94 research outputs found
RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order
We present a specific prescription for the calculation of cosmological power
spectra, exploited here at two-loop order in perturbation theory (PT), based on
the multi-point propagator expansion. In this approach power spectra are
constructed from the regularized expressions of the propagators that reproduce
both the resummed behavior in the high-k limit and the standard PT results at
low-k. With the help of N-body simulations, we show that such a construction
gives robust and accurate predictions for both the density power spectrum and
the correlation function at percent-level in the weakly non-linear regime. We
then present an algorithm that allows accelerated evaluations of all the
required diagrams by reducing the computational tasks to one-dimensional
integrals. This is achieved by means of pre-computed kernel sets defined for
appropriately chosen fiducial models. The computational time for two-loop
results is then reduced from a few minutes, with the direct method, to a few
seconds with the fast one. The robustness and applicability of this method are
tested against the power spectrum cosmic emulator from which a wide variety of
cosmological models can be explored. The fortran program with which direct and
fast calculations of power spectra can be done, RegPT, is publicly released as
part of this paper.Comment: 28 pages, 15 figure
Non-linear Evolution of Baryon Acoustic Oscillations from Improved Perturbation Theory in Real and Redshift Spaces
We study the non-linear evolution of baryon acoustic oscillations in the
matter power spectrum and correlation function from the improved perturbation
theory (PT). Based on the framework of renormalized PT, we apply the {\it
closure approximation} that truncates the infinite series of loop contributions
at one-loop order, and obtain a closed set of integral equations for power
spectrum and non-linear propagator. The resultant integral expressions keep
important non-perturbative properties which can dramatically improve the
prediction of non-linear power spectrum. Employing the Born approximation, we
then derive the analytic expressions for non-linear power spectrum and the
predictions are made for non-linear evolution of baryon acoustic oscillations
in power spectrum and correlation function. A detailed comparison between
improved PT results and N-body simulations shows that a percent-level agreement
is achieved in a certain range in power spectrum and in a rather wider range in
correlation function. Combining a model of non-linear redshift-space
distortion, we also evaluate the power spectrum and correlation function in
correlation function. In contrast to the results in real space, the agreement
between N-body simulations and improved PT predictions tends to be worse, and a
more elaborate modeling for redshift-space distortion needs to be developed.
Nevertheless, with currently existing model, we find that the prediction of
correlation function has a sufficient accuracy compared with the
cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3
at z>=0.5.Comment: 25 pages, 15 figures, accepted for publication in Phys.Rev.
Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory
We present an improved prescription for matter power spectrum in redshift
space taking a proper account of both the non-linear gravitational clustering
and redshift distortion, which are of particular importance for accurately
modeling baryon acoustic oscillations (BAOs). Contrary to the models of
redshift distortion phenomenologically introduced but frequently used in the
literature, the new model includes the corrections arising from the non-linear
coupling between the density and velocity fields associated with two
competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God
effects. Based on the improved treatment of perturbation theory for
gravitational clustering, we compare our model predictions with monopole and
quadrupole power spectra of N-body simulations, and an excellent agreement is
achieved over the scales of BAOs. Potential impacts on constraining dark energy
and modified gravity from the redshift-space power spectrum are also
investigated based on the Fisher-matrix formalism. We find that the existing
phenomenological models of redshift distortion produce a systematic error on
measurements of the angular diameter distance and Hubble parameter by 1~2%, and
the growth rate parameter by ~5%, which would become non-negligible for future
galaxy surveys. Correctly modeling redshift distortion is thus essential, and
the new prescription of redshift-space power spectrum including the non-linear
corrections can be used as an accurate theoretical template for anisotropic
BAOs.Comment: 18 pages, 10 figure
A Closure Theory for Non-linear Evolution of Cosmological Power Spectra
We apply a non-linear statistical method in turbulence to the cosmological
perturbation theory and derive a closed set of evolution equations for matter
power spectra. The resultant closure equations consistently recover the
one-loop results of standard perturbation theory and beyond that, it is still
capable of treating the non-linear evolution of matter power spectra. We find
the exact integral expressions for the solutions of closure equations. These
analytic expressions coincide with the renormalized one-loop results presented
by Crocce & Scoccimarro (2006,2007). By constructing the non-linear propagator,
we analytically evaluate the non-linear matter power spectra based on the
first-order Born approximation of the integral expressions and compare it with
those of the renormalized perturbation theory.Comment: 22 pages, 4 figures, accepted for publication in Ap
Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity
We present a formalism to calculate the non-linear matter power spectrum in
modified gravity models that explain the late-time acceleration of the Universe
without dark energy. Any successful modified gravity models should contain a
mechanism to recover General Relativity (GR) on small scales in order to avoid
the stringent constrains on deviations from GR at solar system scales. Based on
our formalism, the quasi non-linear power spectrum in the
Dvali-Gabadadze-Porratti (DGP) braneworld models and gravity models are
derived by taking into account the mechanism to recover GR properly. We also
extrapolate our predictions to fully non-linear scales using the Parametrized
Post Friedmann (PPF) framework. In gravity models, the predicted
non-linear power spectrum is shown to reproduce N-body results. We find that
the mechanism to recover GR suppresses the difference between the modified
gravity models and dark energy models with the same expansion history, but the
difference remains large at weakly non-linear regime in these models. Our
formalism is applicable to a wide variety of modified gravity models and it is
ready to use once consistent models for modified gravity are developed.Comment: 25 pages, 8 figures, comparison to N-body simulations in DGP added,
published in PR
Scale Dependence of Halo Bispectrum from Non-Gaussian Initial Conditions in Cosmological N-body Simulations
We study the halo bispectrum from non-Gaussian initial conditions. Based on a
set of large -body simulations starting from initial density fields with
local type non-Gaussianity, we find that the halo bispectrum exhibits a strong
dependence on the shape and scale of Fourier space triangles near squeezed
configurations at large scales. The amplitude of the halo bispectrum roughly
scales as . The resultant scaling on the triangular shape is consistent
with that predicted by Jeong & Komatsu based on perturbation theory. We
systematically investigate this dependence with varying redshifts and halo mass
thresholds. It is shown that the dependence of the halo bispectrum is
stronger for more massive haloes at higher redshifts. This feature can be a
useful discriminator of inflation scenarios in future deep and wide galaxy
redshift surveys.Comment: 27 pages, 10 figures; revised argument in section 6, added appendix
C, JCAP accepted versio
Higher-Order Angular Galaxy Correlations in the SDSS: Redshift and Color Dependence of non-Linear Bias
We present estimates of the N-point galaxy, area-averaged, angular
correlation functions () for = 2,...,7 for
galaxies from the fifth data release of the Sloan Digital Sky Survey. Our
parent sample is selected from galaxies with , and is the
largest ever used to study higher-order correlations. We subdivide this parent
sample into two volume limited samples using photometric redshifts, and these
two samples are further subdivided by magnitude, redshift, and color (producing
early- and late-type galaxy samples) to determine the dependence of
() on luminosity, redshift, and galaxy-type. We
measure () using oversampling techniques and use them
to calculate the projected, . Using models derived from theoretical
power-spectra and perturbation theory, we measure the bias parameters and
, finding that the large differences in both bias parameters ( and
) between early- and late-type galaxies are robust against changes in
redshift, luminosity, and , and that both terms are consistently
smaller for late-type galaxies. By directly comparing their higher-order
correlation measurements, we find large differences in the clustering of
late-type galaxies at redshifts lower than 0.3 and those at redshifts higher
than 0.3, both at large scales ( is larger by at ) and
small scales (large amplitudes are measured at small scales only for ,
suggesting much more merger driven star formation at ). Finally, our
measurements of suggest both that and is negative.Comment: 46 pages, 19 figures, Accepted to Ap
Galaxy clustering constraints on deviations from Newtonian gravity at cosmological scales II: Perturbative and numerical analyses of power spectrum and bispectrum
We explore observational constraints on possible deviations from Newtonian
gravity by means of large-scale clustering of galaxies. We measure the power
spectrum and the bispectrum of Sloan Digital Sky Survey galaxies and compare
the result with predictions in an empirical model of modified gravity. Our
model assumes an additional Yukawa-like term with two parameters that
characterize the amplitude and the length scale of the modified gravity. The
model predictions are calculated using two methods; the second-order
perturbation theory and direct N-body simulations. These methods allow us to
study non-linear evolution of large-scale structure. Using the simulation
results, we find that perturbation theory provides reliable estimates for the
power spectrum and the bispectrum in the modified Newtonian model. We also
construct mock galaxy catalogues from the simulations, and derive constraints
on the amplitude and the length scale of deviations from Newtonian gravity. The
resulting constraints from power spectrum are consistent with those obtained in
our earlier work, indicating the validity of the previous empirical modeling of
gravitational nonlinearity in the modified Newtonian model. If linear biasing
is adopted, the bispectrum of the SDSS galaxies yields constraints very similar
to those from the power spectrum. If we allow for the nonlinear biasing
instead, we find that the ratio of the quadratic to linear biasing
coefficients, b_2/b_1, should satisfy -0.4 < b_2/b_1<0.3 in the modified
Newtonian model.Comment: 12 pages, 7 figure
Combining perturbation theories with halo models for the matter bispectrum
We investigate how unified models should be built to be able to predict the
matter-density bispectrum (and power spectrum) from very large to small scales
and that are at the same time consistent with perturbation theory at low
and with halo models at high . We use a Lagrangian framework to decompose
the bispectrum into "3-halo", "2-halo", and "1-halo" contributions, related to
"perturbative" and "non-perturbative" terms. We describe a simple
implementation of this approach and present a detailed comparison with
numerical simulations. We show that the 1-halo and 2-halo contributions contain
counterterms that ensure their decay at low , as required by physical
constraints, and allow a better match to simulations. Contrary to the power
spectrum, the standard 1-loop perturbation theory can be used for the
perturbative 3-halo contribution because it does not grow too fast at high .
Moreover, it is much simpler and more accurate than two resummation schemes
investigated in this paper. We obtain a good agreement with numerical
simulations on both large and small scales, but the transition scales are
poorly described by the simplest implementation. This cannot be amended by
simple modifications to the halo parameters, but we show how it can be
corrected for the power spectrum and the bispectrum through a simple
interpolation scheme that is restricted to this intermediate regime. Then, we
reach an accuracy on the order of 10% on mildly and highly nonlinear scales,
while an accuracy on the order of 1% is obtained on larger weakly nonlinear
scales. This also holds for the real-space two-point correlation function.Comment: 25 page
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