scholarly journals What does the marked power spectrum measure? Insights from perturbation theory

2020 ◽  
Vol 102 (4) ◽  
Author(s):  
Oliver H. E. Philcox ◽  
Elena Massara ◽  
David N. Spergel
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum

scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

scholarly journals Modelling the post-reionization neutral hydrogen (H i) 21-cm bispectrum

2019 ◽  
Vol 490 (2) ◽  
pp. 2880-2889 ◽  
Author(s):  
Debanjan Sarkar ◽  
Suman Majumdar ◽  
Somnath Bharadwaj
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Cosmological Parameters ◽  
Neutral Hydrogen ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Intensity Mapping ◽  
High Level ◽  
Second Order Perturbation Theory ◽  
Good Agreement

ABSTRACT Measurements of the post-reionization 21-cm bispectrum $B_{{\rm H\,{\small I}}\, }(\boldsymbol {k_1},\boldsymbol {k_2},\boldsymbol {k_3})$ using various upcoming intensity mapping experiments hold the potential for determining the cosmological parameters at a high level of precision. In this paper, we have estimated the 21-cm bispectrum in the z range 1 ≤ z ≤ 6 using seminumerical simulations of the neutral hydrogen (H i) distribution. We determine the k and z range where the 21-cm bispectrum can be adequately modelled using the predictions of second-order perturbation theory, and we use this to predict the redshift evolution of the linear and quadratic H i bias parameters b1 and b2, respectively. The b1 values are found to decrease nearly linearly with decreasing z, and are in good agreement with earlier predictions obtained by modelling the 21-cm power spectrum $P_{{\rm H\,{\small I}}\, }(k)$. The b2 values fall sharply with decreasing z, becomes zero at z ∼ 3 and attains a nearly constant value b2 ≈ −0.36 at z < 2. We provide polynomial fitting formulas for b1 and b2 as functions of z. The modelling presented here is expected to be useful in future efforts to determine cosmological parameters and constrain primordial non-Gaussianity using the 21-cm bispectrum.

scholarly journals Matter power spectrum from a Lagrangian-space regularization of perturbation theory

2013 ◽  
Vol 87 (8) ◽  
Author(s):  
Patrick Valageas ◽  
Takahiro Nishimichi ◽  
Atsushi Taruya
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Matter Power Spectrum

scholarly journals Clustering in massive neutrino cosmologies via Eulerian Perturbation Theory

2021 ◽  
Vol 2021 (11) ◽  
pp. 028
Author(s):  
Alejandro Aviles ◽  
Arka Banerjee ◽  
Gustavo Niz ◽  
Zachary Slepian
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Effective Field ◽  
Tree Level ◽  
Accurate Approximation ◽  
Bias Parameter ◽  
Wave Numbers ◽  
Massive Neutrinos ◽  
Correct Estimation ◽  
The One

Abstract We introduce an Eulerian Perturbation Theory to study the clustering of tracers for cosmologies in the presence of massive neutrinos. Our approach is based on mapping recently-obtained Lagrangian Perturbation Theory results to the Eulerian framework. We add Effective Field Theory counterterms, IR-resummations and a biasing scheme to compute the one-loop redshift-space power spectrum. To assess our predictions, we compare the power spectrum multipoles against synthetic halo catalogues from the QUIJOTE simulations, finding excellent agreement on scales k ≲ 0.25 h Mpc-1. One can obtain the same fitting accuracy using higher wave-numbers, but then the theory fails to give a correct estimation of the linear bias parameter. We further discuss the implications for the tree-level bispectrum. Finally, calculating loop corrections is computationally costly, hence we derive an accurate approximation wherein we retain only the main features of the kernels, as produced by changes to the growth rate. As a result, we show how FFTLog methods can be used to further accelerate the loop computations with these reduced kernels.

scholarly journals Galaxy power spectrum multipoles covariance in perturbation theory

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
Digvijay Wadekar ◽  
Román Scoccimarro
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum

scholarly journals Impact of cosmological signatures in two-point statistics beyond the linear regime

2020 ◽  
Author(s):  
D V Gomez-Navarro ◽  
A J Mead ◽  
A Aviles ◽  
A de la Macorra
Keyword(s):  
Perturbation Theory ◽  
Correlation Function ◽  
Power Spectrum ◽  
Large Scale ◽  
Line Of Sight ◽  
Linear Regime ◽  
Dark Sector ◽  
Linear Evolution ◽  
Matter Power Spectrum ◽  
Small Scales

Abstract Some beyond ΛCDM cosmological models have dark-sector energy densities that suffer phase transitions. Fluctuations entering the horizon during such a transition can receive enhancements that ultimately show up as a distinctive bump in the power spectrum relative to a model with no phase transition. In this work, we study the non-linear evolution of such signatures in the matter power spectrum and correlation function using N-body simulations, perturbation theory and hmcode- a halo-model based method. We focus on modelling the response, computed as the ratio of statistics between a model containing a bump and one without it, rather than in the statistics themselves. Instead of working with a specific theoretical model, we inject a parametric family of Gaussian bumps into otherwise standard ΛCDM spectra. We find that even when the primordial bump is located at linear scales, non-linearities tend to produce a second bump at smaller scales. This effect is understood within the halo model due to a more efficient halo formation. In redshift space these nonlinear signatures are partially erased because of the damping along the line-of-sight direction produced by non-coherent motions of particles at small scales. In configuration space, the bump modulates the correlation function reflecting as oscillations in the response, as it is clear in linear Eulerian theory; however, they become damped because large scale coherent flows have some tendency to occupy regions more depleted of particles. This mechanism is explained within Lagrangian Perturbation Theory and well captured by our simulations.

scholarly journals Simulations and symmetries

2020 ◽  
Vol 492 (4) ◽  
pp. 5754-5763 ◽  
Author(s):  
Chirag Modi ◽  
Shi-Fan Chen ◽  
Martin White
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Galaxy Formation ◽  
Hybrid Approach ◽  
Limited Range ◽  
Real Space ◽  
Equivalent Model ◽  
The Real ◽  
Body Dynamics ◽  
The Cost

ABSTRACT We investigate the range of applicability of a model for the real-space power spectrum based on N-body dynamics and a (quadratic) Lagrangian bias expansion. This combination uses the highly accurate particle displacements that can be efficiently achieved by modern N-body methods with a symmetries-based bias expansion which describes the clustering of any tracer on large scales. We show that at low redshifts, and for moderately biased tracers, the substitution of N-body-determined dynamics improves over an equivalent model using perturbation theory by more than a factor of two in scale, while at high redshifts and for highly biased tracers the gains are more modest. This hybrid approach lends itself well to emulation. By removing the need to identify haloes and subhaloes, and by not requiring any galaxy-formation-related parameters to be included, the emulation task is significantly simplified at the cost of modelling a more limited range in scale.

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