63 research outputs found
Classical resolution of singularities in dilaton cosmologies
For models of dilaton-gravity with a possible exponential potential, such as
the tensor-scalar sector of IIA supergravity, we show how cosmological
solutions correspond to trajectories in a 2D Milne space (parametrized by the
dilaton and the scale factor). Cosmological singularities correspond to points
at which a trajectory meets the Milne horizon, but the trajectories can be
smoothly continued through the horizon to an instanton solution of the
Euclidean theory. We find some exact cosmology/instanton solutions that lift to
black holes in one higher dimension. For one such solution, the singularities
of a big crunch to big bang transition mediated by an instanton phase lift to
the black hole and cosmological horizons of de Sitter Schwarzschild spacetimes.Comment: 24 pages, 2 figure
Time-dependent compactification to de Sitter space: a no-go theorem
Abstract: It is known that the Einstein gravitational field equations in D > 4 spacetime dimensions have no time-independent non-singular compactification solutions to de Sitter space if the D-dimensional stress tensor satisfies the Strong Energy Condition (SEC). Here we show, by example, that the SEC alone does not exclude time-dependent non-singular compactifications to de Sitter space, in Einstein conformal frame. However, this possibility is excluded by the combined SEC and Dominant Energy Condition (DEC) because the DEC forces a time-evolution towards a singular D-metric
Cosmological D-instantons and Cyclic Universes
For models of gravity coupled to hyperbolic sigma models, such as the
metric-scalar sector of IIB supergravity, we show how smooth trajectories in
the `augmented target space' connect FLRW cosmologies to non-extremal
D-instantons through a cosmological singularity. In particular, we find closed
cyclic universes that undergo an endless sequence of big-bang to big-crunch
cycles separated by instanton `phases'. We also find `big-bounce' universes in
which a collapsing closed universe bounces off its cosmological singularity to
become an open expanding universe.Comment: 21 pages, 4 figures. v2: minor change
Cosmology as Relativistic Particle Mechanics: From Big Crunch to Big Bang
Cosmology can be viewed as geodesic motion in an appropriate metric on an
`augmented' target space; here we obtain these geodesics from an effective
relativistic particle action. As an application, we find some exact (flat and
curved) cosmologies for models with N scalar fields taking values in a
hyperbolic target space for which the augmented target space is a Milne
universe. The singularities of these cosmologies correspond to points at which
the particle trajectory crosses the Milne horizon, suggesting a novel
resolution of them, which we explore via the Wheeler-deWitt equation.Comment: 17 pages, 3 figures, references and comments adde
Dilaton Domain Walls and Dynamical Systems
Domain wall solutions of -dimensional gravity coupled to a dilaton field
with an exponential potential are shown
to be governed by an autonomous dynamical system, with a transcritical
bifurcation as a function of the parameter when . All
phase-plane trajectories are found exactly for , including
separatrices corresponding to walls that interpolate between and
adS_{d-1} \times\bR, and the exact solution is found for . Janus-type
solutions are interpreted as marginal bound states of these ``separatrix
walls''. All flat domain wall solutions, which are given exactly for any
, are shown to be supersymmetric for some superpotential ,
determined by the solution.Comment: 30 pp, 11 figs, significant revision of original. Minor additional
corrections in version to appear in journa
Cosmology as Geodesic Motion
For gravity coupled to N scalar fields with arbitrary potential V, it is
shown that all flat (homogeneous and isotropic) cosmologies correspond to
geodesics in an (N+1)-dimensional `augmented' target space of Lorentzian
signature (1,N), timelike if V>0, null if V=0 and spacelike if V<0.
Accelerating cosmologies correspond to timelike geodesics that lie within an
`acceleration subcone' of the `lightcone'. Non-flat (k=-1,+1) cosmologies are
shown to evolve as projections of geodesic motion in a space of dimension
(N+2), of signature (1,N+1) for k=-1 and signature (2,N) for k=+1. This
formalism is illustrated by cosmological solutions of models with an
exponential potential, which are comprehensively analysed; the late-time
behviour for other potentials of current interest is deduced by comparison.Comment: 26 pages, 2 figures, journal version with additional reference
From Wave Geometry to Fake Supergravity
The `Wave Geometry' equation of the pre-WWII Hiroshima program is also the
key equation of the current `fake supergravity' program. I review the status of
(fake) supersymmetric domain walls and (fake) pseudo-supersymmetric
cosmologies. An extension of the domain-wall/cosmology correspondence to a
triple correspondence with instantons shows that `pseudo-supersymmetry' has
another interpretation as Euclidean supersymmetry.Comment: 14 pages. Minor Revisions to original. To appear in proceedings of
the 5th International Symposium on Quantum Theory and Symmetries (QTS5),
Vallodolid, July 2007. in version
On d=4,5,6 Vacua with 8 Supercharges
We show how all known N=2, d=4,5,6 maximally supersymmetric vacua (Hpp-waves
and aDSxS solutions) are related through dimensional reduction/oxidation
preserving all the unbroken supersymmetries. In particular we show how the N=2,
d=5 family of vacua (which are the near-horizon geometry of supersymmetric
rotating black holes) interpolates between aDS_2xS^3 and aDS_3xS^2 in parameter
space and how it can be dimensionally reduced to an N=2, d=4 dyonic
Robinson-Bertotti solution with geometry aDS_2xS^2 and oxidized to an N=2, d=6
solution with aDS_3xS^3 geometry (which is the near-horizon of the self-dual
string).Comment: Latex2e, 19 pages, 1 figure. v2: typos corrected, refs. added. v3:
very minor corrections, more refs. added, version to be published in
Classical and Quantum Gravit
Exact solutions of closed string theory
We review explicitly known exact solutions with Minkowski signature in
closed bosonic string theory. Classical string solutions with space-time
interpretation are represented by conformal sigma models. Two large
(intersecting) classes of solutions are described by gauged WZW models and
`chiral null models' (models with conserved chiral null current). The latter
class includes plane-wave type backgrounds (admitting a covariantly constant
null Killing vector) and backgrounds with two null Killing vectors (e.g.,
fundamental string solution). chiral null models describe some exact
solutions with electromagnetic fields, for example, extreme electric
black holes, charged fundamental strings and their generalisations. In
addition, there exists a class of conformal models representing axially
symmetric stationary magnetic flux tube backgrounds (including, in particular,
the dilatonic Melvin solution). In contrast to spherically symmetric chiral
null models for which the corresponding conformal field theory is not known
explicitly, the magnetic flux tube models (together with some non-semisimple
WZW models) are among the first examples of solvable unitary conformal string
models with non-trivial curved space-time interpretation. For these
models one is able to express the quantum hamiltonian in terms of free fields
and to find explicitly the physical spectrum and string partition function.Comment: 50 pages, harvma
Phase Space Analysis of Quintessence Cosmologies with a Double Exponential Potential
We use phase space methods to investigate closed, flat, and open
Friedmann-Robertson-Walker cosmologies with a scalar potential given by the sum
of two exponential terms. The form of the potential is motivated by the
dimensional reduction of M-theory with non-trivial four-form flux on a
maximally symmetric internal space. To describe the asymptotic features of
run-away solutions we introduce the concept of a `quasi fixed point.' We give
the complete classification of solutions according to their late-time behavior
(accelerating, decelerating, crunch) and the number of periods of accelerated
expansion.Comment: 46 pages, 5 figures; v2: minor changes, references added; v3: title
changed, refined classification of solutions, 3 references added, version
which appeared in JCA
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