CosmoPower-JAX: high-dimensional Bayesian inference with differentiable cosmological emulators

We present CosmoPower-JAX, a JAX-based implementation of the CosmoPower framework, which accelerates cosmological inference by building neural emulators of cosmological power spectra. We show how, using the automatic differentiation, batch evaluation and just-in-time compilation features of JAX, and running the inference pipeline on graphics processing units (GPUs), parameter estimation can be accelerated by orders of magnitude with advanced gradient-based sampling techniques. These can be used to efficiently explore high-dimensional parameter spaces, such as those needed for the analysis of next-generation cosmological surveys. We showcase the accuracy and computational efficiency of CosmoPower-JAX on two simulated Stage IV configurations. We first consider a single survey performing a cosmic shear analysis totalling 37 model parameters. We validate the contours derived with CosmoPower-JAX and a Hamiltonian Monte Carlo sampler against those derived with a nested sampler and without emulators, obtaining a speed-up factor of O(103 ). We then consider a combination of three Stage IV surveys, each performing a joint cosmic shear and galaxy clustering (3x2pt) analysis, for a total of 157 model parameters. Even with such a high-dimensional parameter space, CosmoPower-JAX provides converged posterior contours in 3 days, as opposed to the estimated 6 years required by standard methods. CosmoPower-JAX is fully written in Python, and we make it publicly available to help the cosmological community meet the accuracy requirements set by next-generation surveys

Testing modified gravity theories with weak gravitational lensing

‘Cosmic shear’ is the weak gravitational lensing effect generated by fluctuations of the gravitational tidal fields of the large-scale structure that induce correlations in the distortion of observed galaxy shapes. Being sensitive to spacetime geometry and the growth of cosmic structure, cosmic shear is one of the primary probes to test gravity with current and future surveys. In this thesis we analyse the power of cosmic shear to constrain alternatives to the standard cosmological model that could explain cosmic acceleration. We focus in particular on a large class of alternatives to General Relativity, the Horndeski class, which includes the majority of universally coupled extensions to ΛCDM with one scalar degree of freedom in addition to the metric. Given a fixed background, the evolution of linear perturbations in Horndeski gravity is described by a set of four functions of time only. First, we forecast the sensitivity to these functions that will be achieved by future cosmic shear surveys like Euclid. We produce our forecasts with two methods to analyse a cosmic shear survey: a tomographic approach, based on correlations of the lensing signal in different redshift bins, and a fully 3D spherical Fourier-Bessel decomposition of the shear field. We show how the latter produces tighter constraints on all cosmological parameters with a sensitivity gain of the order of 20% in particular on the ones that describe Horndeski gravity. We then consider the possibility of using cross-correlations of cosmic shear with other probes to constrain Horndeski theories of gravity. We analyse a combination of cosmic shear, galaxy-galaxy lensing and galaxy clustering data from the Kilo Degree Survey and Galaxy And Mass Assembly survey and set constraints on the aforementioned Horndeski parameters. We also forecast the expected sensitivity to the same parameters that could be achieved with future cross-correlations of Stage IV cosmic shear, galaxy clustering and CMB experiments. While current constraints are not very tight, our implementation could be used in the future with data coming from Stage IV surveys, which we show to have great constraining power on these theories. Finally, we present in detail the numerical techniques that we used to produce our 3D cosmic shear forecasts and compare our predictions with an alternative, independent method developed with the same purpose. We find excellent agreement between the two methods and use our simulated 3D cosmic shear covariance matrices within a new algorithm that we develop to generate 3D lensing random fields. We calculate the Minkowski Functionals associated to our random fields and use them to test our field-generation procedure, as well as to demonstrate the possibility of a new approach to cosmological inference leveraging the estimated Minkowski Functionals

Improving Fisher matrix forecasts for galaxy surveys: window function, bin cross-correlation and bin redshift uncertainty

The Fisher matrix is a widely used tool to forecast the performance of future experiments and approximate the likelihood of large data sets. Most of the forecasts for cosmological parameters in galaxy clustering studies rely on the Fisher matrix approach for large-scale experiments like DES, Euclid or SKA. Here, we improve upon the standard method by taking into account three effects: the finite window function, the correlation between redshift bins and the uncertainty on the bin redshift. The first two effects are negligible only in the limit of infinite surveys. The third effect, in contrast, is negligible for infinitely small bins. Here, we show how to take into account these effects and what the impact on forecasts of a Euclid-type experiment will be. The main result of this paper is that the windowing and the bin cross-correlation induce a considerable change in the forecasted errors, of the order of 10–30 per cent for most cosmological parameters, while the redshift bin uncertainty can be neglected for bins smaller than Δz = 0.1 roughly

Towards fast machine-learning-assisted Bayesian posterior inference of realistic microseismic events

Bayesian inference applied to microseismic activity monitoring allows for principled estimation of the coordinates of microseismic events from recorded seismograms, and their associated uncertainties. However, forward modelling of these microseismic events, necessary to perform Bayesian source inversion, can be prohibitively expensive in terms of computational resources. A viable solution is to train a surrogate model based on machine learning techniques, to emulate the forward model and thus accelerate Bayesian inference. In this paper, we improve on previous work, which considered only sources with isotropic moment tensor. We train a machine learning algorithm on the power spectrum of the recorded pressure wave and show that the trained emulator allows for the complete and fast retrieval of the event coordinates for $\textit{any}$ source mechanism. Moreover, we show that our approach is computationally inexpensive, as it can be run in less than 1 hour on a commercial laptop, while yielding accurate results using less than $10^4$ training seismograms. We additionally demonstrate how the trained emulators can be used to identify the source mechanism through the estimation of the Bayesian evidence. This work lays the foundations for the efficient localisation and characterisation of any recorded seismogram, thus helping to quantify human impact on seismic activity and mitigate seismic hazard.Comment: 13 pages, 11 figures, 2 tables. Under revie

Investigating scalar–tensor gravity with statistics of the cosmic large-scale structure

Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy component, and the addition of neutrinos changing structures on small scales. Here we study Horndeski theories of gravity, the most general minimally coupled scalar–tensor theories of second order. While the cosmological background evolution can be described by an effective equation of state, the perturbations are characterized by four free functions of time. We consider a specific parametrization of these functions tracing the dark energy component. The likelihood of the full parameter set resulting from combining cosmic microwave background primary anisotropies including their gravitational lensing signal, tomographic angular galaxy clustering, and weak cosmic shear, together with all possible non-vanishing cross-correlations is evaluated; both with the Fisher formalism as well as without the assumption of a specific functional form of the posterior through Monte-Carlo Markov-chains (MCMCs). Our results show that even complex cosmological models can be constrained and could exclude variations of the effective Newtonian gravitational coupling larger than 10 per cent over the age of the Universe. In particular, we confirm strong correlations between parameter groups. Furthermore, we find that the expected contours from MCMC are significantly larger than those from the Fisher analysis even with the vast amount of signal provided by stage IV experiments, illustrating the importance of a proper treatment of non-Gaussian likelihoods and the high level of precision needed for unlocking the sensitivity on gravitational parameters

CosmoPower: Emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys

We present CosmoPower, a suite of neural cosmological power spectrum emulators providing orders-of-magnitude acceleration for parameter estimation from two-point statistics analyses of Large-Scale Structure (LSS) and Cosmic Microwave Background (CMB) surveys. The emulators replace the computation of matter and CMB power spectra from Boltzmann codes; thus, they do not need to be re-trained for different choices of astrophysical nuisance parameters or redshift distributions. The matter power spectrum emulation error is less than $0.4{{\ \rm per\ cent}}$ in the wavenumber range k ∈ [10−5, 10] Mpc−1, for redshift z ∈ [0, 5]. CosmoPower emulates CMB temperature, polarisation and lensing potential power spectra in the 5σ region of parameter space around the Planck best fit values with an error $\lesssim 10{{\ \rm per\ cent}}$ of the expected shot noise for the forthcoming Simons Observatory. CosmoPower is showcased on a joint cosmic shear and galaxy clustering analysis from the Kilo-Degree Survey, as well as on a Stage IV Euclid-like simulated cosmic shear analysis. For the CMB case, CosmoPower is tested on a Planck 2018 CMB temperature and polarisation analysis. The emulators always recover the fiducial cosmological constraints with differences in the posteriors smaller than sampling noise, while providing a speed-up factor up to O(104) to the complete inference pipeline. This acceleration allows posterior distributions to be recovered in just a few seconds, as we demonstrate in the Planck likelihood case. CosmoPower is written entirely in Python, can be interfaced with all commonly used cosmological samplers and is publicly available

Fast emulation of anisotropies induced in the cosmic microwave background by cosmic strings

Cosmic strings are linear topological defects that may have been produced during symmetry-breaking phase transitions in the very early Universe. In an expanding Universe the existence of causally separate regions prevents such symmetries from being broken uniformly, with a network of cosmic string inevitably forming as a result. To faithfully generate observables of such processes requires computationally expensive numerical simulations, which prohibits many types of analyses. We propose a technique to instead rapidly emulate observables, thus circumventing simulation. Emulation is a form of generative modelling, often built upon a machine learning backbone. End-to-end emulation often fails due to high dimensionality and insufficient training data. Consequently, it is common to instead emulate a latent representation from which observables may readily be synthesised. Wavelet phase harmonics are an excellent latent representations for cosmological fields, both as a summary statistic and for emulation, since they do not require training and are highly sensitive to non-Gaussian information. Leveraging wavelet phase harmonics as a latent representation, we develop techniques to emulate string induced CMB anisotropies over a 7.2 degree field of view, with sub-arcminute resolution, in under a minute on a single GPU. Beyond generating high fidelity emulations, we provide a technique to ensure these observables are distributed correctly, providing a more representative ensemble of samples. The statistics of our emulations are commensurate with those calculated on comprehensive Nambu-Goto simulations. Our findings indicate these fast emulation approaches may be suitable for wide use in, e.g., simulation based inference pipelines. We make our code available to the community so that researchers may rapidly emulate cosmic string induced CMB anisotropies for their own analysis

A quadratic estimator for the matter power spectrum from weak gravitational lensing

In this thesis a new quadratic estimator for the power spectrum, based on weak lensing measurements, is developed. According to the Cramer-Rao inequality, the estimator is guaranteed to have the minimum variance and is therefore the best unbiased estimator of the power spectrum. The properties of this estimator are explored, in particular its window functions which are optimised to be as narrow as possible in k-space. This would permit to isolate the effects of physical processes that act on different scales. A major goal here is to detect features at k~1 hMp(c^-1) arising from non-zero neutrino masses. A second is to develop statistics that are insensitive to the high-k regime (k > 1 hMp(c^-1)) that may be affected by uncertain baryon feedback processes