18 research outputs found
Age-dependent decay in the landscape
The picture of the "multiverse" arising in diverse cosmological scenarios
involves transitions between metastable vacuum states. It was pointed out by
Krauss and Dent that the transition rates decrease at very late times, leading
to a dependence of the transition probability between vacua on the age of each
vacuum region. I investigate the implications of this non-Markovian,
age-dependent decay on the global structure of the spacetime in landscape
scenarios. I show that the fractal dimension of the eternally inflating domain
is precisely equal to 3, instead of being slightly below 3 in scenarios with
purely Markovian, age-independent decay. I develop a complete description of a
non-Markovian landscape in terms of a nonlocal master equation. Using this
description I demonstrate by an explicit calculation that, under some technical
assumptions about the landscape, the probabilistic predictions of our position
in the landscape are essentially unchanged, regardless of the measure used to
extract these predictions. I briefly discuss the physical plausibility of
realizing non-Markovian vacuum decay in cosmology in view of the possible
decoherence of the metastable quantum state.Comment: 10 pages, RevTeX4, 1 figure included. Clarification of approximation
used, conclusions weakene
A volume-weighted measure for eternal inflation
I propose a new volume-weighted probability measure for cosmological
"multiverse" scenarios involving eternal inflation. The "reheating-volume (RV)
cutoff" calculates the distribution of observable quantities on a portion of
the reheating hypersurface that is conditioned to be finite. The RV measure is
gauge-invariant, does not suffer from the "youngness paradox," and is
independent of initial conditions at the beginning of inflation. In slow-roll
inflationary models with a scalar inflaton, the RV-regulated probability
distributions can be obtained by solving nonlinear diffusion equations. I
discuss possible applications of the new measure to "landscape" scenarios with
bubble nucleation. As an illustration, I compute the predictions of the RV
measure in a simple toy landscape.Comment: Version accepted for publication in Phys.Re
Attractor scenarios and superluminal signals in k-essence cosmology
Cosmological scenarios with k-essence are invoked in order to explain the
observed late-time acceleration of the universe. These scenarios avoid the need
for fine-tuned initial conditions (the "coincidence problem") because of the
attractor-like dynamics of the k-essence field \phi. It was recently shown that
all k-essence scenarios with Lagrangians p=L(X)/\phi^2, necessarily involve an
epoch where perturbations of \phi propagate faster than light (the "no-go
theorem"). We carry out a comprehensive study of attractor-like cosmological
solutions ("trackers") involving a k-essence scalar field \phi and another
matter component. The result of this study is a complete classification of
k-essence Lagrangians that admit asymptotically stable tracking solutions,
among all Lagrangians of the form p=K(\phi)L(X) . Using this classification, we
select the class of models that describe the late-time acceleration and avoid
the coincidence problem through the tracking mechanism. An analogous "no-go
theorem" still holds for this class of models, indicating the existence of a
superluminal epoch. In the context of k-essence cosmology, the superluminal
epoch does not lead to causality violations. We discuss the implications of
superluminal signal propagation for possible causality violations in
Lorentz-invariant field theories.Comment: 27 pages, RevTeX4. Minor cosmetic changes, references adde
Self-reproduction in k-inflation
We study cosmological self-reproduction in models of inflation driven by a
scalar field with a noncanonical kinetic term (-inflation). We
develop a general criterion for the existence of attractors and establish
conditions selecting a class of -inflation models that admit a unique
attractor solution. We then consider quantum fluctuations on the attractor
background. We show that the correlation length of the fluctuations is of order
, where is the speed of sound. By computing the magnitude
of field fluctuations, we determine the coefficients of Fokker-Planck equations
describing the probability distribution of the spatially averaged field .
The field fluctuations are generally large in the inflationary attractor
regime; hence, eternal self-reproduction is a generic feature of -inflation.
This is established more formally by demonstrating the existence of stationary
solutions of the relevant FP equations. We also show that there exists a
(model-dependent) range within which large
fluctuations are likely to drive the field towards the upper boundary
, where the semiclassical consideration breaks down. An exit
from inflation into reheating without reaching will occur almost
surely (with probability 1) only if the initial value of is below
. In this way, strong self-reproduction effects constrain models of
-inflation.Comment: RevTeX 4, 17 pages, 1 figur
Reheating-volume measure for random-walk inflation
The recently proposed "reheating-volume" (RV) measure promises to solve the
long-standing problem of extracting probabilistic predictions from cosmological
"multiverse" scenarios involving eternal inflation. I give a detailed
description of the new measure and its applications to generic models of
eternal inflation of random-walk type. For those models I derive a general
formula for RV-regulated probability distributions that is suitable for
numerical computations. I show that the results of the RV cutoff in random-walk
type models are always gauge-invariant and independent of the initial
conditions at the beginning of inflation. In a toy model where equal-time
cutoffs lead to the "youngness paradox," the RV cutoff yields unbiased results
that are distinct from previously proposed measures.Comment: Figure 1 updated, version accepted for publication in Phys.Rev.