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.Comment: An informal summary of an invited talk given at the IAU symposium "Statistical Challenges in 21st Century Cosmology", accepted in the Proceedings IAU Symposium No. 306, 2014 (A.F. Heavens, J.-L. Starck, A. Krone-Martins eds.). 7 pages, 1 figure. Comments welcom

Exploiting the full potential of photometric quasar surveys: Optimal power spectra through blind mitigation of systematics

We present optimal measurements of the angular power spectrum of the XDQSOz catalogue of photometric quasars from the Sloan Digital Sky Survey. These measurements rely on a quadratic maximum likelihood estimator that simultaneously measures the auto- and cross-power spectra of four redshift samples, and provides minimum-variance, unbiased estimates even at the largest angular scales. Since photometric quasars are known to be strongly affected by systematics such as spatially-varying depth and stellar contamination, we introduce a new framework of extended mode projection to robustly mitigate the impact of systematics on the power spectrum measurements. This technique involves constructing template maps of potential systematics, decorrelating them on the sky, and projecting out modes which are significantly correlated with the data. Our method is able to simultaneously process several thousands of nonlinearly-correlated systematics, and mode projection is performed in a blind fashion. Using our final power spectrum measurements, we find a good agreement with theoretical predictions, and no evidence for further contamination by systematics. Extended mode projection not only obviates the need for aggressive sky and quality cuts, but also provides control over the level of systematics in the measurements, enabling the search for small signals of new physics while avoiding confirmation bias.Comment: 13 pages, 8 figures. v2: version accepted by MNRAS. v3: systematics templates publicly available on www.earlyuniverse.org/code, no change to pape

On Minimally-Parametric Primordial Power Spectrum Reconstruction and the Evidence for a Red Tilt

The latest cosmological data seem to indicate a significant deviation from scale invariance of the primordial power spectrum when parameterized either by a power law or by a spectral index with non-zero "running". This deviation, by itself, serves as a powerful tool to discriminate among theories for the origin of cosmological structures such as inflationary models. Here, we use a minimally-parametric smoothing spline technique to reconstruct the shape of the primordial power spectrum. This technique is well-suited to search for smooth features in the primordial power spectrum such as deviations from scale invariance or a running spectral index, although it would recover sharp features of high statistical significance. We use the WMAP 3 year results in combination with data from a suite of higher resolution CMB experiments (including the latest ACBAR 2008 release), as well as large-scale structure data from SDSS and 2dFGRS. We employ cross-validation to assess, using the data themselves, the optimal amount of smoothness in the primordial power spectrum consistent with the data. This minimally-parametric reconstruction supports the evidence for a power law primordial power spectrum with a red tilt, but not for deviations from a power law power spectrum. Smooth variations in the primordial power spectrum are not significantly degenerate with the other cosmological parameters.Comment: 18 pages, 8 figures, JCAP. Minor changes to match published versio

Genetically modified halos: towards controlled experiments in Λ\LambdaCDM 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 time of three individual halos are varied at fixed final mass, showing good agreement with previous statistical studies using large simulation suites. Second, we modify the $z=0$ mass of halos 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.Comment: Version accepted by MNRAS; 13 pages, 6 Figures, comments still welcom

Weak lensing deflection of three-point correlation functions

Weak gravitational lensing alters the apparent separations between observed sources, potentially affecting clustering statistics. We derive a general expression for the lensing deflection which is valid for any three-point statistic, and investigate its effect on the three-point clustering correlation function. We find that deflection of the clustering correlation function is greatest at around $z=2$. It is most prominent in regions where the correlation function varies rapidly, in particular at the baryon acoustic oscillation scale where it smooths out the peaks and troughs, reducing the peak-to-trough difference by about 0.1 percent at $z=1$ and around 2.3 percent at $z=10$. The modification due to lensing deflection is typically at the per cent level of the expected errors in a Euclid-like survey and therefore undetectable.Comment: 15 pages + appendices, 7 figures, minor changes to match version published in JCA

Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys

Accurately characterizing the redshift distributions of galaxies is essential for analysing deep photometric surveys and testing cosmological models. We present a technique to simultaneously infer redshift distributions and individual redshifts from photometric galaxy catalogues. Our model constructs a piecewise constant representation (effectively a histogram) of the distribution of galaxy types and redshifts, the parameters of which are efficiently inferred from noisy photometric flux measurements. This approach can be seen as a generalization of template-fitting photometric redshift methods and relies on a library of spectral templates to relate the photometric fluxes of individual galaxies to their redshifts. We illustrate this technique on simulated galaxy survey data, and demonstrate that it delivers correct posterior distributions on the underlying type and redshift distributions, as well as on the individual types and redshifts of galaxies. We show that even with uninformative priors, large photometric errors and parameter degeneracies, the redshift and type distributions can be recovered robustly thanks to the hierarchical nature of the model, which is not possible with common photometric redshift estimation techniques. As a result, redshift uncertainties can be fully propagated in cosmological analyses for the first time, fulfilling an essential requirement for the current and future generations of surveys.Comment: 10 pages, matches version accepted in MNRAS, including new appendix describing the effect of Bayesian shrinkage in a simplified settin

Is there evidence for additional neutrino species from cosmology?

It has been suggested that recent cosmological and flavor-oscillation data favor the existence of additional neutrino species beyond the three predicted by the Standard Model of particle physics. We apply Bayesian model selection to determine whether there is indeed any evidence from current cosmological datasets for the standard cosmological model to be extended to include additional neutrino flavors. The datasets employed include cosmic microwave background temperature, polarization and lensing power spectra, and measurements of the baryon acoustic oscillation scale and the Hubble constant. We also consider other extensions to the standard neutrino model, such as massive neutrinos, and possible degeneracies with other cosmological parameters. The Bayesian evidence indicates that current cosmological data do not require any non-standard neutrino properties.Comment: 17 pages, 7 figures. v3: replaced with version published in JCAP (typo fixes, including Figure 1 units