5 research outputs found
Fast and Slow Coherent Cascades in Anti-de Sitter Spacetime
We study the phase and amplitude dynamics of small perturbations in 3+1
dimensional Anti-de Sitter spacetime using the truncated resonant
approximation, also known as the Two Time Framework (TTF). We analyse the phase
spectrum for different classes of initial data and find that higher frequency
modes turn on with coherently aligned phases. Combining numerical and
analytical results, we conjecture that there is a class of initial conditions
that collapse in infinite slow time and to which the well-studied case of the
two-mode, equal energy initial data belongs. We additionally study
perturbations that collapse in finite time, and find that the energy spectrum
approaches a power law, with the energy per mode scaling approximately as the
inverse first power of the frequency.Comment: 19 pages, multiple figures. v2: version published in CQ
Vacua and correlators in hyperbolic de Sitter space
We study the power - and bi -spectrum of vacuum fluctuations in a hyperbolic
section of de Sitter space, comparing two states of physical interest: the
Bunch-Davies and hyperbolic vacuum. We introduce a one -parameter family of de
Sitter hyperbolic sections and their natural vacua, and identify a limit in
which it reduces to the planar section and the corresponding Bunch -Davies
vacuum state. Selecting the Bunch -Davies vacuum for a massless scalar field
implies a mixed reduced density matrix in a hyperbolic section of de Sitter
space. We stress that in the Bunch -Davies state the hyperbolic de Sitter
-point correlation functions have to match the planar de Sitter -point
correlation functions. The expressions for the planar and hyperbolic Bunch
-Davies correlation functions only appear different because of the
transformation from planar to hyperbolic coordinates. Initial state induced
deviations from the standard inflationary predictions are instead obtained by
considering the pure hyperbolic vacuum, as we verify explicitly by computing
the power - and bi -spectrum. For the bi -spectrum in the hyperbolic vacuum we
find that the corrections as compared to the standard Bunch -Davies result are
not enhanced in specific momentum configurations and strongly suppressed for
momenta large compared to the hyperbolic curvature scale. We close with some
final remarks, in particular regarding the implications of these results for
more realistic inflationary bubble scenarios.Comment: Added references, removed typos, added author, extensions in first
section and conclusions. 34 pages, 4 figure
Position space analysis of the AdS (in)stability problem
We investigate whether arbitrarily small perturbations in global AdS space
are generically unstable and collapse into black holes on the time scale set by
gravitational interactions. We argue that current evidence, combined with our
analysis, strongly suggests that a set of nonzero measure in the space of
initial conditions does not collapse on this time scale. We perform an analysis
in position space to study this puzzle, and our formalism allows us to directly
study the vanishing-amplitude limit. We show that gravitational
self-interaction leads to tidal deformations which are equally likely to focus
or defocus energy, and we sketch the phase diagram accordingly. We also clarify
the connection between gravitational evolution in global AdS and holographic
thermalization.Comment: 40 pages, 12 figures, updated to the version published on JHE