335 research outputs found
Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
The most direct probe of non-Gaussian initial conditions has come from
bispectrum measurements of temperature fluctuations in the Cosmic Microwave
Background and of the matter and galaxy distribution at large scales. Such
bispectrum estimators are expected to continue to provide the best constraints
on the non-Gaussian parameters in future observations. We review and compare
the theoretical and observational problems, current results and future
prospects for the detection of a non-vanishing primordial component in the
bispectrum of the Cosmic Microwave Background and large-scale structure, and
the relation to specific predictions from different inflationary models.Comment: 82 pages, 23 figures; Invited Review for the special issue "Testing
the Gaussianity and Statistical Isotropy of the Universe" for Advances in
Astronom
Rapid Separable Analysis of Higher Order Correlators in Large Scale Structure
We present an efficient separable approach to the estimation and
reconstruction of the bispectrum and the trispectrum from observational (or
simulated) large scale structure data. This is developed from general CMB
(poly-)spectra methods which exploit the fact that the bispectrum and
trispectrum in the literature can be represented by a separable mode expansion
which converges rapidly (with terms). With an
effective grid resolution (number of particles/grid points
), we present a bispectrum estimator which requires only
operations, along with a
corresponding method for direct bispectrum reconstruction. This method is
extended to the trispectrum revealing an estimator which requires only operations. The complexity in
calculating the trispectrum in this method is now involved in the original
decomposition and orthogonalisation process which need only be performed once
for each model. However, for non-diagonal trispectra these processes present
little extra difficulty and may be performed in
operations. A discussion of how the methodology may be applied to the
quadspectrum is also given. An efficient algorithm for the generation of
arbitrary nonGaussian initial conditions for use in N-body codes using this
separable approach is described. This prescription allows for the production of
nonGaussian initial conditions for arbitrary bispectra and trispectra. A brief
outline of the key issues involved in parameter estimation, particularly in the
non-linear regime, is also given
Cosmology with phase statistics: parameter forecasts and detectability of BAO
We consider an alternative to conventional three-point statistics such as the bispectrum, which is purely based on the Fourier phases of the density field: the line correlation function. This statistic directly probes the non-linear clustering regime and contains information highly complementary to that contained in the power spectrum. In this work, we determine, for the first time, its potential to constrain cosmological parameters and detect baryon acoustic oscillations (hereafter BAOs). We show how to compute the line correlation function for a discrete sampled set of tracers that follow a local Lagrangian biasing scheme and demonstrate how it breaks the degeneracy between the amplitude of density fluctuations and the bias parameters of the model.We then derive analytic expressions for its covariance and show that it can be written as a sum of a Gaussian piece plus non-Gaussian corrections.We compare our predictions with a large ensemble of N-body simulations and confirm that BAOs do indeed modulate the signal of the line correlation function for scales 50–100 h−1Mpc and that the characteristic S-shape feature would be detectable in upcoming Stage IV surveys at the level of ∼4σ.We then focus on the cosmological information content and compute Fisher forecasts for an idealized Stage III galaxy redshift survey of volume V ∼ 10 h−3 Gpc3 and out to z = 1. We show that combining the line correlation function with the galaxy power spectrum and a Planck-like microwave background survey yields improvements up to a factor of 2 for parameters such as σ8, b1 and b2, compared with using only the two-point information alone
The matter bispectrum in N-body simulations with non-Gaussian initial conditions
We present measurements of the dark matter bispectrum in N-body simulations with non-Gaussian initial conditions of the local kind for a large variety of triangular configurations and compare them with predictions from Eulerian perturbation theory up to one-loop corrections. We find that the effects of primordial non-Gaussianity at large scales, when compared to perturbation theory, are well described by the initial component of the matter bispectrum, linearly extrapolated at the redshift of interest. In addition, we find that for fNL= 100, the non-linear corrections due to non-Gaussian initial conditions are of the order of ∼3-4 per cent for generic triangles and up to ∼20 per cent for squeezed configurations, at any redshift. We show that the predictions of perturbation theory at the tree level fail to describe the simulation results at redshift z= 0 at scales corresponding to k∼ 0.02-0.08 h Mpc−1, depending on the triangle, while one-loop corrections can significantly extend their validity to smaller scales. At higher redshift, one-loop perturbation theory indeed provides quite accurate predictions, particularly with respect to the relative correction due to primordial non-Gaussianit
The Matter Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
We present measurements of the dark matter bispectrum in N-body simulations
with non-Gaussian initial conditions of the local kind for a large variety of
triangular configurations and compare them with predictions from Eulerian
Perturbation Theory up to one-loop corrections. We find that the effects of
primordial non-Gaussianity at large scales, when compared to Perturbation
Theory, are well described by the initial component of the matter bispectrum,
linearly extrapolated at the redshift of interest. In addition, we find that,
for f_NL=100, the nonlinear corrections due to non-Gaussian initial conditions
are of the order of ~3, 4% for generic triangles up to ~20% for squeezed
configurations, at any redshift. We show that the predictions of Perturbation
Theory at tree-level fail to describe the simulation results at redshift z=0
already at scales corresponding to k ~ 0.02 - 0.08 h/Mpc, depending on the
triangle, while one-loop corrections can significantly extend their validity to
smaller scales. At higher redshift, one-loop Perturbation Theory provides
indeed quite accurate predictions, particularly with respect to the relative
correction due to primordial non-Gaussianity.Comment: 17 pages, 7 figures. Revised to match journal version with updated
references. Accepted for publication in MNRAS
Galaxy-CMB and galaxy-galaxy lensing on large scales: sensitivity to primordial non-Gaussianity
A convincing detection of primordial non-Gaussianity in the local form of the
bispectrum, whose amplitude is given by the fNL parameter, offers a powerful
test of inflation. In this paper we calculate the modification of two-point
cross-correlation statistics of weak lensing - galaxy-galaxy lensing and
galaxy-Cosmic Microwave Background (CMB) cross-correlation - due to fNL. We
derive and calculate the covariance matrix of galaxy-galaxy lensing including
cosmic variance terms. We focus on large scales (l<100) for which the shape
noise of the shear measurement becomes irrelevant and cosmic variance dominates
the error budget. For a modest degree of non-Gaussianity, fNL=+/-50,
modifications of the galaxy-galaxy lensing signal at the 10% level are seen on
scales R~300 Mpc, and grow rapidly toward larger scales as \propto R^2. We also
see a clear signature of the baryonic acoustic oscillation feature in the
matter power spectrum at ~150 Mpc, which can be measured by next-generation
lensing experiments. In addition we can probe the local-form primordial
non-Gaussianity in the galaxy-CMB lensing signal by correlating the lensing
potential reconstructed from CMB with high-z galaxies. For example, for
fNL=+/-50, we find that the galaxy-CMB lensing cross power spectrum is modified
by ~10% at l~40, and by a factor of two at l~10, for a population of galaxies
at z=2 with a bias of 2. The effect is greater for more highly biased
populations at larger z; thus, high-z galaxy surveys cross-correlated with CMB
offer a yet another probe of primordial non-Gaussianity.Comment: 21 pages, 30 figure
Cosmology and the Bispectrum
The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in 50 Mpc/h spheres, and remarkably little is known about the information encoded in it about cosmological parameters beyond the power spectrum. In this work we present an attempt to bridge this gap by studying the bispectrum, paying particular attention to a joint analysis with the power spectrum and their combination with CMB data. We address the covariance properties of the power spectrum and bispectrum including the effects of beat coupling that lead to interesting cross-correlations, and discuss how baryon acoustic oscillations break degeneracies. We show that the bispectrum has significant information on cosmological parameters well beyond its power in constraining galaxy bias, and when combined with the power spectrum is more complementary than combining power spectra of different samples of galaxies, since non-Gaussianity provides a somewhat different direction in parameter space. In the framework of flat cosmological models we show that most of the improvement of adding bispectrum information corresponds to parameters related to the amplitude and effective spectral index of perturbations, which can be improved by almost a factor of two. Moreover, we demonstrate that the expected statistical uncertainties in sigma8 of a few percent are robust to relaxing the dark energy beyond a cosmological constant
The Halo Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
We present measurements of the bispectrum of dark matter halos in numerical
simulations with non-Gaussian initial conditions of the local type. We show, in
the first place, that the overall effect of primordial non-Gaussianity on the
halo bispectrum is larger than on the halo power spectrum when all measurable
configurations are taken into account. We then compare our measurements with a
tree-level perturbative prediction finding good agreement at large scale when
the constant Gaussian bias parameter, both linear and quadratic, and their
constant non-Gaussian corrections are fitted for. The best-fit values of the
Gaussian bias factors and their non-Gaussian, scale-independent corrections are
in qualitative agreement with the peak-background split expectations. In
particular, we show that the effect of non-Gaussian initial conditions on
squeezed configurations is fairly large (up to 30% for f_NL=100 at redshift
z=0.5) and results from contributions of similar amplitude induced by the
initial matter bispectrum, scale-dependent bias corrections as well as from
nonlinear matter bispectrum corrections. We show, in addition, that effects at
second order in f_NL are irrelevant for the range of values allowed by CMB and
galaxy power spectrum measurements, at least on the scales probed by our
simulations. Finally, we present a Fisher matrix analysis to assess the
possibility of constraining primordial non-Gaussianity with future measurements
of the galaxy bispectrum. We find that a survey with a volume of about 10 cubic
Gpc at mean redshift z ~ 1 could provide an error on f_NL of the order of a
few. This shows the relevance of a joint analysis of galaxy power spectrum and
bispectrum in future redshift surveys.Comment: 37 pages, 15 figure
Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background
Quasi-single field inflation predicts a peculiar momentum dependence in the
squeezed limit of the primordial bispectrum which smoothly interpolates between
the local and equilateral models. This dependence is directly related to the
mass of the isocurvatons in the theory which is determined by the
supersymmetry. Therefore, in the event of detection of a non-zero primordial
bispectrum, additional constraints on the parameter controlling the
momentum-dependence in the squeezed limit becomes an important question. We
explore the effects of these non-Gaussian initial conditions on large-scale
structure and the cosmic microwave background, with particular attention to the
galaxy power spectrum at large scales and scale-dependence corrections to
galaxy bias. We determine the simultaneous constraints on the two parameters
describing the QSF bispectrum that we can expect from upcoming large-scale
structure and cosmic microwave background observations. We find that for
relatively large values of the non-Gaussian amplitude parameters, but still
well within current uncertainties, galaxy power spectrum measurements will be
able to distinguish the QSF scenario from the predictions of the local model. A
CMB likelihood analysis, as well as Fisher matrix analysis, shows that there is
also a range of parameter values for which Planck data may be able distinguish
between QSF models and the related local and equilateral shapes. Given the
different observational weightings of the CMB and LSS results, degeneracies can
be significantly reduced in a joint analysis.Comment: 27 pages, 14 figure
Galaxy Bias and Halo-Occupation Numbers from Large-Scale Clustering
We show that current surveys have at least as much signal to noise in
higher-order statistics as in the power spectrum at weakly nonlinear scales. We
discuss how one can use this information to determine the mean of the galaxy
halo occupation distribution (HOD) using only large-scale information, through
galaxy bias parameters determined from the galaxy bispectrum and trispectrum.
After introducing an averaged, reasonably fast to evaluate, trispectrum
estimator, we show that the expected errors on linear and quadratic bias
parameters can be reduced by at least 20-40%. Also, the inclusion of the
trispectrum information, which is sensitive to "three-dimensionality" of
structures, helps significantly in constraining the mass dependence of the HOD
mean. Our approach depends only on adequate modeling of the abundance and
large-scale clustering of halos and thus is independent of details of how
galaxies are distributed within halos. This provides a consistency check on the
traditional approach of using two-point statistics down to small scales, which
necessarily makes more assumptions. We present a detailed forecast of how well
our approach can be carried out in the case of the SDSS.Comment: 16 pages, 9 figure
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