arXiv subjects

Alan Heavens

Publications and source records attributed to Alan Heavens.

At least 19 recordsLinked to original sources

arXiv2026

Three-dimensional wave optics for weak-field lensing of gravitational waves

We develop a perturbative Green's function approach to gravitational lensing by weak gravitational potentials that need not be localized on a thin lens plane and that applies in both the wave optics and geometric optics regimes. We recast position-space integrals as Fourier, or momentum-space, integrals that appear in scattering amplitude calculations. The method gives the Born approximation directly in three dimensions and can be systematically extended to post-Born orders. For a Schwarzschild lens, we compute the leading Born term and new post-Born contributions arising from the order $\mathcal{O}(G^2)$ correction to the potential, keeping finite-distance corrections beyond the usual paraxial expansion. We show that these general-relativistic corrections are controlled by the parameter $GM\omega\,b/\chi_{\rm eff}$ in the small-angle regime, and are therefore negligible for standard weak-lensing configurations but become relevant in more extreme geometries (such as hierarchical triples with very small source--lens separations). We also discuss higher-order Newtonian corrections, their infrared sensitivity for a long-range potential, and the regulated form of the Newtonian potential given by the Yukawa potential. Finally, we formulate the corresponding calculation in an FLRW background, identifying the leading flat-space limit and estimating the size of curvature-induced corrections including tails. This method clarifies the regime of validity of the Born, large-distance, and paraxial approximations in gravitational-wave lensing and provides a framework for treating generic lensing potentials.

gr-qc↗

arXiv2026

On combining estimated and analytic covariance matrices

The statistical analysis of cosmological data often assumes a Gaussian sampling distribution and relies on covariance matrices estimated from simulations. In this setting, the likelihood function of the data is not Gaussian but is instead a multivariate Student-t distribution, arising from marginalisation over an inverse-Wishart distribution for the true covariance matrix. This framework, introduced by Sellentin & Heavens (2016) and extended by Percival et al. (2022), provides a principled drop-in replacement to the Gaussian likelihood with Hartlap correction (Hartlap et al. 2007). The latter removes bias in the precision matrix; it is still widely used, despite failing to reproduce the heavy tails of the true distribution (thus yielding inaccurate probabilities, especially in the case of tensions between datasets). In practice, cosmological analyses frequently involve additional Gaussian error contributions, for example from instrumental noise, foregrounds, super-sample covariance, or emulator uncertainties. The resulting likelihood function is a convolution of the Sellentin-Heavens or Percival likelihoods with an extra Gaussian contribution, and does not have a simple expression. In this note, we derive an accurate approximation for the combined likelihood function, another multivariate Student-t distribution which inherits the heavy tails. The parameters of the Student-t distribution are determined by matching the covariance and multivariate kurtosis to those of the true distribution. We also include a slightly more expensive but fast sampling algorithm, based on the mixture representation of the Student-t distribution, which avoids the approximation altogether, but is not the drop-in replacement for the normal Gaussian or Hartlap likelihood function that the Student-t approximation in this paper provides. (Abridged)

astro-ph.CO↗

arXiv2026

Opportunities in AI/ML for the Rubin LSST Dark Energy Science Collaboration

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.

astro-ph.IM↗

arXiv2025

Two per cent measurement of $H_0$ from Cepheids alone

One of the most pressing problems in current cosmology is the cause of the Hubble tension. We revisit a two-rung distance ladder, composed only of Cepheid periods and magnitudes, anchor distances in the Milky Way, Large Magellanic Cloud, NGC 4258, and host galaxy redshifts. We adopt the SH0ES data for the most up-to-date and carefully vetted measurements, where the Cepheid hosts were selected to harbour also Type Ia supernovae. We introduce two important improvements: a rigorous selection modelling and a state-of-the-art density and peculiar velocity model using Manticore-Local, based on the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm. We infer $H_0 = 71.1 \pm 1.4~\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, assuming the Cepheid host sample was selected by supernova magnitudes. However, the actual selection criteria are not clear, and other assumptions can increase $H_0$ by up to one statistical standard deviation. The posterior has a lower central value and a 41 per cent smaller uncertainty than a previous study using the same distance-ladder data. This result is lower than the supernova-based SH0ES inferred value of $H_0 = 73.2 \pm 0.9~\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ at about $1.3\sigma$, and is in $2.8\sigma$ tension with the latest cosmic microwave background results in the standard cosmological model. These results demonstrate that a measurement of $H_0$ of sufficient precision to weigh in on the Hubble tension is achievable using second-rung data alone, underscoring the importance of robust and accurate statistical and velocity-field modelling.

astro-ph.CO↗

arXiv2025

The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. [Abridged]

astro-ph.CO↗

arXiv2024

Hybrid Summary Statistics

We present a way to capture high-information posteriors from training sets that are sparsely sampled over the parameter space for robust simulation-based inference. In physical inference problems, we can often apply domain knowledge to define traditional summary statistics to capture some of the information in a dataset. We show that augmenting these statistics with neural network outputs to maximise the mutual information improves information extraction compared to neural summaries alone or their concatenation to existing summaries and makes inference robust in settings with low training data. We introduce 1) two loss formalisms to achieve this and 2) apply the technique to two different cosmological datasets to extract non-Gaussian parameter information.

stat.ML↗

arXiv2024

Hybrid summary statistics: neural weak lensing inference beyond the power spectrum

In inference problems, we often have domain knowledge which allows us to define summary statistics that capture most of the information content in a dataset. In this paper, we present a hybrid approach, where such physics-based summaries are augmented by a set of compressed neural summary statistics that are optimised to extract the extra information that is not captured by the predefined summaries. The resulting statistics are very powerful inputs to simulation-based or implicit inference of model parameters. We apply this generalisation of Information Maximising Neural Networks (IMNNs) to parameter constraints from tomographic weak gravitational lensing convergence maps to find summary statistics that are explicitly optimised to complement angular power spectrum estimates. We study several dark matter simulation resolutions in low- and high-noise regimes. We show that i) the information-update formalism extracts at least $3\times$ and up to $8\times$ as much information as the angular power spectrum in all noise regimes, ii) the network summaries are highly complementary to existing 2-point summaries, and iii) our formalism allows for networks with smaller, physically-informed architectures to match much larger regression networks with far fewer simulations needed to obtain asymptotically optimal inference.

astro-ph.CO↗

arXiv2023

Field-level inference of cosmic shear with intrinsic alignments and baryons

We construct a field-based Bayesian Hierarchical Model for cosmic shear that includes, for the first time, the important astrophysical systematics of intrinsic alignments and baryon feedback, in addition to a gravity model. We add to the BORG-WL framework the tidal alignment and tidal torquing model (TATT) for intrinsic alignments and compare them with the non-linear alignment (NLA) model. With synthetic data, we have shown that adding intrinsic alignments and sampling the TATT parameters does not reduce the constraining power of the method and the field-based approach lifts the weak lensing degeneracy. We add baryon effects at the field level using the enthalpy gradient descent (EGD) model. This model displaces the dark matter particles without knowing whether they belong to a halo and allows for self-calibration of the model parameters, which are inferred from the data. We have also illustrated the effects of model misspecification for the baryons. The resulting model now contains the most important physical effects and is suitable for application to data.

astro-ph.CO↗

arXiv2022

The Cosmic Graph: Optimal Information Extraction from Large-Scale Structure using Catalogues

We present an implicit likelihood approach to quantifying cosmological information over discrete catalogue data, assembled as graphs. To do so, we explore cosmological parameter constraints using mock dark matter halo catalogues. We employ Information Maximising Neural Networks (IMNNs) to quantify Fisher information extraction as a function of graph representation. We a) demonstrate the high sensitivity of modular graph structure to the underlying cosmology in the noise-free limit, b) show that graph neural network summaries automatically combine mass and clustering information through comparisons to traditional statistics, c) demonstrate that networks can still extract information when catalogues are subject to noisy survey cuts, and d) illustrate how nonlinear IMNN summaries can be used as asymptotically optimal compressed statistics for Bayesian simulation-based inference. We reduce the area of joint $Ω_m, σ_8$ parameter constraints with small ($\sim$100 object) halo catalogues by a factor of 42 over the two-point correlation function, and demonstrate that the networks automatically combine mass and clustering information. This work utilises a new IMNN implementation over graph data in Jax, which can take advantage of either numerical or auto-differentiability. We also show that graph IMNNs successfully compress simulations away from the fiducial model at which the network is fitted, indicating a promising alternative to n-point statistics in catalogue simulation-based analyses.

astro-ph.CO↗

arXiv2022

Field-Based Physical Inference From Peculiar Velocity Tracers

We present a Bayesian hierarchical modelling approach to reconstruct the initial cosmic matter density field constrained by peculiar velocity observations. As our approach features a model for the gravitational evolution of dark matter to connect the initial conditions to late-time observations, it reconstructs the final density and velocity fields as natural byproducts. We implement this field-based physical inference approach by adapting the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm, which explores the high-dimensional posterior through the use of Hamiltonian Monte Carlo sampling. We test the self-consistency of the method using random sets of mock tracers, and assess its accuracy in a more complex scenario where peculiar velocity tracers are non-linearly evolved mock haloes. We find that our framework self-consistently infers the initial conditions, density and velocity fields, and shows some robustness to model mis-specification. As compared to the state-of-the-art approach of constrained Gaussian random fields/Wiener filtering, our method produces more accurate final density and velocity field reconstructions. It also allows us to constrain the initial conditions by peculiar velocity observations, complementing in this aspect previous field-based approaches based on other cosmological observables.

astro-ph.CO↗

arXiv2022

Report of the Topical Group on Cosmic Probes of Fundamental Physics for for Snowmass 2021

Cosmic Probes of Fundamental Physics take two primary forms: Very high energy particles (cosmic rays, neutrinos, and gamma rays) and gravitational waves. Already today, these probes give access to fundamental physics not available by any other means, helping elucidate the underlying theory that completes the Standard Model. The last decade has witnessed a revolution of exciting discoveries such as the detection of high-energy neutrinos and gravitational waves. The scope for major developments in the next decades is dramatic, as we detail in this report.

hep-ph↗

arXiv2022

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $σ_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,σ$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $Ω_m$, and the amplitude or rate of the growth of structure ($σ_8,fσ_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged]

astro-ph.CO↗

arXiv2022

Light bending by the cosmological constant

We revisit the question of whether the cosmological constant $Λ$ affects the cosmological gravitational bending of light, by numerical integration of the geodesic equations for a Swiss cheese model consisting of a point mass and a compensated vacuole, in a Friedmann-Robertson-Walker background. We find that there is virtually no dependence of the light bending on the cosmological constant that is not already accounted for in the angular diameter distances of the standard lensing equations, plus small modifications that arise because the bending is restricted to a finite region covered by the hole. The residual $Λ$ dependence for a $10^{13}\,M_{\odot}$ lens is at the level of 1 part in $10^7$, and even this might be accounted for by small changes in the hole size evolution as the photon crosses. We therefore conclude that there is no need for modification of the standard cosmological lensing equations in the presence of a cosmological constant.

astro-ph.CO↗

arXiv2021

Matching Bayesian and frequentist coverage probabilities when using an approximate data covariance matrix

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the intervals indicate concordance or discordance between models and with measurements from other data. Intermediate statistics (e.g. the power spectrum) are usually measured and inferences made by fitting models to these rather than the raw data, assuming that the likelihood for these statistics has multivariate Gaussian form. The covariance matrix used to calculate the likelihood is often estimated from simulations, such that it is itself a random variable. This is a standard problem in Bayesian statistics, which requires a prior to be placed on the true model parameters and covariance matrix, influencing the joint posterior distribution. As an alternative to the commonly-used Independence-Jeffreys prior, we introduce a prior that leads to a posterior that has approximately frequentist matching coverage. This is achieved by matching the covariance of the posterior to that of the distribution of true values of the parameters around the maximum likelihood values in repeated trials, under certain assumptions. Using this prior, credible intervals derived from a Bayesian analysis can be interpreted approximately as confidence intervals, containing the truth a certain proportion of the time for repeated trials. Linking frequentist and Bayesian approaches that have previously appeared in the astronomical literature, this offers a consistent and conservative approach for credible intervals quoted on model parameters for problems where the covariance matrix is itself an estimate.

astro-ph.IM↗

arXiv2021

The Kaiser-Rocket effect: three decades and counting

The peculiar motion of the observer, if not accurately accounted for, is bound to induce a well-defined clustering signal in the distribution of galaxies. This signal is related to the Kaiser rocket effect. Here we examine the amplitude and form of this effect, both analytically and numerically, and discuss possible implications for the analysis and interpretation of forthcoming cosmological surveys. For an idealistic cosmic variance dominated full-sky survey with a Gaussian selection function peaked at $z\sim 1.5$ it is a $> 5σ$ effect and it can in principle bias very significantly the inference of cosmological parameters, especially for primordial non-Gaussianity. For forthcoming surveys, with realistic masks and selection functions, the Kaiser rocket is not a significant concern for cosmological parameter inference. However, it is a systematic effect whose origin, nature and imprint on galaxy maps are well known and thus should be subtracted or mitigated. We present several approaches to do so.

astro-ph.CO↗

arXiv2021

Lifting weak lensing degeneracies with a field-based likelihood

We present a field-based approach to the analysis of cosmic shear data to infer jointly cosmological parameters and the dark matter distribution. This forward modelling approach samples the cosmological parameters and the initial matter fluctuations, using a physical gravity model to link the primordial fluctuations to the non-linear matter distribution. Cosmological parameters are sampled and updated consistently through the forward model, varying (1) the initial matter power spectrum, (2) the geometry through the distance-redshift relationship, and (3) the growth of structure and light-cone effects. Our approach extracts more information from the data than methods based on two-point statistics. We find that this field-based approach lifts the strong degeneracy between the cosmological matter density, $Ω_\mathrm{m}$, and the fluctuation amplitude, $σ_8$, providing tight constraints on these parameters from weak lensing data alone. In the simulated four-bin tomographic experiment we consider, the field-based likelihood yields marginal uncertainties on $σ_8$ and $Ω_\mathrm{m}$ that are, respectively, a factor of 3 and 5 smaller than those from a two-point power spectrum analysis applied to the same underlying data.

astro-ph.CO↗

arXiv2021

On the accuracy and precision of correlation functions and field-level inference in cosmology

We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and their two-point correlation function. Although a simplified analytic model, the log-normal model produces fields that share many of the essential characteristics of the present-day non-Gaussian cosmological density fields. We use three different statistical techniques: (i) a standard likelihood-based analysis of the two-point correlation function; (ii) a likelihood-free (simulation-based) analysis of the two-point correlation function; (iii) a field-level analysis, made possible by the more sophisticated data assimilation technique. We find that (a) standard assumptions made to write down a likelihood for correlation functions can cause significant biases, a problem that is alleviated with simulation-based inference; and (b) analysing the entire field offers considerable advantages over correlation functions, through higher accuracy, higher precision, or both. The gains depend on the degree of non-Gaussianity, but in all cases, including for weak non-Gaussianity, the advantage of analysing the full field is substantial.

astro-ph.CO↗

arXiv2021

Quantum coherence of photons at cosmological distances

We identify potential sources of decoherence for $U(1)$ gauge bosons from a cosmological standpoint. Besides interactions with different species in the cosmological medium, we also consider effects due to the expansion of the Universe, which can produce particles (especially scalars) than can potentially interact with the photon in a quantum state. We look in particular at the case of axion-like particles and their predicted decay channels in our analysis. These interactions are shown to have a negligible effect as far as decoherence goes. Interaction rates with CMB radiation or through Thomson scattering are small, so that the interstellar medium remains the biggest decoherence factor. Thus, quantum teleportation experiments with photon energies in the range $1$-$10$ keV should be feasible at cosmological distances up to the galaxy formation epoch or beyond ($z \sim 100$).

hep-ph↗