827 research outputs found
Populating the Landscape: A Top Down Approach
We put forward a framework for cosmology that combines the string landscape
with no boundary initial conditions. In this framework, amplitudes for
alternative histories for the universe are calculated with final boundary
conditions only. This leads to a top down approach to cosmology, in which the
histories of the universe depend on the precise question asked. We study the
observational consequences of no boundary initial conditions on the landscape,
and outline a scheme to test the theory. This is illustrated in a simple model
landscape that admits several alternative inflationary histories for the
universe. Only a few of the possible vacua in the landscape will be populated.
We also discuss in what respect the top down approach differs from other
approaches to cosmology in the string landscape, like eternal inflation.Comment: 22 pages, 1 figur
The Physics of 'Now'
The world is four-dimensional according to fundamental physics, governed by
basic laws that operate in a spacetime that has no unique division into space
and time. Yet our subjective experience is divided into present, past, and
future. This paper discusses the origin of this division in terms of simple
models of information gathering and utilizing systems (IGUSes). Past, present,
and future are not properties of four-dimensional spacetime but notions
describing how individual IGUSes process information. Their origin is to be
found in how these IGUSes evolved or were constructed. The past, present, and
future of an IGUS is consistent with the four-dimensional laws of physics and
can be described in four-dimensional terms. The present, for instance, is not a
moment of time in the sense of a spacelike surface in spacetime. Rather there
is a localized notion of present at each point along an IGUS' world line. The
common present of many localized IGUSes is an approximate notion appropriate
when they are sufficiently close to each other and have relative velocities
much less than that of light. But modes of organization that are different from
present, past and future can be imagined that are consistent with the physical
laws. We speculate why the present, past, and future organization might be
favored by evolution and therefore a cognitive universal.Comment: 12 pages, 4 figures, Revtex4, minor correction
The No-Boundary Measure in the Regime of Eternal Inflation
The no-boundary wave function (NBWF) specifies a measure for prediction in
cosmology that selects inflationary histories and remains well behaved for
spatially large or infinite universes. This paper explores the predictions of
the NBWF for linear scalar fluctuations about homogeneous and isotropic
backgrounds in models with a single scalar field moving in a quadratic
potential. We treat both the space-time geometry of the universe and the
observers inhabiting it quantum mechanically. We evaluate top-down
probabilities for local observations that are conditioned on the NBWF and on
part of our data as observers of the universe. For models where the most
probable histories do not have a regime of eternal inflation, the NBWF predicts
homogeneity on large scales, a specific non-Gaussian spectrum of observable
fluctuations, and a small amount of inflation in our past. By contrast, for
models where the dominant histories have a regime of eternal inflation, the
NBWF predicts significant inhomogeneity on scales much larger than the present
horizon, a Gaussian spectrum of observable fluctuations, and a long period of
inflation in our past. The absence or presence of local non-Gaussianity
therefore provides information about the global structure of the universe,
assuming the NBWF.Comment: 29 pages, 8 figure
The No-Boundary Measure of the Universe
We consider the no-boundary proposal for homogeneous isotropic closed
universes with a cosmological constant and a scalar field with a quadratic
potential. In the semi-classical limit, it predicts classical behavior at late
times if the initial scalar field is more than a certain minimum. If the
classical late time histories are extended back, they may be singular or bounce
at a finite radius. The no-boundary proposal provides a probability measure on
the classical solutions which selects inflationary histories but is heavily
biased towards small amounts of inflation. This would not be compatible with
observations. However we argue that the probability for a homogeneous universe
should be multiplied by exp(3N) where N is the number of e-foldings of slow
roll inflation to obtain the probability for what we observe in our past light
cone. This volume weighting is similar to that in eternal inflation. In a
landscape potential, it would predict that the universe would have a large
amount of inflation and that it would start in an approximately de Sitter state
near a saddle-point of the potential. The universe would then have always been
in the semi-classical regime.Comment: 4 pages, revtex4, minor corrections to accord with published versio
Vector Fields in Holographic Cosmology
We extend the holographic formulation of the semiclassical no-boundary wave
function (NBWF) to models with Maxwell vector fields. It is shown that the
familiar saddle points of the NBWF have a representation in which a regular,
Euclidean asymptotic AdS geometry smoothly joins onto a Lorentzian
asymptotically de Sitter universe through a complex transition region. The tree
level probabilities of Lorentzian histories are fully specified by the action
of the AdS region of the saddle points. The scalar and vector matter profiles
in this region are complex from an AdS viewpoint, with universal asymptotic
phases. The dual description of the semiclassical NBWF thus involves complex
deformations of Euclidean CFTs.Comment: 17 pages, 3 fig
No Time Asymmetry from Quantum Mechanics
With CPT-invariant initial conditions that commute with CPT-invariant final
conditions, the respective probabilities (when defined) of a set of histories
and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me
to question whether the asymmetry of the Gell-Mann--Hartle decoherence
functional for ordinary quantum mechanics should be interpreted as an asymmetry
of {\it time} .Comment: 14 pages, Alberta-Thy-11-9
Anti-de Sitter wormhole kink
The metric describing a given finite sector of a four-dimensional
asymptotically anti-de Sitter wormhole can be transformed into the metric of
the time constant sections of a Tangherlini black hole in a five-dimensional
anti-de Sitter spacetime when one allows light cones to tip over on the
hypersurfaces according to the conservation laws of an one-kink. The resulting
kinked metric can be maximally extended, giving then rise to an instantonic
structure on the euclidean continuation of both the Tangherlini time and the
radial coordinate. In the semiclassical regime, this kink is related to the
existence of closed timelike curves.Comment: 10 pages, to appear in IJMP
Universal properties of the near-horizon optical geometry
We make use of the fact that the optical geometry near a static
non-degenerate Killing horizon is asymptotically hyperbolic to investigate
universal features of black hole physics. We show how the Gauss-Bonnet theorem
allows certain lensing scenarios to be ruled in or out. We find rates for the
loss of scalar, vector and fermionic `hair' as objects fall quasi- statically
towards the horizon. In the process we find the Lienard-Wiechert potential for
hyperbolic space and calculate the force between electrons mediated by
neutrinos, extending the flat space result of Feinberg and Sucher. We use the
enhanced conformal symmetry of the Schwarzschild and Reissner-Nordstrom
backgrounds to re-derive the electrostatic field due to a point charge in a
simple fashion
A Closed Contour of Integration in Regge Calculus
The analytic structure of the Regge action on a cone in dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra
Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences
We consider the product of infinitely many copies of a spin-
system. We construct projection operators on the corresponding nonseparable
Hilbert space which measure whether the outcome of an infinite sequence of
measurements has any specified property. In many cases, product
states are eigenstates of the projections, and therefore the result of
measuring the property is determined. Thus we obtain a nonprobabilistic quantum
analogue to the law of large numbers, the randomness property, and all other
familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe
- âŠ