Considerations in the Interpretation of Cosmological Anomalies

Anomalies drive scientific discovery – they are associated with the cutting edge of the research frontier, and thus typically exploit data in the low signal-to-noise regime. In astronomy, the prevalence of systematics –- both “known unknowns” and “unknown unknowns” – combined with increasingly large datasets, the widespread use of ad hoc estimators for anomaly detection, and the “look-elsewhere” effect, can lead to spurious false detections. In this informal note, I argue that anomaly detection leading to discoveries of new physics requires a combination of physical understanding, careful experimental design to avoid confirmation bias, and self-consistent statistical methods. These points are illustrated with several concrete examples from cosmology

Unbiased methods for removing systematics from galaxy clustering measurements

Measuring the angular clustering of galaxies as a function of redshift is a powerful method for extracting information from the three-dimensional galaxy distribution. The precision of such measurements will dramatically increase with ongoing and future wide-field galaxy surveys. However, these are also increasingly sensitive to observational and astrophysical contaminants. Here, we study the statistical properties of three methods proposed for controlling such systematics – template subtraction, basic mode projection, and extended mode projection – all of which make use of externally supplied template maps, designed to characterize and capture the spatial variations of potential systematic effects. Based on a detailed mathematical analysis, and in agreement with simulations, we find that the template subtraction method in its original formulation returns biased estimates of the galaxy angular clustering. We derive closed-form expressions that should be used to correct results for this shortcoming. Turning to the basic mode projection algorithm, we prove it to be free of any bias, whereas we conclude that results computed with extended mode projection are biased. Within a simplified setup, we derive analytical expressions for the bias and discuss the options for correcting it in more realistic configurations. Common to all three methods is an increased estimator variance induced by the cleaning process, albeit at different levels. These results enable unbiased high-precision clustering measurements in the presence of spatially varying systematics, an essential step towards realizing the full potential of current and planned galaxy surveys

Genetically modified haloes: towards controlled experiments in ΛCDM galaxy formation

We propose a method to generate ‘genetically modified’ (GM) initial conditions for high-resolution simulations of galaxy formation in a cosmological context. Building on the Hoffman–Ribak algorithm, we start from a reference simulation with fully random initial conditions, then make controlled changes to specific properties of a single halo (such as its mass and merger history). The algorithm demonstrably makes minimal changes to other properties of the halo and its environment, allowing us to isolate the impact of a given modification. As a significant improvement over previous work, we are able to calculate the abundance of the resulting objects relative to the reference simulation. Our approach can be applied to a wide range of cosmic structures and epochs; here we study two problems as a proof of concept. First, we investigate the change in density profile and concentration as the collapse times of three individual haloes are varied at fixed final mass, showing good agreement with previous statistical studies using large simulation suites. Secondly, we modify the z = 0 mass of haloes to show that our theoretical abundance calculations correctly recover the halo mass function. The results demonstrate that the technique is robust, opening the way to controlled experiments in galaxy formation using hydrodynamic zoom simulations

Accretion of a symmetry-breaking scalar field by a Schwarzschild black hole

We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry-breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory

Angular momentum evolution can be predicted from cosmological initial conditions

The angular momentum of dark matter haloes controls their spin magnitude and orientation, which in turn influences the galaxies therein. However, the process by which dark matter haloes acquire angular momentum is not fully understood; in particular, it is unclear whether angular momentum growth is stochastic. To address this question, we extend the genetic modification technique to allow control over the angular momentum of any region in the initial conditions. Using this technique to produce a sequence of modified simulations, we can then investigate whether changes to the angular momentum of a specified region in the evolved universe can be accurately predicted from changes in the initial conditions alone. We find that the angular momentum in regions with modified initial conditions can be predicted between 2 and 4 times more accurately than expected from applying tidal torque theory. This result is masked when analysing the angular momentum of haloes, because particles in the outskirts of haloes dominate the angular momentum budget. We conclude that the angular momentum of Lagrangian patches is highly predictable from the initial conditions, with apparent chaotic behaviour being driven by stochastic changes to the arbitrary boundary defining the halo

An interpretable machine learning framework for dark matter halo formation

We present a generalization of our recently proposed machine-learning framework, aiming to provide new physical insights into dark matter halo formation. We investigate the impact of the initial density and tidal shear fields on the formation of haloes over the mass range 11.4 ≤ log (M/M⊙) ≤ 13.4. The algorithm is trained on an N-body simulation to infer the final mass of the halo to which each dark matter particle will later belong. We then quantify the difference in the predictive accuracy between machine-learning models using a metric based on the Kullback–Leibler divergence. We first train the algorithm with information about the density contrast in the particles’ local environment. The addition of tidal shear information does not yield an improved halo collapse model over one based on density information alone; the difference in their predictive performance is consistent with the statistical uncertainty of the density-only based model. This result is confirmed as we verify the ability of the initial conditions-to-halo mass mapping learnt from one simulation to generalize to independent simulations. Our work illustrates the broader potential of developing interpretable machine-learning frameworks to gain physical understanding of non-linear large-scale structure formation

Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses

We present new methods for mapping the curl-free (E-mode) and divergence-free (B-mode) components of spin 2 signals using spin directional wavelets. Our methods are equally applicable to measurements of the polarisation of the cosmic microwave background (CMB) and the shear of galaxy shapes due to weak gravitational lensing. We derive pseudo and pure wavelet estimators, where E-B mixing arising due to incomplete sky coverage is suppressed in wavelet space using scale- and orientation-dependent masking and weighting schemes. In the case of the pure estimator, ambiguous modes (which have vanishing curl and divergence simultaneously on the incomplete sky) are also cancelled. On simulations, we demonstrate the improvement (i.e., reduction in leakage) provided by our wavelet space estimators over standard harmonic space approaches. Our new methods can be directly interfaced in a coherent and computationally-efficient manner with component separation or feature extraction techniques that also exploit wavelets

Simulating the universe(s) Ill: observables for the full bubble collision spacetime

This is the third paper in a series establishing a quantitative relation between inflationary scalar field potential landscapes and the relic perturbations left by the collision between bubbles produced during eternal inflation. We introduce a new method for computing cosmological observables from numerical relativity simulations of bubble collisions in one space and one time dimension. This method tiles comoving hypersurfaces with locally-perturbed Friedmann-Robertson-Walker coordinate patches. The method extends previous work, which was limited to the spacetime region just inside the future light cone of the collision, and allows us to explore the full bubble-collision spacetime. We validate our new methods against previous work, and present a full set of predictions for the comoving curvature perturbation and local negative spatial curvature produced by identical and non-identical bubble collisions, in single scalar field models of eternal inflation. In both collision types, there is a non-zero contribution to the spatial curvature and cosmic microwave background quadrupole. Some collisions between non-identical bubbles excite wall modes, giving extra structure to the predicted temperature anisotropies. We comment on the implications of our results for future observational searches. For non-identical bubble collisions, we also find that the surfaces of constant field can readjust in the presence of a collision to produce spatially infinite sections that become nearly homogeneous deep into the region affected by the collision. Contrary to previous assumptions, this is true even in the bubble into which the domain wall is accelerating

Inverted initial conditions: Exploring the growth of cosmic structure and voids

We introduce and explore "paired" cosmological simulations. A pair consists of an A and B simulation with initial conditions related by the inversion δAðx; tinitialÞ ¼ −δBðx; tinitialÞ (underdensities substituted for overdensities and vice versa). We argue that the technique is valuable for improving our understanding of cosmic structure formation. The A and B fields are by definition equally likely draws from ΛCDM initial conditions, and in the linear regime evolve identically up to the overall sign. As nonlinear evolution takes hold, a region that collapses to form a halo in simulation A will tend to expand to create a void in simulation B. Applications include (i) contrasting the growth of A-halos and B-voids to test excursion-set theories of structure formation, (ii) cross-correlating the density field of the A and B universes as a novel test for perturbation theory, and (iii) canceling error terms by averaging power spectra between the two boxes. Generalizations of the method to more elaborate field transformations are suggested

Photometric Supernova Classification With Machine Learning

Automated photometric supernova classification has become an active area of research in recent years in light of current and upcoming imaging surveys such as the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope, given that spectroscopic confirmation of type for all supernovae discovered will be impossible. Here, we develop a multi-faceted classification pipeline, combining existing and new approaches. Our pipeline consists of two stages: extracting descriptive features from the light curves and classification using a machine learning algorithm. Our feature extraction methods vary from model-dependent techniques, namely SALT2 fits, to more independent techniques that fit parametric models to curves, to a completely model-independent wavelet approach. We cover a range of representative machine learning algorithms, including naive Bayes, k-nearest neighbors, support vector machines, artificial neural networks, and boosted decision trees (BDTs). We test the pipeline on simulated multi-band DES light curves from the Supernova Photometric Classification Challenge. Using the commonly used area under the curve (AUC) of the Receiver Operating Characteristic as a metric, we find that the SALT2 fits and the wavelet approach, with the BDTs algorithm, each achieve an AUC of 0.98, where 1 represents perfect classification. We find that a representative training set is essential for good classification, whatever the feature set or algorithm, with implications for spectroscopic follow-up. Importantly, we find that by using either the SALT2 or the wavelet feature sets with a BDT algorithm, accurate classification is possible purely from light curve data, without the need for any redshift information