No evidence for dust B-mode decorrelation in Planck data

Constraints on inflationary $B$-modes using Cosmic Microwave Background polarization data commonly rely on either template cleaning or cross-spectra between maps at different frequencies to disentangle galactic foregrounds from the cosmological signal. Assumptions about how the foregrounds scale with frequency are therefore crucial to interpreting the data. Recent results from the Planck satellite collaboration claim significant evidence for a decorrelation in the polarization signal of the spatial pattern of galactic dust between 353 GHz and 217 GHz. Such a decorrelation would suppress power in the cross spectrum between high frequency maps, where the dust is strong, and lower frequency maps, where the sensitivity to cosmological $B$-modes is strongest. Alternatively, it would leave residuals in lower frequency maps cleaned with a template derived from the higher frequency maps. If not accounted for, both situations would result in an underestimate of the dust contribution and thus an upward bias on measurements of the tensor-to-scalar ratio, $r$. In this paper we revisit this measurement and find that the no-decorrelation hypothesis cannot be excluded with the Planck data. There are three main reasons for this: i) there is significant noise bias in cross spectra between Planck data splits that needs to be accounted for; ii) there is strong evidence for unknown instrumental systematics whose amplitude we estimate using alternative Planck data splits; iii) there are significant correlations between measurements in different sky patches that need to be taken into account when assessing the statistical significance. Between $\ell=55-90$ and over $72\%$ of the sky, the dust $BB$ correlation between 217 GHz and 353 GHz is $1.001^{+.004/.021}_{-.004/.000}$ ($68\%~stat./syst.$) and shows no significant trend with sky fraction.Comment: 16 pages, 13 figure

Alignment of galaxy spins in the vicinity of voids

We provide limits on the alignment of galaxy orientations with the direction to the void center for galaxies lying near the edges of voids. We locate spherical voids in volume limited samples of galaxies from the Sloan Digital Sky Survey using the HB inspired void finder and investigate the orientation of (color selected) spiral galaxies that are nearly edge-on or face-on. In contrast with previous literature, we find no statistical evidence for departure from random orientations. Expressed in terms of the parameter c, introduced by Lee & Pen to describe the strength of such an alignment, we find that c<0.11(0.13) at 95% (99.7%) confidence limit within a context of a toy model that assumes a perfectly spherical voids with sharp boundaries.Comment: 8 pages, 4 figures; v2 discussion expanded, references fixed, matches version accepted by JCA

A unified pseudo-CℓC_\ell framework

The pseudo-$C_\ell$ is an algorithm for estimating the angular power and cross-power spectra that is very fast and, in realistic cases, also nearly optimal. The algorithm can be extended to deal with contaminant deprojection and $E/B$ purification, and can therefore be applied in a wide variety of scenarios of interest for current and future cosmological observations. This paper presents NaMaster, a public, validated, accurate and easy-to-use software package that, for the first time, provides a unified framework to compute angular cross-power spectra of any pair of spin-0 or spin-2 fields, contaminated by an arbitrary number of linear systematics and requiring $B$- or $E$-mode purification, both on the sphere or in the flat-sky approximation. We describe the mathematical background of the estimator, including all the features above, and its software implementation in NaMaster. We construct a validation suite that aims to resemble the types of observations that next-generation large-scale structure and ground-based CMB experiments will face, and use it to show that the code is able to recover the input power spectra in the most complex scenarios with no detectable bias. NaMaster can be found at https://github.com/LSSTDESC/NaMaster, and is provided with comprehensive documentation and a number of code examples.Comment: 27 pages, 17 figures, accepted in MNRAS. Code can be found at https://github.com/LSSTDESC/NaMaste

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 $\delta_A(x, t_{initial})=-\delta_B(x,t_{initial})$ (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 {\Lambda}CDM initial conditions, and in the linear regime evolve identically up to the overall sign. As non-linear 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.Comment: 10 pages (including appendix), 6 figures. To be submitted to PR

How to estimate the 3D power spectrum of the Lyman-α\alpha forest

We derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-$\alpha$ (Ly-$\alpha$) forest flux fluctuations. The algorithm exploits the unique geometry of Ly-$\alpha$ forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. The key to fast evaluation is to approximate the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.Comment: 29 pages, many figures. Minor changes in v2, accepted in JCA