3,154 research outputs found
Large-Scale Structure and Gravitational Waves III: Tidal Effects
The leading locally observable effect of a long-wavelength metric
perturbation corresponds to a tidal field. We derive the tidal field induced by
scalar, vector, and tensor perturbations, and use second order perturbation
theory to calculate the effect on the locally measured small-scale density
fluctuations. For sub-horizon scalar perturbations, we recover the standard
perturbation theory result ( kernel). For tensor modes of wavenumber
, we find that effects persist for , i.e. even long after
the gravitational wave has entered the horizon and redshifted away, i.e. it is
a "fossil" effect. We then use these results, combined with the "ruler
perturbations" of arXiv:1204.3625, to predict the observed distortion of the
small-scale matter correlation function induced by a long-wavelength tensor
mode. We also estimate the observed signal in the B mode of the cosmic shear
from a gravitational wave background, including both tidal (intrinsic
alignment) and projection (lensing) effects. The non-vanishing tidal effect in
the limit significantly increases the intrinsic alignment
contribution to shear B modes, especially at low redshifts .Comment: 24 pages, 4 figures; v2: added references and corrected typos; v3:
corrected factor of 2 in Sec. VI and intrinsic alignment matching,
conclusions unchange
How Gaussian can our Universe be?
Gravity is a non-linear theory, and hence, barring cancellations, the initial
super-horizon perturbations produced by inflation must contain some minimum
amount of mode coupling, or primordial non-Gaussianity. In single-field
slow-roll models, where this lower bound is saturated, non-Gaussianity is
controlled by two observables: the tensor-to-scalar ratio, which is uncertain
by more than fifty orders of magnitude; and the scalar spectral index, or tilt,
which is relatively well measured. It is well known that to leading and
next-to-leading order in derivatives, the contributions proportional to the
tilt disappear from any local observable, and suspicion has been raised that
this might happen to all orders, allowing for an arbitrarily low amount of
primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show
explicitly that this is not the case. Instead, a contribution of order the tilt
appears in local observables. In summary, the floor of physical primordial
non-Gaussianity in our Universe has a squeezed-limit scaling of
, similar to equilateral and orthogonal shapes, and a
dimensionless amplitude of order .Comment: 26 + 18 pages, 2 figures. References added and minor typos corrected.
Matches published versio
Conformal Fermi Coordinates
Fermi Normal Coordinates (FNC) are a useful frame for isolating the locally
observable, physical effects of a long-wavelength spacetime perturbation. Their
cosmological application, however, is hampered by the fact that they are only
valid on scales much smaller than the horizon. We introduce a generalization
that we call Conformal Fermi Coordinates (CFC). CFC preserve all the advantages
of FNC, but in addition are valid outside the horizon. They allow us to
calculate the coupling of long- and short-wavelength modes on all scales larger
than the sound horizon of the cosmological fluid, starting from the epoch of
inflation until today, by removing the complications of the second order
Einstein equations to a large extent, and eliminating all gauge ambiguities. As
an application, we present a calculation of the effect of long-wavelength
tensor modes on small scale density fluctuations. We recover previous results,
but clarify the physical content of the individual contributions in terms of
locally measurable effects and "projection" terms.Comment: 43 pages, two figures. v2: minor changes, added references, expanded
subsec 3.
On Separate Universes
(abridged version) The separate universe conjecture states that in General
Relativity a density perturbation behaves locally (i.e. on scales much smaller
than the wavelength of the mode) as a separate universe with different
background density and curvature. We prove this conjecture for a spherical
compensated tophat density perturbation of arbitrary amplitude and radius in
CDM. We then use Conformal Fermi Coordinates to generalize this result
to scalar perturbations of arbitrary configuration and scale. In this case, the
separate universe conjecture holds for the isotropic part of the perturbations.
The anisotropic part on the other hand is exactly captured by a tidal field in
the Newtonian form. We show that the separate universe picture is restricted to
scales larger than the sound horizons of all fluid components. We then derive
an expression for the locally measured matter bispectrum induced by a
long-wavelength mode of arbitrary wavelength. We show that nonlinear
gravitational dynamics does not generate observable contributions that scale
like local-type non-Gaussianity , and hence does not
contribute to a scale-dependent galaxy bias on large
scales; rather, the locally measurable long-short mode coupling assumes a form
essentially identical to subhorizon perturbation theory results, once the
long-mode density perturbation is replaced by the synchronous-comoving gauge
density perturbation. Apparent -type contributions arise
through projection effects on photon propagation, which depend on the specific
large-scale structure tracer and observable considered, and are in principle
distinguishable from the local mode coupling induced by gravity. We conclude
that any observation of beyond these projection effects
signals a departure from standard single-clock inflation.Comment: 36 pages and 1 figure. To be submitted to JCAP. Comments are welcome.
Version 2: Abstract improved. Added Section 5.2 to clarity the initial
condition in CFC for single-clock inflatio
Parametric Weighting Functions
This paper provides behavioral foundations for parametric weighting functions under rankdependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by restricting the conditions to subsets of the probability interval, foundations of rank-dependent utility with parametric inverse-S shaped weighting functions are obtained. --Comonotonic independence,probability weighting function,preference foundation,rank-dependent utility
Privacy and Curiosity in Mobile Interactions with Public Displays.
Personal multimedia devices like mobile phones create new needs for larger displays distributed at specific points in the environment to look up information about the current place, playing games or exchanging multimedia data. The technical prerequisites are covered; however, using public displays always exposing information. In this paper we look at these issues from the privacy as well as from the curiosity perspective with several studies showing and confirming users’ reservations against public interactions. Interactive advertisements can exploit this best using specific types of interaction techniques
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