6,832 research outputs found
The three dimensional skeleton: tracing the filamentary structure of the universe
The skeleton formalism aims at extracting and quantifying the filamentary
structure of the universe is generalized to 3D density fields; a numerical
method for computating a local approximation of the skeleton is presented and
validated here on Gaussian random fields. This method manages to trace well the
filamentary structure in 3D fields such as given by numerical simulations of
the dark matter distribution on large scales and is insensitive to monotonic
biasing. Two of its characteristics, namely its length and differential length,
are analyzed for Gaussian random fields. Its differential length per unit
normalized density contrast scales like the PDF of the underlying density
contrast times the total length times a quadratic Edgeworth correction
involving the square of the spectral parameter. The total length scales like
the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+
n) where n is the power index of the underlying field. This dependency implies
that the total length can be used to constrain the shape of the underlying
power spectrum, hence the cosmology. Possible applications of the skeleton to
galaxy formation and cosmology are discussed. As an illustration, the
orientation of the spin of dark halos and the orientation of the flow near the
skeleton is computed for dark matter simulations. The flow is laminar along the
filaments, while spins of dark halos within 500 kpc of the skeleton are
preferentially orthogonal to the direction of the flow at a level of 25%.Comment: 17 pages, 11 figures, submitted to MNRA
On Gaussian Random Supergravity
We study the distribution of metastable vacua and the likelihood of slow roll
inflation in high dimensional random landscapes. We consider two examples of
landscapes: a Gaussian random potential and an effective supergravity potential
defined via a Gaussian random superpotential and a trivial K\"ahler potential.
To examine these landscapes we introduce a random matrix model that describes
the correlations between various derivatives and we propose an efficient
algorithm that allows for a numerical study of high dimensional random fields.
Using these novel tools, we find that the vast majority of metastable critical
points in dimensional random supergravities are either approximately
supersymmetric with or supersymmetric. Such
approximately supersymmetric points are dynamical attractors in the landscape
and the probability that a randomly chosen critical point is metastable scales
as . We argue that random supergravities lead to potentially
interesting inflationary dynamics.Comment: 36 pages, 9 figure
The distribution of extremal points of Gaussian scalar fields
We consider the signed density of the extremal points of (two-dimensional)
scalar fields with a Gaussian distribution. We assign a positive unit charge to
the maxima and minima of the function and a negative one to its saddles. At
first, we compute the average density for a field in half-space with Dirichlet
boundary conditions. Then we calculate the charge-charge correlation function
(without boundary). We apply the general results to random waves and random
surfaces. Furthermore, we find a generating functional for the two-point
function. Its Legendre transform is the integral over the scalar curvature of a
4-dimensional Riemannian manifold.Comment: 22 pages, 8 figures, corrected published versio
The Skeleton: Connecting Large Scale Structures to Galaxy Formation
We report on two quantitative, morphological estimators of the filamentary
structure of the Cosmic Web, the so-called global and local skeletons. The
first, based on a global study of the matter density gradient flow, allows us
to study the connectivity between a density peak and its surroundings, with
direct relevance to the anisotropic accretion via cold flows on galactic halos.
From the second, based on a local constraint equation involving the
derivatives of the field, we can derive predictions for powerful statistics,
such as the differential length and the relative saddle to extrema counts of
the Cosmic web as a function of density threshold (with application to
percolation of structures and connectivity), as well as a theoretical framework
to study their cosmic evolution through the onset of gravity-induced
non-linearities.Comment: 10 pages, 8 figures; proceedings of the "Invisible Universe" 200
Non-Gaussian Minkowski functionals & extrema counts in redshift space
In the context of upcoming large-scale structure surveys such as Euclid, it
is of prime importance to quantify the effect of peculiar velocities on
geometric probes. Hence the formalism to compute in redshift space the
geometrical and topological one-point statistics of mildly non-Gaussian 2D and
3D cosmic fields is developed. Leveraging the partial isotropy of the target
statistics, the Gram-Charlier expansion of the joint probability distribution
of the field and its derivatives is reformulated in terms of the corresponding
anisotropic variables. In particular, the cosmic non-linear evolution of the
Minkowski functionals, together with the statistics of extrema are investigated
in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian
redshift distortion correction is estimated for these geometric probes. In 3D,
gravitational perturbation theory is implemented in redshift space to predict
the cosmic evolution of all relevant Gram-Charlier coefficients. Applications
to the estimation of the cosmic parameters sigma(z) and beta=f/b1 from upcoming
surveys is discussed. Such statistics are of interest for anisotropic fields
beyond cosmology.Comment: 35 pages, 15 figures, matches version published in MNRAS with a typo
corrected in eq A1
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