arXiv subjects

E. P. S. Shellard

Publications and source records attributed to E. P. S. Shellard.

At least 37 records · Page 2Linked to original sources

arXiv2019

Advancing the matter bispectrum estimation of large-scale structure: a comparison of dark matter codes

Cosmological information from forthcoming galaxy surveys, such as LSST and Euclid, will soon exceed that available from the CMB. Higher order correlation functions, like the bispectrum, will be indispensable for realising this potential. The interpretation of this data faces many challenges because gravitational collapse of matter is a complex non-linear process, typically modelled by computationally expensive N-body simulations. Proposed alternatives using fast dark matter codes (e.g. 2LPT or particle-mesh) are primarily evaluated on their ability to reproduce clustering statistics linked to the matter power spectrum. The accuracy of these codes can be tested in more detail by looking at higher-order statistics, and in this paper we will present an efficient and optimal methodology (MODAL-LSS) to reconstruct the full bispectrum of any 3D density field. We make quantitative comparisons between a number of fast dark matter codes and Gadget at redshift $z=0.5$. This will serve as an important diagnostic tool for dark matter/halo mock catalogues and lays the foundation for realistic high precision analysis with the galaxy bispectrum. In particular, we show that the lack of small-scale power in the bispectrum of fast codes can be ameliorated by a simple `boosting' technique for the power spectrum. We also investigate the covariance of the MODAL-LSS bispectrum estimator, demonstrating the plateauing of non-Gaussian errors in contrast to simple Gaussian extrapolations. This has important consequences for the extraction of information from the bispectrum and hence parameter estimation. Finally we make quantitative comparisons of simulation bispectra with theoretical models, discussing the initial parameters required to create mock catalogues with accurate bispectra.

astro-ph.CO↗

arXiv2017

Matter bispectrum of large-scale structure with Gaussian and non-Gaussian initial conditions: Halo models, perturbation theory, and a three-shape model

We study the matter bispectrum of large-scale structure by comparing the predictions of different perturbative and phenomenological models with the full three-dimensional bispectrum from $N$-body simulations estimated using modal methods. We show that among the perturbative approaches, effective field theory succeeds in extending the range of validity furthest on intermediate scales, at the cost of free additional parameters. By studying the halo model, we show that although it is satisfactory in the deeply non-linear regime, it predicts a deficit of power on intermediate scales, worsening at redshifts $z>0$. By comparison with the $N$-body bispectrum on those scales, we show that there is a significant squeezed component underestimated in the halo model. On the basis of these results, we propose a new three-shape model, based on the tree-level, squeezed and constant bispectrum shapes we identified in the halo model; after calibration this fits the simulations on all scales and redshifts of interest. We extend this model further to primordial non-Gaussianity of the local and equilateral types by showing that the same shapes can be used to describe the additional non-Gaussian component in the matter bispectrum. This method provides a HALOFIT-like prototype of the bispectrum that could be used to describe and test parameter dependencies and should be relevant for the bispectrum of weak gravitational lensing and wider applications.

astro-ph.CO↗

arXiv2016

Stretching and Kibble scaling regimes for Hubble-damped defect networks

The cosmological evolution of topological defect networks can broadly be divided into two stages. At early times they are friction-dominated due to particle scattering and therefore non-relativistic, and may either be conformally stretched or evolve in the Kibble regime. At late times they are relativistic and evolve in the well known linear scaling regime. In this work we show that a sufficiently large Hubble damping (that is a sufficiently fast expansion rate) leads to a linear scaling regime where the network is non-relativistic. This is therefore another realization of a Kibble scaling regime, and also has a conformal stretching regime counterpart which we characterize for the first time. We describe these regimes using analytic arguments in the context of the velocity-dependent one-scale model, and we confirm them using high-resolution $4096^3$ field theory simulations of domain wall networks. We also use these simulations to improve the calibration of this analytic model for the case of domain walls.

hep-ph↗

arXiv2016

Models for Small-Scale Structure on Cosmic Strings: II. Scaling and its stability

We make use of the formalism described in a previous paper [Martins {\it et al.} Phys. Rev. D90 (2014) 043518] to address general features of wiggly cosmic string evolution. In particular, we highlight the important role played by poorly understood energy loss mechanisms and propose a simple ansatz which tackles this problem in the context of an extended velocity-dependent one-scale model. We find a general procedure to determine all the scaling solutions admitted by a specific string model and study their stability, enabling a detailed comparison with future numerical simulations. A simpler comparison with previous Goto-Nambu simulations supports earlier evidence that scaling is easier to achieve in the matter era than in the radiation era. In addition, we also find that the requirement that a scaling regime be stable seems to notably constrain the allowed range of energy loss parameters.

astro-ph.CO↗

arXiv2016

Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations

We study the matter bispectrum of the large-scale structure by comparing different perturbative and phenomenological models with measurements from $N$-body simulations obtained with a modal bispectrum estimator. Using shape and amplitude correlators, we directly compare simulated data with theoretical models over the full three-dimensional domain of the bispectrum, for different redshifts and scales. We review and investigate the main perturbative methods in the literature that predict the one-loop bispectrum: standard perturbation theory, effective field theory, resummed Lagrangian and renormalised perturbation theory, calculating the latter also at two loops for some triangle configurations. We find that effective field theory (EFT) succeeds in extending the range of validity furthest into the mildly nonlinear regime, albeit at the price of free extra parameters requiring calibration on simulations. For the more phenomenological halo model, we confirm that despite its validity in the deeply nonlinear regime it has a deficit of power on intermediate scales, which worsens at higher redshifts; this issue is ameliorated, but not solved, by combined halo-perturbative models. We show from simulations that in this transition region there is a strong squeezed bispectrum component that is significantly underestimated in the halo model at earlier redshifts. We thus propose a phenomenological method for alleviating this deficit, which we develop into a simple phenomenological "three-shape" benchmark model based on the three fundamental shapes we have obtained from studying the halo model. When calibrated on the simulations, this three-shape benchmark model accurately describes the bispectrum on all scales and redshifts considered, providing a prototype bispectrum HALOFIT-like methodology that could be used to describe and test parameter dependencies.

astro-ph.CO↗

arXiv2016

Extending the velocity-dependent one-scale model for domain walls

We report on an extensive study of the evolution of domain wall networks in Friedmann-Lema\^ıtre-Robertson-Walker universes by means of the largest currently available field-theory simulations. These simulations were done in $4096^3$ boxes and for a range of different fixed expansion rates, as well as for the transition between the radiation and matter eras. A detailed comparison with the velocity-dependent one-scale (VOS) model shows that this cannot accurately reproduce the results of the entire range of simulated regimes if one assumes that the phenomenological energy loss and momentum parameters are constants. We therefore discuss how a more accurate modeling of these parameters can be done, specifically by introducing an additional mechanism of energy loss (scalar radiation, which is particularly relevant for regimes with relatively little damping) and a modified momentum parameter which is a function of velocity (in analogy to what was previously done for cosmic strings). We finally show that this extended model, appropriately calibrated, provides an accurate fit to our simulations.

hep-ph↗

arXiv2016

Separable projection integrals for higher-order correlators of the cosmic microwave sky: Acceleration by factors exceeding 100

We present a case study describing efforts to optimise and modernise "Modal", the simulation and analysis pipeline used by the Planck satellite experiment for constraining general non-Gaussian models of the early universe via the bispectrum (or three-point correlator) of the cosmic microwave background radiation. We focus on one particular element of the code: the projection of bispectra from the end of inflation to the spherical shell at decoupling, which defines the CMB we observe today. This code involves a three-dimensional inner product between two functions, one of which requires an integral, on a non-rectangular domain containing a sparse grid. We show that by employing separable methods this calculation can be reduced to a one-dimensional summation plus two integrations, reducing the overall dimensionality from four to three. The introduction of separable functions also solves the issue of the non-rectangular sparse grid. This separable method can become unstable in certain cases and so the slower non-separable integral must be calculated instead. We present a discussion of the optimisation of both approaches. We show significant speed-ups of ~100x, arising from a combination of algorithmic improvements and architecture-aware optimisations targeted at improving thread and vectorisation behaviour. The resulting MPI/OpenMP hybrid code is capable of executing on clusters containing processors and/or coprocessors, with strong-scaling efficiency of 98.6% on up to 16 nodes. We find that a single coprocessor outperforms two processor sockets by a factor of 1.3x and that running the same code across a combination of both microarchitectures improves performance-per-node by a factor of 3.38x. By making bispectrum calculations competitive with those for the power spectrum (or two-point correlator) we are now able to consider joint analysis for cosmological science exploitation of new data.

cs.DC↗

arXiv2015

Using inpainting to construct accurate cut-sky CMB estimators

The direct evaluation of manifestly optimal, cut-sky CMB power spectrum and bispectrum estimators is numerically very costly, due to the presence of inverse-covariance filtering operations. This justifies the investigation of alternative approaches. In this work, we mostly focus on an inpainting algorithm that was introduced in recent CMB analyses to cure cut-sky suboptimalities of bispectrum estimators. First, we show that inpainting can equally be applied to the problem of unbiased estimation of power spectra. We then compare the performance of a novel inpainted CMB temperature power spectrum estimator to the popular apodised pseudo-$C_l$ (PCL) method and demonstrate, both numerically and with analytic arguments, that inpainted power spectrum estimates significantly outperform PCL estimates. Finally, we study the case of cut-sky bispectrum estimators, comparing the performance of three different approaches: inpainting, apodisation and a novel low-l leaning scheme. Providing an analytic argument why the local shape is typically most affected we mainly focus on local type non-Gaussianity. Our results show that inpainting allows to achieve optimality also for bispectrum estimation, but interestingly also demonstrate that appropriate apodisation, in conjunction with low-l cleaning, can lead to comparable accuracy.

astro-ph.CO↗

arXiv2015

Polyspectra searches for sharp oscillatory features in cosmic microwave sky data

We undertake a thorough search for signatures of sharp oscillatory features in the WMAP9 power spectrum and bispectrum as well as in the Planck power spectrum. For the first time, we carry out searches in both the power spectrum and bispectrum simultaneously, employing well-defined look-elsewhere statistics to assess significances in a rigorous manner. Developing efficient methods to scan power spectrum likelihoods for oscillatory features, we present results for the phenomenological bare sine and cosine modulations, allowing validation against existing Planck Likelihood surveys, as well as templates that include the correct sharp feature scaling. In particular, we study degeneracies between feature and cosmological parameters. For frequencies beyond the scale set by the acoustic peaks, the dependencies are realised through uninteresting adjustments of the comoving distance to last scattering. Hence, it is sufficient to keep cosmological parameters fixed and employ fast Gaussian approximations to the likelihood as a function of the feature model amplitude. In cases where results can be compared to the literature, our method shows excellent agreement. We supplement results from the Planck Likelihood with an analysis based on the Planck SMICA component separation map that, working on the assumption that the component separation algorithm is reliable, allows for the inclusion of a larger sky fraction. In principle, this allows us to place the most stringent constraints to date on the amplitudes of feature models in the temperature power spectrum. Invoking the WMAP bispectrum, we perform a combined power spectrum and bispectrum survey. We use and slightly generalise statistics developed in previous work to reliably judge the significance of large feature model amplitude estimates. We conclude that our results are entirely consistent with a featureless realisation of a Gaussian CMB.

astro-ph.CO↗

arXiv2015

CMB power spectrum of Nambu-Goto cosmic strings

We improve predictions of the cosmic microwave background (CMB) power spectrum induced by cosmic strings by using source terms obtained from Nambu-Goto network simulations in an expanding universe. We use three high-resolution cosmic string simulations that cover the entire period from recombination until late-time $Λ$ domination to calculate unequal time correlators (UETCs) for scalar, vector and tensor components of the cosmic-string energy-momentum tensor. We calculate the CMB angular power spectrum from strings in two ways. First, to aid comparison with previous work, we fit our simulated UETCs to those obtained from different parameter combinations from the unconnected segment model and then calculate the CMB power spectra using these parameters to represent the string network. Second and more accurately, we decompose the UETCs into their corresponding eigenvalues and eigenvectors and input them directly into an Einstein-Boltzmann solver to calculate the power spectrum for each of the three simulation time periods. We combine the three simulations together, using each of them in its relevant redshift range and we obtain overall power spectra in temperature and polarisation channels. Finally, we use the power spectra obtained with the latest Planck and BICEP2 likelihoods to obtain constraints on the cosmic string tension.

astro-ph.CO↗

arXiv2015

Contribution of domain wall networks to the CMB power spectrum

We use three domain wall simulations from the radiation era to the late time dark energy domination era based on the PRS algorithm to calculate the energy-momentum tensor components of domain wall networks in an expanding universe. Unequal time correlators in the radiation, matter and cosmological constant epochs are calculated using the scaling regime of each of the simulations. The CMB power spectrum of a network of domain walls is determined. The first ever quantitative constraint for the domain wall surface tension is obtained using a Markov chain Monte Carlo method; an energy scale of domain walls of 0.93 MeV, which is close but below the Zel'dovich bound, is determined.

astro-ph.CO↗

arXiv2015

Constraints on the Nambu-Goto cosmic string contribution to the CMB power spectrum in light of new temperature and polarisation data

Cosmic strings generate vector and tensor modes in the B-channel of polarization, as well as the usual temperature power spectrum and E-mode polarization spectrum. We use the power spectrum obtained from high-resolution Nambu-Goto cosmic string simulations together with the Planck and BICEP2 likelihoods to explore the degeneracies appearing between cosmic strings and other cosmological parameters in different inflationary scenarios, as well as the constraints that can be imposed on cosmic strings in each of these situations. In standard $Λ$CDM, the Planck likelihood yields an upper limit $Gμ<1.49 \times 10^{-7}$ (95% confidence). We also analyse the possibility of explaining the BB power spectrum signal recently detected by the BICEP2 probe. We find that cosmic strings alone are able to explain only part of the B-mode polarization signal. Apart from the standard $Λ$CDM model, we look at the following non-minimal parameters: the running of the spectral index, non-zero tensor-to-scalar ratio, additional degrees of freedom ($N_{eff}$) and sterile neutrinos. We find that in both Planck and BICEP2 scenarios adding $N_{eff}$ induces degeneracies between cosmic strings and $N_{eff}$ and other $Λ$CDM parameters. With $N_{eff}$ a larger contribution from cosmic strings is allowed, even favoured, but after combining with large-scale structure data, such as BAOs, strings remain strongly constrained.

astro-ph.CO↗

arXiv2015

Combining power spectrum and bispectrum measurements to detect oscillatory features

The simplest inflationary models present us with few observable parameters to discriminate between them. A detection of features in the spectra of primordial density perturbations could provide valuable insights and lead to stringent tests of models of the early Universe. So far, searches for oscillatory features have not produced statistically significant results. In this work we consider a combined search for features in the power spectrum and bispectrum. We show that possible dependencies between the estimates of feature model amplitudes based on the two- and three-point correlators are largely statistically independent under the assumption of the null hypothesis of a nearly Gaussian featureless CMB. Building on this conclusion we propose an optimal amplitude estimator for a combined search and study the look-elsewhere effect in feature model surveys. In particular we construct analytic models for the distribution of amplitude estimates that allow for a reliable assessment of the significance of potential findings. We also propose a well-behaved integrated statistic that is designed to detect evidence for models exhibiting features at multiple frequencies.

astro-ph.CO↗

arXiv2014

Models for Small-Scale Structure on Cosmic Strings: I. Mathematical Formalism

We describe the formalism of a quantitative analytic model for the evolution of realistic wiggly (as opposed to Goto-Nambu) cosmic strings. The model is particularly suited for describing the evolution of small-scale structure on string networks. We discuss model solutions in the extreme limit where the wiggles make up a high fraction of the total energy of the string network (which physically corresponds to the tensionless limit) and also provide a brief discussion of the opposite (linear) limit where wiggles are a small fraction of the total energy. A companion paper will discuss the detailed modelling and scaling behavior of the small-scale wiggles in the general model, together with a basic comparison with numerical simulations.

hep-ph↗

arXiv2013

Towards efficient and optimal analysis of CMB anisotropies on a masked sky

Strong foreground contamination in high resolution CMB data requires masking which introduces statistical anisotropies and renders a full maximum likelihood analysis numerically intractable. Standard analysis methods like the pseudo-C_l framework lead to information loss due to estimator suboptimalities. We set out and validate a methodology for numerically efficient estimators for a masked sky that recover nearly as much information as a full maximum likelihood procedure. In addition to the standard pseudo-C_l statistic, the approach introduces an augmented basis designed to account for the mode coupling due to the masking of the sky. We motivate the choice of this basis by describing the basic structure of the covariance matrix. We demonstrate that the augmented estimator can achieve near-optimal results in the presence of a WMAP-realistic mask.

astro-ph.CO↗

arXiv2013

CMB Bispectrum from Non-linear Effects during Recombination

We study cosmological perturbations by solving the governing Boltzmann and Einstein Field equations up to second order, and calculate the corresponding CMB bispectrum during recombination. We include all the second-order Liouville and collision terms, truncating the multipole hierarchy at $l=10$, consistently including all $m\neq 0$ terms when calculating the bispectrum in the flat-sky limit. At this stage, we focus on contributions at recombination and we neglect 2nd-order vector and tensor terms, lensing effects, and late time non-linear ISW. We find that the signal-to-noise for the bispectrum is 0.69 for $l_{max}=2000$, yielding an overall signal $F_{\rm NL} = 3.19$ (normalised relative to the local model). We find that the effective $f_{NL}$'s of the equilateral and local type are 5.11 and 0.88 respectively. This recombination signal will have to be taken into account in a quantitative analysis of the Planck data.

astro-ph.CO↗

arXiv2012

Accurate Calibration of the Velocity-dependent One-scale Model for Domain Walls

We study the asymptotic scaling properties of standard domain wall networks in several cosmological epochs. We carry out the largest field theory simulations achieved to date, with simulation boxes of size 20483, and confirm that a scale-invariant evolution of the network is indeed the attractor solution. The simulations are also used to obtain an accurate calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values $c_w = 0.34\pm0.16$ and $k_w = 0.98\pm0.07$, which are higher precision than (but in agreement with) earlier estimates.

hep-ph↗

arXiv2012

The CMB Bispectrum

We use a separable mode expansion estimator with WMAP data to estimate the bispectrum for all the primary families of non-Gaussian models. We review the late-time mode expansion estimator methodology which can be applied to any non-separable primordial and CMB bispectrum model, and we demonstrate how the method can be used to reconstruct the CMB bispectrum from an observational map. We extend the previous validation of the general estimator using local map simulations. We apply the estimator to the coadded WMAP 5-year data, reconstructing the WMAP bispectrum using $l<500$ multipoles and $n=31$ orthonormal 3D eigenmodes. We constrain all popular nearly scale-invariant models, ensuring that the theoretical bispectrum is well-described by a convergent mode expansion. Constraints from the local model $ \fnl=54.4\pm 29.4$ and the equilateral model $\fnl=143.5\pm 151.2$ ($\Fnl = 25.1\pm 26.4$) are consistent with previously published results. (Here, we use a nonlinearity parameter $\Fnl$ normalised to the local case, to allow more direct comparison between different models.) Notable new constraints from our method include those for the constant model $\Fnl = 35.1 \pm 27.4 $, the flattened model $\Fnl = 35.4\pm 29.2$, and warm inflation $\Fnl = 10.3\pm 27.2$. We investigate feature models surveying a wide parameter range in both the scale and phase, and we find no significant evidence of non-Gaussianity in the models surveyed. We propose a measure $\barFnl$ for the total integrated bispectrum and find that the measured value is consistent with the null hypothesis that CMB anisotropies obey Gaussian statistics. We argue that this general bispectrum survey with the WMAP data represents the best evidence for Gaussianity to date and we discuss future prospects, notably from the Planck satellite.

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