Space Power Spectrum Research Articles

High precision accelerator for our hybrid model of the redshift space power spectrum

Abstract Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modelling these statistics may require theoretical templates that go beyond two-loop order perturbation theory, especially for achieving precision at smaller scales. In our previous work, we introduced a hybrid model for the redshift space power spectrum of galaxies. This model combines two-loop order templates with N-body simulations to capture the influence of scale-independent parameters on the galaxy power spectrum. However, the impact of scale-dependent parameters was addressed by precomputing a set of input statistics derived from computationally expensive N-body simulations. As a result, exploring the scale-dependent parameter space was not feasible in this approach. To address this challenge, we present an accelerated methodology that utilizes Gaussian processes, a machine learning technique, to emulate these input statistics. Our emulators exhibit remarkable accuracy, achieving reliable results with just 13 N-body simulations for training. Our emulators can reproduce the set of statistics we are interested in with less than 0.1% error in the parameter space within 5σ of the Planck ΛCDM predictions, specifically for scales around k > 0.1 h Mpc−1. Following the training of our emulators, we can predict all inputs for our hybrid model in approximately 0.2 seconds at a specified redshift. Given that performing 13 N-body simulations is a manageable task, our present methodology enables us to construct efficient and highly accurate models of the galaxy power spectra within a manageable time frame.

Revisiting the effects of baryon physics on small-scale redshift space distortions

Abstract Redshift space distortions are an important probe of the growth of large-scale structure and for constraining cosmological parameters in general. As galaxy redshift surveys approach percent level precision in their observations of the two point clustering statistics, it is timely to review what effects baryons and associated processes such as feedback may have on small-scale clustering in redshift space. Contrary to previous studies in the literature, we show using the large-volume Bahamas hydrodynamic simulations that the effect of baryons can be as much as 1 per cent in the k ∼ 0.1 h Mpc−1 range for the monopole and 5 per cent for quadrupole, and that this could rise to as much as 10 per cent at k ∼ 10 h Mpc−1 in both measurements. For the halo power spectra, this difference can be as much 3-4 per cent in the monopole on scales of 0.05 < k < 0.3 h Mpc−1 for 1013 h−1 M⊙ haloes. We find that these deviations can be mitigated to the sub-percent level in the both the monopole and quadrupole up to k ∼ 0.3 h Mpc−1 if the baryon corrected halo masses are used to calculate the redshift space power spectra. Finally, we use the cosmo-OWLS simulation suite to explore the changes in the redshift space power spectra with different feedback prescriptions, finding that there is a maximum of 15-20 per cent difference between the redshift space monopole and quadrupole with and without baryons at k ∼ 1–2 h Mpc−1 within these models.

A hybrid EEG classification model using layered cascade deep learning architecture.

The problem of multi-class classification is always a challenge in the field of EEG (electroencephalogram)-based seizure detection. The traditional studies focus on computing or learning a set of features from EEG to distinguish between different patterns. However, the extraction of characteristic information becomes increasingly difficult as the number of EEG types increases. To address this issue, a creative EEG classification technique is proposed by employing a principal component analysis network (PCANet) coupled with phase space reconstruction (PSR) and power spectrum density (PSD). We have introduced the PSR and PSD to prepare the inputs, where dynamic and frequency information are exposed from deep within PCANet. It is remarkable that a layered cascade strategy is designed to make a powerful deep learner according to the rule of one network vs one task (OVO). The proposed method has achieved greater effects than the individual models and shown superior performance in comparison with state-of-the-art algorithms, which present 98.0% of sensitivity, 99.90% of specificity, and 99.07% of accuracy. Our ensemble PCANet model works in an assembly line-like manner, obviating the need for hand-craft features. Results demonstrate that the proposed scheme can greatly enhances the accuracy and robustness of seizure detection from EEG signals.

Cosmology with the galaxy bispectrum multipoles: Optimal estimation and application to BOSS data

We present a framework for self-consistent cosmological analyses of the full-shape anisotropic bispectrum, including the quadrupole $(\ell=2)$ and hexadecapole $(\ell=4)$ moments. This features a novel window-free algorithm for extracting the latter quantities from data, derived using a maximum-likelihood prescription. Furthermore, we introduce a theoretical model for the bispectrum multipoles (which does not introduce new free parameters), and test both aspects of the pipeline on several high-fidelity mocks, including the PT Challenge suite of gigantic cumulative volume. This establishes that the systematic error is significantly below the statistical threshold, both for the measurement and modeling. As a realistic example, we extract the large-scale bispectrum multipoles from BOSS DR12 and analyze them in combination with the power spectrum data. Assuming a minimal $\Lambda$CDM model, with a BBN prior on the baryon density and a \textit{Planck} prior on $n_s$, we can extract the remaining cosmological parameters directly from the clustering data. The inclusion of the unwindowed higher-order $(\ell>0)$ large-scale bispectrum multipoles is found to moderately improve one-dimensional cosmological parameter posteriors (at the $5\%-10\%$ level), though these multipoles are detected only in three out of four BOSS data segments at $\approx 5\sigma$. Combining information from the power spectrum and bispectrum multipoles, the real space power spectrum, and the post-reconstructed BAO data, we find $H_0 = 68.2\pm 0.8~\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, $\Omega_m =0.33\pm 0.01$ and $\sigma_8 = 0.736\pm 0.033$ (the tightest yet found in perturbative full-shape analyses). Our estimate of the growth parameter $S_8=0.77\pm 0.04$ agrees with both weak lensing and CMB results.

Studying large-scale structure probes of modified gravity with COLA

We study the effect of two Modified Gravity (MG) theories, f(R) and nDGP, on three probes of large-scale structure, the real space power spectrum estimator Q 0, bispectrum and voids, and validate fast approximate COLA simulations against full N-body simulations for the prediction of these probes.We find that using the first three even multipoles of the redshift space power spectrum to estimate Q 0 is enough to reproduce the MG boost factors of the real space power spectrum for both halo and galaxy catalogues. By analysing the bispectrum and reduced bispectrum of Dark Matter (DM), we show that the strong MG signal present in the DM bispectrum is mainly due to the enhanced power spectrum. We warn about adopting screening approximations in simulations as this neglects non-linear contributions that can source a significant component of the MG bispectrum signal at the DM level, but we argue that this is not a problem for the bispectrum of galaxies in redshift space where the signal is dominated by the non-linear galaxy bias. Finally, we search for voids in our mock galaxy catalogues using the ZOBOV watershed algorithm.To apply a linear model for Redshift-Space Distortion (RSD) in the void-galaxy cross-correlation function, we first examine the effects of MG on the void profiles entering into the RSD model. We find relevant MG signals in the integrated-density, velocity dispersion and radial velocity profiles in the nDGP theory. Fitting the RSD model for the linear growth rate, we recover the linear theory prediction in an nDGP model, which is larger than the ΛCDM predictionat the 3σ level. In f(R) theory we cannot naively compare the results of the fit with the linear theory prediction as this is scale-dependent, but we obtain results that are consistent with the ΛCDM prediction.

Fast computation of non-linear power spectrum in cosmologies with massive neutrinos

We compute 1-loop corrections to the redshift space galaxy power spectrum in cosmologies containing additional scales, and hence kernels different from Einstein-de Sitter (EdS). Specifically, our method is tailored for cosmologies in the presence of massive neutrinos and some modified gravity models; in this article we concentrate on the former case. The perturbative kernels have contributions that we notice appear either from the logarithmic growth rate f(k,t), which is scale-dependent because of the neutrino free-streaming, or from the failure of the commonly used approximation f 2 = Ω m . The latter contributions make the computation of loop corrections quite slow, precluding full-shape analyses for parameter estimation. However, we identify that the dominant pieces of the kernels come from the growth factor, allowing us to simplify the kernels but retaining the characteristic free-streaming scale introduced by the neutrinos' mass. Moreover, with this simplification one can exploit FFTLog methods to speed up the computations even more. We validate our analytical modeling and numerical method with halo catalogs extracted from the Quijote simulations finding good agreement with the, a priori, known cosmological parameters. We make public our Python code FOLPSν to compute the redshift space power spectrum in a fraction of second. Code available at https://github.com/henoriega/FOLPS-nu.

Cosmological constraints without nonlinear redshift-space distortions

Non-linear redshift-space distortions ("fingers of God") are challenging to model analytically, a fact that limits the applicability of perturbation theory in redshift space as compared to real space. We show how this problem can be mitigated using a new observable, $Q_0$, which can be easily estimated from the redshift space clustering data and is approximately equal to the real space power spectrum. The new statistic does not suffer from fingers of God and can be accurately described with perturbation theory down to $k_{\rm max}\simeq 0.4~h~\text{Mpc}^{-1}$. It can be straightforwardly included in the likelihood at negligible additional computational cost, and yields noticeable improvements on cosmological parameters compared to standard power spectrum multipole analyses. Using both simulations and observational data from the Baryon Oscillation Spectroscopic Survey, we show that improvements vary from $10\%$ to $100\%$ depending on the cosmological parameter considered, the galaxy sample and the survey volume.

Contributions from primordial non-Gaussianity and general relativity to the galaxy power spectrum

We compute the real space galaxy power spectrum, including the leading order effects of General Relativity and primordial non-Gaussianity from the f NL and g NL parameters. Such contributions come from the one-loop matter power spectrum terms dominant at large scales, and from the factors of the non-linear bias parameter b NL (akin to the Newtonian b ϕ). We assess the detectability of these contributions in Stage-IV surveys. In particular, we note that specific values of the bias parameter may erase the primordial and relativistic contributions to the configuration space power spectrum.

Bursting mechanism in a memristive Lorenz based system and function projective synchronization in its-fractional-order form: Digital implementation under ATmega328P microcontroller

In this paper, bifurcation mechanism of bursting oscillations and function projective synchronization of the fractional order form for a memristive Lorenz based system are investigated. One of the key results is the dependance of relaxation time of bursting oscillation on the fractional order derivative. The newly proposed system has a line equilibrium and accordingly, features hidden attractors. When the system is divided into two subsystems labeled slow subsystem(SS) and fast subsystem(FS), stability analysis indicates that bursting oscillations result from the switching of the equilibrium point of the(FS) between stable and unstable states. We refer this class of bursting as ”source/bursting”. The second aspect of this paper deals with the study of fractional order of the system precisely function projective synchronization in a relay topology. By using some standard nonlinear diagnostic tools such as bifurcation diagram, largest Lyapunov exponent, phase space trajectory and power spectrum, the study of the fractional model reveals that the dynamics strongly depends on system parameters , fractional order q as well as on initial conditions. With a set of chosen parameters , the proposed scheme achieves function projective synchronization in a finite time despite the unpredictability of the scaling function. The Results of digital implementation based on a ATmega328P microcontroller are in good agreement with those found by numerical simulations.

Fast generation of mock galaxy catalogues in modified gravity models with COLA

We investigate the viability of producing galaxy mock catalogues with COmoving Lagrangian Acceleration (COLA) simulations in Modified Gravity (MG) models employing the Halo Occupation Distribution (HOD) formalism. In this work, we focus on two theories of MG: f(R) gravity with the chameleon mechanism, and a braneworld model (nDGP) that incorporates the Vainshtein mechanism. We use a suite of full N-body simulations in MG as a benchmark to test the accuracy of COLA simulations. At the level of Dark Matter (DM), we show that COLA accurately reproduces the matter power spectrum up to k ∼ 1 h Mpc-1, while it is less accurate in reproducing the velocity field. To produce halo catalogues, we find that the rockstar halo-finder does not perform well with COLA simulations. On the other hand, using a simple Friends-of-Friends (FoF) finder and an empirical mass conversion from FoF to spherical over-density masses, we are able to produce halo catalogues in COLA that are in good agreement with those in N-body simulations. To consider the effects of the MG fifth force on the halo profile, we derive simple fitting formulae for the concentration-mass and the velocity dispersion-mass relations that we calibrate using rockstar halo catalogues in N-body simulations. We then use these results to extend the HOD formalism to modified gravity simulations in COLA. We use an HOD model with five parameters that we tune to obtain galaxy catalogues in redshift space. We find that despite the great freedom of the HOD model, MG leaves characteristic imprints in the redshift space power spectrum multipoles and these features are well captured by the COLA galaxy catalogues.

Toward a more stringent test of gravity with the redshift space power spectrum: Simultaneous probe of growth and amplitude of large-scale structure

Redshift-space distortions (RSD) offers an exciting opportunity to test the gravity on cosmological scales. In the presence of galaxy bias, however, the RSD measurement at large scales, where the linear theory prediction is safely applied, is known to exhibit a degeneracy between the parameters of structure growth f and fluctuation amplitude sigma8, and one can only constrain the parameters in the form of fsigma8. In order to disentangle this degeneracy, in this paper, we go beyond the linear theory, and consider the model of RSD applicable to a weakly nonlinear regime. Based on the Fisher matrix analysis, we show explicitly that the degeneracy of the parameter fsigma8 can be broken, and sigma8 is separately estimated in the presence of galaxy bias. Performing further the Markov chain Monte Carlo analysis, we verify that our model correctly reproduces the fiducial values of fsigma8 and sigma8, with the statistical errors consistent with those estimated from the Fisher matrix analysis. We show that upcoming galaxy survey of the stage-IV class can unambiguously determine sigma8 at the precision down to 10% at higher redshifts even if we restrict the accessible scales to k<0.16h/Mpc

Redshift space power spectrum beyond Einstein-de Sitter kernels

We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the k-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the ΛCDM and the Hu-Sawicki f(R) models, and compare our numerical results against the elephant suite of N-body simulations, finding very good agreement up to k = 0.27 Mpc-1 h at z = 0.5 for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from ΛCDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST.

Hybrid Pℓ(k): general, unified, non-linear matter power spectrum in redshift space

Constraints on gravity and cosmology will greatly benefit from performing joint clustering and weak lensing analyses on large-scale structure data sets. Utilising non-linear information coming from small physical scales can greatly enhance these constraints. At the heart of these analyses is the matter power spectrum. Here we employ a simple method, dubbed “Hybrid Pℓ(k)”, based on the Gaussian Streaming Model (GSM), to calculate the quasi non-linear redshift space matter power spectrum multipoles. This employs a fully non-linear and theoretically general prescription for the matter power spectrum. We test this approach against comoving Lagrangian acceleration simulation measurements performed in GR, DGP and f(R) gravity and find that our method performs comparably or better to the dark matter TNS redshift space power spectrum model {for dark matter. When comparing the redshift space multipoles for halos, we find that the Gaussian approximation of the GSM with a linear bias and a free stochastic term, N, is competitive to the TNS model.} Our approach offers many avenues for improvement in accuracy as well as further unification under the halo model.

Assessing non-linear models for galaxy clustering – II. Model validation and forecasts for Stage IV surveys

ABSTRACT Accurate modelling of non-linear scales in galaxy clustering will be crucial for data analysis of Stage IV galaxy surveys. A selection of competing non-linear models must be made based on validation studies. We provide a comprehensive set of forecasts of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large-scale structure (EFTofLSS) inspired model. Using simulation data and a least-χ2 analysis, we determine ranges of validity for the models. We then conduct an exploratory Fisher analysis using the full anisotropic power spectrum to investigate parameter degeneracies. We proceed to perform an MCMC analysis utilizing the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order to avoid biasing our growth rate, f, constraint. We find that the TNS model with a Lorentzian damping and standard Eulerian perturbative modelling outperforms other variants of the TNS model. Our MCMC analysis finds that the EFTofLSS-based model may provide tighter marginalized constraints on f at z = 0.5 and z = 1 than the TNS model, despite having additional nuisance parameters. However this depends on the range of scales used as well as the fiducial values and priors on the EFT nuisance parameters. Finally, we extend previous work to provide a consistent comparison between the Fisher matrix and MCMC forecasts using the multipole expansion formalism, and find good agreement between them.

Assessing non-linear models for galaxy clustering I: unbiased growth forecasts from multipole expansion

We assess the performance of the Taruya, Nishimichi and Saito (TNS) model for the halo redshift space power spectrum, focusing on utilising mildly non-linear scales to constrain the growth rate of structure f. Using simulations with volume and number density typical of forthcoming Stage IV galaxy surveys, we determine ranges of validity for the model at redshifts z = 0.5 and z = 1. We proceed to perform a Bayesian MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, followed by an exploratory Fisher matrix analysis. As previously noted in other forecasts as well as in real data analyses, we find that including the hexadecapole can significantly improve the constraints. However, a restricted range of scales is required for the hexadecapole in order for the growth parameter estimation to remain unbiased, limiting the improvement. We consistently quantify these effects by employing the multipole expansion formalism in both our Fisher and MCMC forecasts.

One simulation to have them all: performance of the Bias Assignment Method against N-body simulations

Abstract In this paper we demonstrate that the information encoded in one single (sufficiently large) N-body simulation can be used to reproduce arbitrary numbers of halo catalogues, using approximated realisations of dark matter density fields with different initial conditions. To this end we use as a reference one realisation (from an ensemble of 300) of the Minerva N-body simulations and the recently published Bias Assignment Method to extract the local and non-local bias linking the halo to the dark matter distribution. We use an approximate (and fast) gravity solver to generate 300 dark matter density fields from the down-sampled initial conditions of the reference simulation and sample each of these fields using the halo-bias and a kernel, both calibrated from the arbitrarily chosen realisation of the reference simulation. We show that the power spectrum, its variance and the three-point statistics are reproduced within $\sim 2\%$ (up to k ∼ 1.0 h Mpc−1), $\sim 5-10\%$ and $\sim 10\%$, respectively. Using a model for the real space power spectrum (with three free bias parameters), we show that the covariance matrices obtained from our procedure lead to parameter uncertainties that are compatible within $\sim 10\%$ with respect to those derived from the reference covariance matrix, and motivate approaches that can help to reduce these differences to $\sim 1\%$. Our method has the potential to learn from one simulation with moderate volumes and high-mass resolution and extrapolate the information of the bias and the kernel to larger volumes, making it ideal for the construction of mock catalogues for present and forthcoming observational campaigns such as Euclid or DESI.

Assessing non-linear models for galaxy clustering III: theoretical accuracy for stage IV surveys

We provide in depth MCMC comparisons of two different models for the halo redshift space power spectrum, namely a variant of the commonly applied Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using many simulation realisations and Stage IV survey-like specifications for the covariance matrix, we check each model's range of validity by testing for bias in the recovery of the fiducial growth rate of structure formation. The robustness of the determined range of validity is then tested by performing additional MCMC analyses using higher order multipoles, a larger survey volume and a more highly biased tracer catalogue. We find that under all tests, the TNS model's range of validity remains robust and is found to be much higher than previous estimates. The EFTofLSS model fails to capture the spectra for highly biased tracers as well as becoming biased at lower wavenumbers when considering a very large survey volume. Further, we find that the marginalised constraints on f for all analyses are stronger when using the TNS model.

The Aemulus Project. I. Numerical Simulations for Precision Cosmology

Abstract The rapidly growing statistical precision of galaxy surveys has led to a need for ever more precise predictions of the observables used to constrain cosmological and galaxy formation models. The primary avenue through which such predictions will be obtained is suites of numerical simulations. These simulations must span the relevant model parameter spaces, be large enough to obtain the precision demanded by upcoming data, and be thoroughly validated in order to ensure accuracy. In this paper, we present one such suite of simulations, forming the basis for the Aemulus Project, a collaboration devoted to precision emulation of galaxy survey observables. We have run a set of 75 (1.05 h −1 Gpc)3 simulations with mass resolution and force softening of and 20 h −1 kpc, respectively, in 47 different wCDM cosmologies spanning the range of parameter space allowed by the combination of recent cosmic microwave background, baryon acoustic oscillation, and Type Ia supernova results. We present convergence tests of several observables including spherical overdensity halo mass functions, galaxy projected correlation functions, galaxy clustering in redshift space, and matter and halo correlation functions and power spectra. We show that these statistics are converged to 1% (2%) or to the sample variance of the statistic, whichever is larger, for halos with more than 500 (200) particles, respectively, and scales of r &gt; 200 h −1 kpc in real space or k ∼ 3 h Mpc−1 in harmonic space for z ≤ 1. We find that the dominant source of uncertainty comes from varying the particle loading of the simulations. This leads to large systematic errors for statistics using halos with fewer than 200 particles and scales smaller than k ∼ 4 h Mpc−1. We provide the halo catalogs and snapshots detailed in this work to the community at https://AemulusProject.github.io.

Perturbation theory challenge for cosmological parameters estimation: Matter power spectrum in real space

We study the accuracy with which cosmological parameters can be determined from real space power spectrum of matter density contrast at weakly nonlinear scales using analytical approaches. From power spectra measured in $N$-body simulations and using Markov chain Monte-Carlo technique, the best-fitting cosmological input parameters are determined with several analytical methods as a theoretical template, such as the standard perturbation theory, the regularized perturbation theory, and the effective field theory. We show that at redshift 1, all two-loop level calculations can fit the measured power spectrum down to scales $k \sim 0.2 \, h \, \mathrm{Mpc}^{-1}$ and cosmological parameters are successfully estimated in an unbiased way. Introducing the Figure of bias (FoB) and Figure of merit (FoM) parameter, we determine the validity range of those models and then evaluate their relative performances. With one free parameter, namely the damping scale, the regularized perturbation theory is found to be able to provide the largest FoM parameter while keeping the FoB in the acceptance range.

Time-dependent fluctuations in the metagalactic photoionization background

We present a formalism for computing time-dependent fluctuations in the cosmological photoionizing radiation background, extending background fluctuations models beyond the steady-state approximation. We apply this formalism to estimate fluctuations in the HI LyA flux redshift space power spectrum and its spatial correlation function at redshifts 2<z<4, assuming the photoionization background is dominated by Quasi-stellar Objects (QSOs) and/or galaxies. We show the shot noise in the power spectrum due to discrete sources is strongly suppressed relative to the steady-state value at low wavenumbers by a factor proportional to the lifetime of the sources, and that this suppression may be used to constrain QSO lifetimes. The total HI LyA power spectrum including shot noise is affected at tens of percent on short scales, and by as much as an order of magnitude or more on scales exceeding the mean free path. The spatial correlation function is similarly found to be sensitive to the shot noise, although moderately insensitive to the effects of time-dependence on the non-shotnoise contribution. Photoionization rate fluctuations substantially modify the shape of the Baryonic Acoustic Oscillation peak in the correlation function, including a small increase in its position that must be accounted for to avoid biasing estimates of cosmological parameters based on the peak position. We briefly investigate solving the full frequency dependent equation, finding that it agrees with the frequency-independent to better than percent accuracy. Simple formulas are provided for the power spectrum of fluctuations in the photoionization rate that approximate the full computations.