381 research outputs found
Position-dependent power spectrum: a new observable in the large-scale structure
We present a new observable, position-dependent power spectrum, to measure
the large-scale structure bispectrum in the squeezed configuration, where one
wavenumber is much smaller than the other two. The squeezed-limit bispectrum
measures how the small-scale power spectrum is modulated by a long-wavelength
overdensity, which is due to gravitational evolution and possibly inflationary
physics. We divide a survey into small subvolumes, compute the local power
spectrum and the mean overdensity in each subvolume, and measure the
correlation between them. The correlation measures the integral of the
bispectrum, which is dominated by squeezed configurations if the scale of the
local power spectrum is much smaller than the subvolume size. We use the
separate universe approach to model how the small-scale power spectrum is
affected by a long-wavelength overdensity gravitationally. This models the
nonlinearity of the bispectrum better than the perturbation theory approach.
Not only the new observable is easy to interpret, but it sidesteps the
complexity of the full bispectrum estimation as both power spectrum and mean
overdensity are easier to estimate than the full bispectrum. We report on the
first measurement of the position-dependent correlation function from the
SDSS-III BOSS DR10 CMASS sample. We detect the bispectrum of the CMASS sample,
and constrain their nonlinear bias combining with anisotropic clustering and
weak lensing. We finally study the response of the small-scale power spectrum
to 1-3 long-wavelength overdensities. We compare the separate universe approach
to separate universe simulations to unprecedented accuracy. We test the
standard perturbation theory (SPT) hypothesis that the nonlinear n-point
function is fully predicted by the linear power spectrum at the same time. We
find discrepancies on small scales, which suggest that SPT fails even if it is
calculated to all orders.Comment: Ph.D. dissertation; 160 pages, 34 figures, 4 table
The angle-averaged squeezed limit of nonlinear matter N-point functions
We show that in a certain, angle-averaged squeezed limit, the -point
function of matter is related to the response of the matter power spectrum to a
long-wavelength density perturbation,
, with . By performing
N-body simulations with a homogeneous overdensity superimposed on a flat
Friedmann-Robertson-Lema\^itre-Walker (FRLW) universe using the \emph{separate
universe} approach, we obtain measurements of the nonlinear matter power
spectrum response up to , which is equivalent to measuring the fully
nonlinear matter to point function in this squeezed limit. The
sub-percent to few percent accuracy of those measurements is unprecedented. We
then test the hypothesis that nonlinear -point functions at a given time are
a function of the linear power spectrum at that time, which is predicted by
standard perturbation theory (SPT) and its variants that are based on the ideal
pressureless fluid equations. Specifically, we compare the responses computed
from the separate universe simulations and simulations with a rescaled initial
(linear) power spectrum amplitude. We find discrepancies of 10\% at for to point functions at . The
discrepancy occurs at higher wavenumbers at . Thus, SPT and its variants,
carried out to arbitrarily high order, are guaranteed to fail to describe
matter -point functions () around that scale.Comment: 32 pages, 5 figures. Submitted to JCA
Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
The influence of large-scale density fluctuations on structure formation on
small scales is described by the three-point correlation function (bispectrum)
in the so-called "squeezed configurations," in which one wavenumber, say ,
is much smaller than the other two, i.e., . This
bispectrum is generated by non-linear gravitational evolution and possibly also
by inflationary physics. In this paper, we use this fact to show that the
bispectrum in the squeezed configurations can be measured without employing
three-point function estimators. Specifically, we use the "position-dependent
power spectrum," i.e., the power spectrum measured in smaller subvolumes of the
survey (or simulation box), and correlate it with the mean overdensity of the
corresponding subvolume. This correlation directly measures an integral of the
bispectrum dominated by the squeezed configurations. Measuring this correlation
is only slightly more complex than measuring the power spectrum itself, and
sidesteps the considerable complexity of the full bispectrum estimation. We use
cosmological -body simulations of collisionless particles with Gaussian
initial conditions to show that the measured correlation between the
position-dependent power spectrum and the long-wavelength overdensity agrees
with the theoretical expectation. The position-dependent power spectrum thus
provides a new, efficient, and promising way to measure the squeezed-limit
bispectrum from large-scale structure observations such as galaxy redshift
surveys.Comment: 23 pages, 6 figures; dependence on cosmological parameters added;
JCAP accepte
Separate Universe Simulations
The large-scale statistics of observables such as the galaxy density are
chiefly determined by their dependence on the local coarse-grained matter
density. This dependence can be measured directly and efficiently in N-body
simulations by using the fact that a uniform density perturbation with respect
to some fiducial background cosmology is equivalent to modifying the background
and including curvature, i.e., by simulating a "separate universe". We derive
this mapping to fully non-linear order, and provide a step-by-step description
of how to perform and analyse the separate universe simulations. This technique
can be applied to a wide range of observables. As an example, we calculate the
response of the non-linear matter power spectrum to long-wavelength density
perturbations, which corresponds to the angle-averaged squeezed limit of the
matter bispectrum and higher -point functions. Using only a modest
simulation volume, we obtain results with percent-level precision over a wide
range of scales.Comment: 5 pages, 2 figures, submitted to MNRAS. References added, typos
corrected. Added a paragraph on DE perturbation
Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman- forest power spectrum
The squeezed-limit bispectrum, which is generated by nonlinear gravitational
evolution as well as inflationary physics, measures the correlation of three
wavenumbers, in the configuration where one wavenumber is much smaller than the
other two. Since the squeezed-limit bispectrum encodes the impact of a
large-scale fluctuation on the small-scale power spectrum, it can be understood
as how the small-scale power spectrum "responds" to the large-scale
fluctuation. Viewed in this way, the squeezed-limit bispectrum can be
calculated using the response approach even in the cases which do not submit to
perturbative treatment. To illustrate this point, we apply this approach to the
cross-correlation between the large-scale quasar density field and small-scale
Lyman- forest flux power spectrum. In particular, using separate
universe simulations which implement changes in the large-scale density,
velocity gradient, and primordial power spectrum amplitude, we measure how the
Lyman- forest flux power spectrum responds to the local,
long-wavelength quasar overdensity, and equivalently their squeezed-limit
bispectrum. We perform a Fisher forecast for the ability of future experiments
to constrain local non-Gaussianity using the bispectrum of quasars and the
Lyman- forest. Combining with quasar and Lyman- forest power
spectra to constrain the biases, we find that for DESI the expected
constraint is . Ability for DESI to measure
through this channel is limited primarily by the aliasing and
instrumental noise of the Lyman- forest flux power spectrum. The
combination of response approach and separate universe simulations provides a
novel technique to explore the constraints from the squeezed-limit bispectrum
between different observables.Comment: 20 pages, 4 figures; matches JCAP accepted versio
Orderly Spanning Trees with Applications
We introduce and study the {\em orderly spanning trees} of plane graphs. This
algorithmic tool generalizes {\em canonical orderings}, which exist only for
triconnected plane graphs. Although not every plane graph admits an orderly
spanning tree, we provide an algorithm to compute an {\em orderly pair} for any
connected planar graph , consisting of a plane graph of , and an
orderly spanning tree of . We also present several applications of orderly
spanning trees: (1) a new constructive proof for Schnyder's Realizer Theorem,
(2) the first area-optimal 2-visibility drawing of , and (3) the best known
encodings of with O(1)-time query support. All algorithms in this paper run
in linear time.Comment: 25 pages, 7 figures, A preliminary version appeared in Proceedings of
the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001),
Washington D.C., USA, January 7-9, 2001, pp. 506-51
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