arXiv subjects

Alan F. Heavens

Publications and source records attributed to Alan F. Heavens.

At least 19 recordsLinked to original sources

arXiv2026

Cluster gravitational redshifts: uncertainties and survey requirements

We investigate the impact of observational and theoretical uncertainties in cluster gravitational redshifts as a probe of modified gravity using an end-to-end forecasting pipeline. We use a generative model to build a halo catalogue with $M_{500}\ge 3\times 10^{13}\,M_\odot$, populate haloes with member galaxies via a five-parameter halo occupation distribution (HOD), assign projected positions from radial density profiles, apply survey-like selections, and infer a linear rescaling of the gravitational potential, $α_\mathrm{MG}$, to parameterise modifications to general relativity (GR). We vary redshift uncertainties, radial and mass-redshift completeness, member abundance, minimum mass and maximum redshift, as well as mis-specify the clusters density and velocity profiles, centres, and mass function. We find that the intracluster velocity dispersion sets an effective floor: improving redshift precision beyond $σ_z\sim 10^{-4}(1+z)$ brings no improvement in the precision of $α_\mathrm{MG}$. Realistic redshift and mass cuts primarily remove low-mass haloes and have minimal impact on the $α_\mathrm{MG}$ precision. In this setting, we find that shallow, narrower spectroscopic surveys are preferable to deep, wide photometric ones for precise modified gravity constraints. We further find that mis-centring can mimic significant departures from GR. Baryonic deviations from a Navarro-Frenk-White profile and velocity anisotropies do not introduce appreciable biases. In the high-S/N regime of upcoming surveys, accurate determination of cluster centres will be essential to avoid interpreting systematic effects as new physics. The Spectroscopic Stage-5 Experiment and the Widefield Spectroscopic Telescope provide a clear route toward establishing gravitational redshifts as a competitive probe of modified gravity.

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arXiv2026

KiDS+VIKING-450 cosmology with Bayesian hierarchical model redshift distributions

Tomographic redshift distributions from photometric data are crucial ingredients in cosmic shear analysis, since they are required for the theoretical calculation of the signal based on the redshift distribution of the galaxies where the shear field is sampled. In this paper, we develop as a proof of concept Leistedt et al.'s template-based Bayesian Hierarchical Model framework into an application to weak lensing data by sampling the redshift distributions of the galaxies in the KiDS+VIKING-450 survey. We also use a principal component analysis to provide a set of representative templates drawn from a large superset. For computational tractability, subsets of $10^5$ galaxies are chosen to determine the redshift distributions, and we test the sensitivity of the cosmological inference to the subset chosen, finding it to be subdominant compared to the statistical error. We marginalise over the inferred redshift distributions and find that the Bayesian method increases the clustering parameter compared with previous studies, alleviating the $S_8$ tension with Planck, where $S_{8}\equivσ_{8}\sqrt{Ω_{\tm{m}}/0.3}=0.756\pm 0.039$, assuming flat $Λ$CDM. The tension with Planck for this survey is reduced from $2.3σ$ to $1.9σ$. We also infer a value for the matter density, $Ω_{\tm{m}}=0.31\pm 0.10$.

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arXiv2026

Almanac: HMC sampling with bounded velocity

In Hamiltonian Monte Carlo sampling, the shape of the potential and the choice of the momentum distribution jointly give rise to the Hamiltonian dynamics of the sampler. An efficient sampler propagates quickly in all regions of the parameter space, so that the chain has a low autocorrelation length and the sampler has a high acceptance rate, with the goal of optimising the number of near-independent samples for given computational cost. Standard Gaussian momentum distributions allow arbitrarily large velocities, which can lead to inefficient exploration in posteriors with ridges or funnel-like geometries. We investigate alternative momentum distributions based on relativistic and Student's t kinetic energies, which naturally limit particle velocities and may improve robustness. Using Almanac, a sampler for cosmological posterior distributions of sky maps and power spectra on the sphere, we test these alternatives in both low- and high-dimensional settings. We find that the choice of parameterization and momentum distribution can improve convergence and effective sample rate, though the achievable gains are generally modest and strongly problem-dependent, reaching up to an order of magnitude in favorable cases. Among the momentum distributions that we tested, those with moderately heavy tails achieved the best balance between efficiency and stability. These results highlight the importance of sampler design and encourage future work on adaptive and self-tuning strategies for kinetic energy parameter optimization in high-dimensional settings.

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arXiv2025

Beyond general relativity: probing gravity with gravitational redshifts

Despite the success of general relativity (GR), the unexplained nature of dark energy on cosmological scales leaves open the question of whether GR provides a complete description of gravity. This quest is further motivated by growing tensions among cosmological observations when interpreted within $Λ$CDM. Gravitational redshifts of cluster member galaxies probe cluster potentials on megaparsec scales directly, complementing conventional large-scale structure tests. Here, we investigate how redshift precision and survey design propagate into constraints on modified gravity using an end-to-end pipeline run on mock catalogues, focusing on mis-centring and spectroscopic completeness. We find that competitive measurements require wide-field spectroscopic cluster surveys explicitly designed to maximise the number of spectroscopically confirmed members per cluster, to enable high-purity stacking, and to control systematic effects.

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arXiv2025

Field-level inference of $H_0$ from simulated type Ia supernovae in a local Universe analogue

Two particular challenges face type Ia supernovae (SNeIa) as probes of the expansion rate of the Universe. One is that they may not be fair tracers of the matter velocity field, and the second is that their peculiar velocities distort the Hubble expansion. Although the latter has been estimated at $\lesssim1.5\%$ for $z>0.023$, this is based either on constrained linear or unconstrained (random) non-linear velocity simulations. In this paper, we address both challenges by incorporating a physical model for the locations of supernovae, and develop a Bayesian Hierarchical Model that accounts for non-linear peculiar velocities in our local Universe, inferred from a Bayesian analysis of the 2M++ spectroscopic galaxy catalogue. With simulated data, the model recovers the ground truth value of the Hubble constant $H_0$ in the presence of peculiar velocities including their correlated uncertainties arising from the Bayesian inference, opening up the potential of including lower redshift SNeIa to measure $H_0$. Ignoring peculiar velocities, the inferred $H_0$ increases minimally by $\sim 0.4 \pm 0.5$ km s$^{-1}$ Mpc$^{-1}$ in the range $0.023<z<0.046$. We conclude it is unlikely that the $H_0$ tension originates in unaccounted-for non-linear velocity dynamics.

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arXiv2023

Extreme data compression for Bayesian model comparison

We develop extreme data compression for use in Bayesian model comparison via the MOPED algorithm, as well as more general score compression. We find that Bayes factors from data compressed with the MOPED algorithm are identical to those from their uncompressed datasets when the models are linear and the errors Gaussian. In other nonlinear cases, whether nested or not, we find negligible differences in the Bayes factors, and show this explicitly for the Pantheon-SH0ES supernova dataset. We also investigate the sampling properties of the Bayesian Evidence as a frequentist statistic, and find that extreme data compression reduces the sampling variance of the Evidence, but has no impact on the sampling distribution of Bayes factors. Since model comparison can be a very computationally-intensive task, MOPED extreme data compression may present significant advantages in computational time.

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arXiv2022

Perfectly parallel cosmological simulations using spatial comoving Lagrangian acceleration

Existing cosmological simulation methods lack a high degree of parallelism due to the long-range nature of the gravitational force, which limits the size of simulations that can be run at high resolution. To solve this problem, we propose a new, perfectly parallel approach to simulate cosmic structure formation, which is based on the spatial COmoving Lagrangian Acceleration (sCOLA) framework. Building upon a hybrid analytical and numerical description of particles' trajectories, our algorithm allows for an efficient tiling of a cosmological volume, where the dynamics within each tile is computed independently. As a consequence, the degree of parallelism is equal to the number of tiles. We optimised the accuracy of sCOLA through the use of a buffer region around tiles and of appropriate Dirichlet boundary conditions around sCOLA boxes. As a result, we show that cosmological simulations at the degree of accuracy required for the analysis of the next generation of surveys can be run in drastically reduced wall-clock times and with very low memory requirements. The perfect scalability of our algorithm unlocks profoundly new possibilities for computing larger cosmological simulations at high resolution, taking advantage of a variety of hardware architectures.

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arXiv2021

Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS

The 3D matter power spectrum, $P_δ(k,z)$ is a fundamental quantity in the analysis of cosmological data such as large-scale structure, 21cm observations, and weak lensing. Existing computer models (Boltzmann codes) such as CLASS can provide it at the expense of immoderate computational cost. In this paper, we propose a fast Bayesian method to generate the 3D matter power spectrum, for a given set of wavenumbers, $k$ and redshifts, $z$. Our code allows one to calculate the following quantities: the linear matter power spectrum at a given redshift (the default is set to 0); the non-linear 3D matter power spectrum with/without baryon feedback; the weak lensing power spectrum. The gradient of the 3D matter power spectrum with respect to the input cosmological parameters is also returned and this is useful for Hamiltonian Monte Carlo samplers. The derivatives are also useful for Fisher matrix calculations. In our application, the emulator is accurate when evaluated at a set of cosmological parameters, drawn from the prior, with the fractional uncertainty, $ΔP_δ/P_δ$ centred on 0. It is also $\sim 300$ times faster compared to CLASS, hence making the emulator amenable to sampling cosmological and nuisance parameters in a Monte Carlo routine. In addition, once the 3D matter power spectrum is calculated, it can be used with a specific redshift distribution, $n(z)$ to calculate the weak lensing and intrinsic alignment power spectra, which can then be used to derive constraints on cosmological parameters in a weak lensing data analysis problem. The software ($\texttt{emuPK}$) can be trained with any set of points and is distributed on Github, and comes with a pre-trained set of Gaussian Process (GP) models, based on 1000 Latin Hypercube (LH) samples, which follow roughly the current priors for current weak lensing analyses.

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arXiv2020

The distribution of dark galaxies and spin bias

In the light of the discovery of numerous (almost) dark galaxies from the ALFALAFA and LITTLE THINGS surveys, we revisit the predictions of Jimenez et al. 1997, based on the Toomre stability of rapidly-spinning gas disks. We have updated the predictions for $Λ$CDM with parameters given by Planck18, computing the expected number densities of dark objects, and their spin parameter and mass distributions. Comparing with the data is more challenging, but where the spins are more reliably determined, the spins are close to the threshold for disks to be stable according to the Toomre criterion, where the expected number density is highest, and reinforces the concept that there is a bias in the formation of luminous galaxies based on the spin of their parent halo.

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arXiv2020

Parameter Inference for Weak Lensing using Gaussian Processes and MOPED

In this paper, we propose a Gaussian Process (GP) emulator for the calculation of a) tomographic weak lensing band-power spectra, and b) coefficients of summary data massively compressed with the MOPED algorithm. In the former case cosmological parameter inference is accelerated by a factor of $\sim 10$-$30$ compared to explicit calls to the Boltzmann solver CLASS when applied to KiDS-450 weak lensing data. Much larger gains will come with future data, where with MOPED compression, the speed up can be up to a factor of $\sim 10^3$ when the common Limber approximation is used. Furthermore, the GP opens up the possibility of dropping the Limber approximation, without which the theoretical calculations may be unfeasibly slow. A potential advantage of GPs is that an error on the emulated function can be computed and this uncertainty incorporated into the likelihood. If speed is of the essence, then the mean of the Gaussian Process can be used and the uncertainty ignored. We compute the Kullback-Leibler divergence between the emulator likelihood and the CLASS likelihood, and on the basis of this and from analysing the uncertainties on the parameters, we find that in this case, the inclusion of the GP uncertainty does not justify the extra computational expense in the test application. For future weak lensing surveys such as Euclid and Legacy Survey of Space and Telescope (LSST), the number of summary statistics will be large, up to $\sim 10^{4}$. The speed of MOPED is determined by the number of parameters, not the number of summary data, so the gains are very large. In the non-Limber case, the speed-up can be a factor of $\sim 10^5$, provided that a fast way to compute the theoretical MOPED coefficients is available. The GP presented here provides such a fast mechanism and enables MOPED to be employed.

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arXiv2019

Gaussian Mixture Models for Blended Photometric Redshifts

Future cosmological galaxy surveys such as the Large Synoptic Survey Telescope (LSST) will photometrically observe very large numbers of galaxies. Without spectroscopy, the redshifts required for the analysis of these data will need to be inferred using photometric redshift techniques that are scalable to large sample sizes. The high number density of sources will also mean that around half are blended. We present a Bayesian photometric redshift method for blended sources that uses Gaussian mixture models to learn the joint flux-redshift distribution from a set of unblended training galaxies, and Bayesian model comparison to infer the number of galaxies comprising a blended source. The use of Gaussian mixture models renders both of these applications computationally efficient and therefore suitable for upcoming galaxy surveys.

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arXiv2019

Measuring the Homogeneity of the Universe Using Polarization Drift

We propose a method to probe the homogeneity of a general universe, without assuming symmetry. We show that isotropy can be tested at remote locations on the past lightcone by comparing the line-of-sight and transverse expansion rates, using the time dependence of the polarization of Cosmic Microwave Background photons that have been inverse-Compton scattered by the hot gas in massive clusters of galaxies. This probes a combination of remote transverse and parallel components of the expansion rate of the metric, and we may use radial baryon acoustic oscillations or cosmic clocks to measure the parallel expansion rate. Thus we can test remote isotropy, which is a key requirement of a homogeneous universe. We provide explicit formulas that connect observables and properties of the metric.

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arXiv2018

The gravitational and lensing-ISW bispectrum of 21cm radiation

Cosmic Microwave Background experiments from COBE to Planck, have launched cosmology into an era of precision science, where many cosmological parameters are now determined to the percent level. Next generation telescopes, focussing on the cosmological 21cm signal from neutral hydrogen, will probe enormous volumes in the low-redshift Universe, and have the potential to determine dark energy properties and test modifications of Einstein's gravity. We study the 21cm bispectrum due to gravitational collapse as well as the contribution by line of sight perturbations in the form of the lensing-ISW bispectrum at low-redshifts ($z \sim 0.35-3$), targeted by upcoming neutral hydrogen intensity mapping experiments. We compute the expected bispectrum amplitudes and use a Fisher forecast model to compare power spectrum and bispectrum observations of intensity mapping surveys by CHIME, MeerKAT and SKA-mid. We find that combined power spectrum and bispectrum observations have the potential to decrease errors on the cosmological parameters by an order of magnitude compared to Planck. Finally, we compute the contribution of the lensing-ISW bispectrum, and find that, unlike for the cosmic microwave background analyses, it can safely be ignored for 21cm bispectrum observations.

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arXiv2018

Bayesian photometric redshifts of blended sources

Photometric redshifts are necessary for enabling large-scale multicolour galaxy surveys to interpret their data and constrain cosmological parameters. While the increased depth of future surveys such as the Large Synoptic Survey Telescope (LSST) will produce higher precision constraints, it will also increase the fraction of sources that are blended. In this paper, we present a Bayesian photometric redshift method for blended sources with an arbitrary number of intrinsic components. This method generalises existing template-based Bayesian photometric redshift (BPZ) methods, and produces joint posterior distributions for the component redshifts that allow uncertainties to be propagated in a principled way. Using Bayesian model comparison, we infer the probability that a source is blended and the number of components that it contains. We extend our formalism to the case where sources are blended in some bands and resolved in others. Applying this to the combination of LSST- and Euclid-like surveys, we find that the addition of resolved photometry results in a significant improvement in the reduction of outliers over the fully-blended case. We make available blendz, a Python implementation of our method.

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arXiv2018

Fast Sampling from Wiener Posteriors for Image Data with Dataflow Engines

We use Dataflow Engines (DFE) to construct an efficient Wiener filter of noisy and incomplete image data, and to quickly draw probabilistic samples of the compatible true underlying images from the Wiener posterior. Dataflow computing is a powerful approach using reconfigurable hardware, which can be deeply pipelined and is intrinsically parallel. The unique Wiener-filtered image is the minimum-variance linear estimate of the true image (if the signal and noise covariances are known) and the most probable true image (if the signal and noise are Gaussian distributed). However, many images are compatible with the data with different probabilities, given by the analytic posterior probability distribution referred to as the Wiener posterior. The DFE code also draws large numbers of samples of true images from this posterior, which allows for further statistical analysis. Naive computation of the Wiener-filtered image is impractical for large datasets, as it scales as $n^3$, where $n$ is the number of pixels. We use a messenger field algorithm, which is well suited to a DFE implementation, to draw samples from the Wiener posterior, that is, with the correct probability we draw samples of noiseless images that are compatible with the observed noisy image. The Wiener-filtered image can be obtained by a trivial modification of the algorithm. We demonstrate a lower bound on the speed-up, from drawing 10$^5$ samples of a 128$^2$ image, of 11.3 ${\pm}$ 0.8 with 8 DFEs in a 1U MPC-X box when compared with a 1U server presenting 32 CPU threads. We also discuss a potential application in astronomy, to provide better dark matter maps and improved determination of the parameters of the Universe.

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arXiv2018

Objective Bayesian analysis of neutrino masses and hierarchy

Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is mathematically minimally informative. Using the constructed uninformative prior, we find that the normal hierarchy is favoured but with inconclusive posterior odds of 5.1:1. Better data is hence needed before the neutrino masses and their hierarchy can be well constrained. We find that the next decade of cosmological data should provide conclusive evidence if the normal hierarchy with negligible minimum mass is correct, and if the uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will be difficult with the same uncertainties. Our uninformative prior was constructed from principles of the Objective Bayesian approach. The prior is called a reference prior and is minimally informative in the specific sense that the information gain after collection of data is maximised. The prior is computed for the combination of neutrino oscillation data and cosmological data and still applies if the data improve.

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arXiv2017

On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods

We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a dataset, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of datapoints which depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnostic, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation functions are significant. With a simple exclusion of the most contaminated datapoints, the posterior for $s_8$ is shifted without broadening, but we find no significant reduction in the tension with $s_8$ derived from Planck Cosmic Microwave Background data. However, we also show that the one-point distributions of the correlation statistics are noticeably skewed, such that sound weak lensing data sets are intrinsically likely to lead to a systematically low lensing amplitude being inferred. The detected non-Gaussianities get larger with increasing angular scale such that for future wide-angle surveys such as Euclid or LSST, with their very small statistical errors, the large-scale modes are expected to be increasingly affected. The shifts in posteriors may then not be negligible and we recommend that these diagnostic tests be run as part of future analyses.

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arXiv2017

On the use of the Edgeworth expansion in cosmology I: how to foresee and evade its pitfalls

Non-linear gravitational collapse introduces non-Gaussian statistics into the matter fields of the late Universe. As the large-scale structure is the target of current and future observational campaigns, one would ideally like to have the full probability density function of these non-Gaussian fields. The only viable way we see to achieve this analytically, at least approximately and in the near future, is via the Edgeworth expansion. We hence rederive this expansion for Fourier modes of non-Gaussian fields and then continue by putting it into a wider statistical context than previously done. We show that in its original form, the Edgeworth expansion only works if the non-Gaussian signal is averaged away. This is counterproductive, since we target the parameter-dependent non-Gaussianities as a signal of interest. We hence alter the analysis at the decisive step and now provide a roadmap towards a controlled and unadulterated analysis of non-Gaussianities in structure formation (with the Edgeworth expansion). Our central result is that, although the Edgeworth expansion has pathological properties, these can be predicted and avoided in a careful manner. We also show that, despite the non-Gaussianity coupling all modes, the Edgeworth series may be applied to any desired subset of modes, since this is equivalent (to the level of the approximation) to marginalising over the exlcuded modes. In this first paper of a series, we restrict ourselves to the sampling properties of the Edgeworth expansion, i.e.~how faithfully it reproduces the distribution of non-Gaussian data. A follow-up paper will detail its Bayesian use, when parameters are to be inferred.

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