauge invariant volume-weighted probability measure for eternal inflation
An improved volume-weighted probability measure for eternal inflation is
proposed. For the models studied in this paper it leads to simple and
intuitively expected gauge-invariant results.Comment: 16 pages, 3 figs, few misprints corrected, comments adde
A Toy Model for Open Inflation
The open inflation scenario based on the theory of bubble formation in the
models of a single scalar field suffered from a fatal defect. In all the
versions of this scenario known so far, the Coleman-De Luccia instantons
describing the creation of an open universe did not exist. We propose a simple
one-field model where the CDL instanton does exist and the open inflation
scenario can be realized.Comment: 7 pages, 4 figures, revtex, a discussion of density perturbations is
extende
Origin of FRW cosmology in slow-roll inflation from noncompact Kaluza-Klein theory
Using a recently introduced formalism we discuss slow-roll inflaton from
Kaluza-Klein theory without the cylinder condition. In particular, some
examples corresponding to polynomic and hyperbolic -potentials are
studied. We find that the evolution of the fifth coordinate should be
determinant for both, the evolution of the early inflationary universe and the
quantum fluctuations.Comment: (final version) to be published in EPJ
Pre-Big-Bang Requires the Universe to be Exponentially Large From the Very Beginning
We show that in a generic case of the pre-big-bang scenario, inflation will
solve cosmological problems only if the universe at the onset of inflation is
extremely large and homogeneous from the very beginning. The size of a
homogeneous part of the universe at the beginning of the stage of pre-big-bang
(PBB) inflation must be greater than , where is the
stringy length. The total mass of an inflationary domain must be greater than
, where . If the universe is initially
radiation dominated, then its total entropy at that time must be greater than
. If the universe is closed, then at the moment of its formation it
must be uniform over causally disconnected domains. The natural
duration of the PBB stage in this scenario is . We argue that the
initial state of the open PBB universe could not be homogeneous because of
quantum fluctuations. Independently of the issue of homogeneity, one must
introduce two large dimensionless parameters, , and , in order to solve the flatness problem in the PBB cosmology. A regime
of eternal inflation does not occur in the PBB scenario. This should be
compared with the simplest versions of the chaotic inflation scenario, where
the regime of eternal inflation may begin in a universe of size
with vanishing initial radiation entropy, mass , and geometric entropy
O(1). We conclude that the current version of the PBB scenario cannot replace
usual inflation even if one solves the graceful exit problem in this scenario.Comment: 14 pages, a discussion of the flatness problem in the PBB cosmology
is adde
Stationarity of Inflation and Predictions of Quantum Cosmology
We describe several different regimes which are possible in inflationary
cosmology. The simplest one is inflation without self-reproduction of the
universe. In this scenario the universe is not stationary. The second regime,
which exists in a broad class of inflationary models, is eternal inflation with
the self-reproduction of inflationary domains. In this regime local properties
of domains with a given density and given values of fields do not depend on the
time when these domains were produced. The probability distribution to find a
domain with given properties in a self-reproducing universe may or may not be
stationary, depending on the choice of an inflationary model. We give examples
of models where each of these possibilities can be realized, and discuss some
implications of our results for quantum cosmology. In particular, we propose a
new mechanism which may help solving the cosmological constant problem.Comment: 30 pages, Stanford preprint SU-ITP-94-24, LaTe
Towards the Theory of Cosmological Phase Transitions
We discuss recent progress (and controversies) in the theory of finite
temperature phase transitions. This includes the structure of the effective
potential at a finite temperature, the infrared problem in quantum statistics
of gauge fields, the theory of formation of critical and subcritical bubbles
and the theory of bubble wall propagation.Comment: 50 p
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