82 research outputs found
Cubic Halo Bias in Eulerian and Lagrangian Space
Predictions of the next-to-leading order, i.e. one-loop, halo power spectra
depend on local and non-local bias parameters up to cubic order. The linear
bias parameter can be estimated from the large scale limit of the halo-matter
power spectrum, and the second order bias parameters from the large scale,
tree-level, bispectrum. Cubic operators would naturally be quantified using the
tree-level trispectrum. As the latter is computationally expensive, we extent
the quadratic field method proposed in Schmittfull et al. 2014 to cubic fields
in order to estimate cubic bias parameters. We cross-correlate a basis set of
cubic bias operators with the halo field and express the result in terms of the
cross-spectra of these operators in order to cancel cosmic variance. We obtain
significant detections of local and non-local cubic bias parameters, which are
partially in tension with predictions based on local Lagrangian bias schemes.
We directly measure the Lagrangian bias parameters of the protohaloes
associated with our halo sample and clearly detect a non-local quadratic term
in Lagrangian space. We do not find a clear detection of non-local cubic
Lagrangian terms for low mass bins, but there is some mild evidence for their
presence for the highest mass bin. While the method presented here focuses on
cubic bias parameters, the approach could also be applied to quantifications of
cubic primordial non-Gaussianity.Comment: 37 pages, 16 figures, 4 tables; figures 14 and 15 are slightly
changed compare to the previous version; comments welcom
On the reach of perturbative descriptions for dark matter displacement fields
We study Lagrangian Perturbation Theory (LPT) and its regularization in the
Effective Field Theory (EFT) approach. We evaluate the LPT displacement with
the same phases as a corresponding -body simulation, which allows us to
compare perturbation theory to the non-linear simulation with significantly
reduced cosmic variance, and provides a more stringent test than simply
comparing power spectra. We reliably detect a non-vanishing leading order EFT
coefficient and a stochastic displacement term, uncorrelated with the LPT
terms. This stochastic term is expected in the EFT framework, and, to the best
of our understanding, is not an artifact of numerical errors or transients in
our simulations. This term constitutes a limit to the accuracy of perturbative
descriptions of the displacement field and its phases, corresponding to a
error on the non-linear power spectrum at /Mpc at . Predicting
the displacement power spectrum to higher accuracy or larger wavenumbers thus
requires a model for the stochastic displacement.Comment: 48 pages, 29 figures, comments welcom
Iterative initial condition reconstruction
Motivated by recent developments in perturbative calculations of the
nonlinear evolution of large-scale structure, we present an iterative algorithm
to reconstruct the initial conditions in a given volume starting from the dark
matter distribution in real space. In our algorithm, objects are first moved
back iteratively along estimated potential gradients, with a progressively
reduced smoothing scale, until a nearly uniform catalog is obtained. The linear
initial density is then estimated as the divergence of the cumulative
displacement, with an optional second-order correction. This algorithm should
undo nonlinear effects up to one-loop order, including the higher-order
infrared resummation piece. We test the method using dark matter simulations in
real space. At redshift , we find that after eight iterations the
reconstructed density is more than correlated with the initial density
at . The reconstruction also reduces the power
in the difference between reconstructed and initial fields by more than 2
orders of magnitude at , and it extends the
range of scales where the full broadband shape of the power spectrum matches
linear theory by a factor of 2-3. As a specific application, we consider
measurements of the baryonic acoustic oscillation (BAO) scale that can be
improved by reducing the degradation effects of large-scale flows. In our
idealized dark matter simulations, the method improves the BAO signal-to-noise
ratio by a factor of 2.7 at and by a factor of 2.5 at , improving
standard BAO reconstruction by at and at , and
matching the optimal BAO signal and signal-to-noise ratio of the linear density
in the same volume. For BAO, the iterative nature of the reconstruction is the
most important aspect.Comment: 26 pages, 14 figures, published version. Code available at
https://github.com/mschmittfull/iterre
On the reach of perturbative methods for dark matter density fields
We study the mapping from Lagrangian to Eulerian space in the context of the
Effective Field Theory (EFT) of Large Scale Structure. We compute Lagrangian
displacements with Lagrangian Perturbation Theory (LPT) and perform the full
non-perturbative transformation from displacement to density. When expanded up
to a given order, this transformation reproduces the standard Eulerian
Perturbation Theory (SPT) at the same order. However, the full transformation
from displacement to density also includes higher order terms. These terms
explicitly resum long wavelength motions, thus making the resulting density
field better correlated with the true non-linear density field. As a result,
the regime of validity of this approach is expected to extend that of the
Eulerian EFT, and match that of the IR-resummed Eulerian EFT. This approach
thus effectively enables a test of the IR-resummed EFT at the field level. We
estimate the size of stochastic, non-perturbative contributions to the matter
density power spectrum. We find that in our highest order calculation, at
redshift z=0 the power spectrum of the density field is reproduced with an
accuracy of 1 % (10 %) up to k=0.25 h/Mpc (k=0.46 h/Mpc). We believe that the
dominant source of the remaining error is the stochastic contribution.
Unfortunately, on these scales the stochastic term does not yet scale as
as it does in the very low-k regime. Thus, modeling this contribution might be
challenging.Comment: 22 pages, 10 figure
Lagrangian perturbation theory at one loop order: successes, failures, and improvements
We apply the convolved Lagrangian perturbation theory (CLPT) formalism, in
which one can express the matter density power spectrum in terms of integrals
over a function of cumulants of the displacement field, allowing for a
resummation of the terms, to evaluate the full one loop power spectrum. We keep
the cumulants up to third order, extending the Zel'dovich approximation and
providing the power spectrum analogous to the calculations recently performed
for the correlation function. We compare the results to the N-body simulations
and to the Lagrangian perturbation simulations up to the second order. We find
that the analytic calculations are in a good agreement with the LPT
simulations, but when compared to full N-body simulations, we find that while
one loop calculations improve upon the Zel'dovich approximation in the power
spectrum, they still significantly lack power. As found previously in the
correlation function one loop CLPT improves slightly against Zel'dovich above
30Mpc/h, but is actually worse than Zel'dovich below that. We investigate the
deficiencies of the CLPT approach and argue that main problem of CLPT is its
inability to trap particles inside dark matter halos, which leads to an
overestimate of the small scale power of the displacement field and to an
underestimate of the small scale power from one halo term effects. We model
this using the displacement field damped at a nonlinear scale (CLPTs). To
explore this in more detail we decompose the power spectrum and correlation
function into three additive components: Zel'dovich, residual BAO wiggle, and
residual broad band. One loop CLPT predicts small modifications to BAO wiggles
that are enhanced in CLPTs, with up to 5\% corrections to correlation function
around BAO scale.Comment: 19 pages, 8 figure
Velocity bias in the distribution of dark matter halos
The standard formalism for the co-evolution of halos and dark matter predicts
that any initial halo velocity bias rapidly decays to zero. We argue that, when
the purpose is to compute statistics like power spectra etc., the coupling in
the momentum conservation equation for the biased tracers must be modified. Our
new formulation predicts the constancy in time of any statistical halo velocity
bias present in the initial conditions, in agreement with peak theory. We test
this prediction by studying the evolution of a conserved halo population in
N-body simulations. We establish that the initial simulated halo density and
velocity statistics show distinct features of the peak model and, thus, deviate
from the simple local Lagrangian bias. We demonstrate, for the first time, that
the time evolution of their velocity is in tension with the rapid decay
expected in the standard approach.Comment: 6+ pages, extended to match published version, conclusions unchange
Near optimal bispectrum estimators for large-scale structure
Clustering of large-scale structure provides significant cosmological
information through the power spectrum of density perturbations. Additional
information can be gained from higher-order statistics like the bispectrum,
especially to break the degeneracy between the linear halo bias and the
amplitude of fluctuations . We propose new simple, computationally
inexpensive bispectrum statistics that are near optimal for the specific
applications like bias determination. Corresponding to the Legendre
decomposition of nonlinear halo bias and gravitational coupling at second
order, these statistics are given by the cross-spectra of the density with
three quadratic fields: the squared density, a tidal term, and a shift term.
For halos and galaxies the first two have associated nonlinear bias terms
and , respectively, while the shift term has none in the absence of
velocity bias (valid in the limit). Thus the linear bias
is best determined by the shift cross-spectrum, while the squared density
and tidal cross-spectra mostly tighten constraints on and once
is known. Since the form of the cross-spectra is derived from optimal
maximum-likelihood estimation, they contain the full bispectrum information on
bias parameters. Perturbative analytical predictions for their expectation
values and covariances agree with simulations on large scales, at with Gaussian
smoothing, for matter-matter-matter, and matter-matter-halo combinations. For
halo-halo-halo cross-spectra the model also needs to include corrections to the
Poisson stochasticity.Comment: 22+6 pages, 11 figures, included minor text improvements to match
published versio
The Effective Field Theory of Large Scale Structure at Two Loops: the apparent scale dependence of the speed of sound
We study the Effective Field Theory of Large Scale Structure for cosmic
density and momentum fields. We show that the finite part of the two-loop
calculation and its counterterms introduce an apparent scale dependence for the
leading order parameter of the EFT starting at k=0.1 h/Mpc.
These terms limit the range over which one can trust the one-loop EFT
calculation at the 1 % level to k<0.1 h/Mpc at redshift z=0. We construct a
well motivated one parameter ansatz to fix the relative size of the one- and
two-loop counterterms using their high-k sensitivity. Although this one
parameter model is a very restrictive choice for the counterterms, it explains
the apparent scale dependence of seen in simulations. It is also
able to capture the scale dependence of the density power spectrum up to
k 0.3 h/Mpc at the 1 % level at redshift . Considering a simple
scheme for the resummation of large scale motions, we find that the two loop
calculation reduces the need for this IR-resummation at k<0.2 h/Mpc. Finally,
we extend our calculation to momentum statistics and show that the same one
parameter model can also describe density-momentum and momentum-momentum
statistics.Comment: 22 pages, 13 figures, fixed typos, results unchanged, published
versio
The Bispectrum in the Effective Field Theory of Large Scale Structure
We study the bispectrum in the Effective Field Theory of Large Scale
Structure, consistently accounting for the effects of short-scale dynamics. We
begin by proving that, as long as the theory is perturbative, it can be
formulated to arbitrary order using only operators that are local in time. We
then derive all the new operators required to cancel the UV-divergences and
obtain a physically meaningful prediction for the one-loop bispectrum. In
addition to new, subleading stochastic noises and the viscosity term needed for
the one-loop power spectrum, we find three new effective operators. The three
new parameters can be constrained by comparing with N-body simulations. The
best fit is precisely what is suggested by the structure of UV-divergences,
hence justifying a formula for the EFTofLSS bispectrum whose only fitting
parameter is already fixed by the power spectrum. This result predicts the
bispectrum of N-body simulations up to
at , an improvement by nearly a factor of two as compared to one-loop
standard perturbation theory.Comment: 63 pages, 18 figures, as published in JCA
Linear response to long wavelength fluctuations using curvature simulations
We study the local response to long wavelength fluctuations in cosmological
-body simulations, focusing on the matter and halo power spectra, halo
abundance and non-linear transformations of the density field. The long
wavelength mode is implemented using an effective curved cosmology and a
mapping of time and distances. The method provides an alternative, most
probably more precise, way to measure the isotropic halo biases. Limiting
ourselves to the linear case, we find generally good agreement between the
biases obtained from the curvature method and the traditional power spectrum
method at the level of a few percent. We also study the response of halo counts
to changes in the variance of the field and find that the slope of the relation
between the responses to density and variance differs from the naive derivation
assuming a universal mass function by 18%. This has implications for
measurements of the amplitude of local non-Gaussianity using scale dependent
bias. We also analyze the halo power spectrum and halo-dark matter
cross-spectrum response to long wavelength fluctuations and derive second order
halo bias from it, as well as the super-sample variance contribution to the
galaxy power spectrum covariance matrix.Comment: 29 pages, 14 figure
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