7 research outputs found
On rolling, tunneling and decaying in some large N vector models
Various aspects of time-dependent processes are studied within the large N
approximation of O(N) vector models in three dimensions. These include the
rolling of fields, the tunneling and decay of vacua. We present an exact
solution for the quantum conformal case and find a solution for more general
potentials when the total change of the value of the field is small.
Characteristic times are found to be shorter when the time dependence of the
field is taken into account in constructing the exact large N effective
potentials. We show that the different approximations yield the same answers in
the regions of the overlap of the validity. A numerical solution of this
potential reveals a tunneling in which the bubble that separates the true
vacuum from the false one is thick
Quantum evolution across singularities: the case of geometrical resolutions
We continue the study of time-dependent Hamiltonians with an isolated
singularity in their time dependence, describing propagation on singular
space-times. In previous work, two of us have proposed a "minimal subtraction"
prescription for the simplest class of such systems, involving Hamiltonians
with only one singular term. On the other hand, Hamiltonians corresponding to
geometrical resolutions of space-time tend to involve multiple operator
structures (multiple types of dependence on the canonical variables) in an
essential way.
We consider some of the general properties of such (near-)singular
Hamiltonian systems, and further specialize to the case of a free scalar field
on a two-parameter generalization of the null-brane space-time. We find that
the singular limit of free scalar field evolution exists for a discrete subset
of the possible values of the two parameters. The coordinates we introduce
reveal a peculiar reflection property of scalar field propagation on the
generalized (as well as the original) null-brane. We further present a simple
family of pp-wave geometries whose singular limit is a light-like hyperplane
(discontinuously) reflecting the positions of particles as they pass through
it.Comment: 25 pages, 1 figur
Challenges for String Cosmology
We critically assess the twin prospects of describing the observed universe
in string theory, and using cosmological experiments to probe string theory.
For the purposes of this short review, we focus on the limitations imposed by
our incomplete understanding of string theory. After presenting an array of
significant obstacles, we indicate a few areas that may admit theoretical
progress in the near future.Comment: 18 pages; contribution to a focus issue on string cosmology for
Classical and Quantum Gravit
Cosmic Bounces and Cyclic Universes
Cosmological models involving a bounce from a contracting to an expanding
universe can address the standard cosmological puzzles and generate
"primordial" density perturbations without the need for inflation. Some such
models, in particular the ekpyrotic and cyclic models that we focus on, fit
rather naturally into string theory. We discuss a number of topics related to
these models: the reasoning that leads to the ekpyrotic phase, the predictions
for upcoming observations, the differences between singular and non-singular
models of the bounce as well as the predictive and explanatory power offered by
these models.Comment: 28 pages. Contribution to the CQG focus issue on String Cosmolog
From Big Crunch to Big Bang with AdS/CFT
4 pages; discussion of backreaction improved, incorporating dependence on width of initial wavepacketThe AdS/CFT correspondence is used to describe five-dimensional cosmology with a big crunch singularity in terms of super-Yang-Mills theory on R times S^3 deformed by a potential which is unbounded below. Classically, a Higgs field in the dual theory rolls to infinity in finite time. But since the S^3 is finite, the unstable mode spreads quantum mechanically and the singularity is resolved when self-adjoint boundary conditions are imposed at infinity. Asymptotic freedom of the coupling governing the instability gives us computational control and the quantum spreading provides a UV cutoff on particle creation. The bulk interpretation of our result is a quantum transition from a big crunch to a big bang. An intriguing consequence of the near scale-invariance of the dual theory is that a nearly scale-invariant spectrum of stress-energy perturbations is automatically generated in the boundary theory. We comment on implications for more realistic cosmologies