CMB power spectrum estimation with non-circular beam and incomplete sky coverage

Over the last decade, measurements of the CMB anisotropy has spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic effects in the increasingly sensitive, high resolution, `full' sky measurements from different CMB experiments pose a stiff challenge. The analysis techniques must not only be computationally fast to contend with the huge size of the data, but, the higher sensitivity also limits the simplifying assumptions which can then be invoked to achieve the desired speed without compromising the final precision goals. While maximum likelihood is desirable, the enormous computational cost makes the suboptimal method of power spectrum estimation using Pseudo-C_l unavoidable for high resolution data. We provide a (semi)analytic framework to estimate bias in the power spectrum due to the effect of beam non-circularity and non-uniform sky coverage including incomplete/masked sky maps and scan strategy. The approach is perturbative in the distortion of the beam from non-circularity, allowing for rapid computations when the beam is mildly non-circular. We advocate that it is computationally advantageous to employ `soft' azimuthally apodized masks whose spherical harmonic transform die down fast with m. We numerically implement our method for non-rotating beams. We present preliminary estimates of the computational cost to evaluate the bias for the upcoming CMB anisotropy probes l_max~3000, with angular resolution comparable to the Planck surveyor mission. We further show that this implementation and estimate is applicable for rotating beams on equal declination scans and possibly can be extended to simple approximations to other scan strategies.Comment: 22 pages, 7 figures. Revised presentation to highlight significance of extended results. Matches version accepted to the MNRA

First CMB Constraints on Direction-Dependent Cosmological Birefringence from WMAP-7

A Chern-Simons coupling of a new scalar field to electromagnetism may give rise to cosmological birefringence, a rotation of the linear polarization of electromagnetic waves as they propagate over cosmological distances. Prior work has sought this rotation, assuming the rotation angle to be uniform across the sky, by looking for the parity-violating TB and EB correlations a uniform rotation produces in the CMB temperature/polarization. However, if the scalar field that gives rise to cosmological birefringence has spatial fluctuations, then the rotation angle may vary across the sky. Here we search for direction-dependent cosmological birefringence in the WMAP-7 data. We report the first CMB constraint on the rotation-angle power spectrum for multipoles between L = 0 and L = 512. We also obtain a 68% confidence-level upper limit of 1 degree on the square root of the quadrupole of a scale-invariant rotation-angle power spectrum.Comment: 14 pages, 12 figures, 4 tables; accepted to PR

LexMAE: Lexicon-Bottlenecked Pretraining for Large-Scale Retrieval

In large-scale retrieval, the lexicon-weighting paradigm, learning weighted sparse representations in vocabulary space, has shown promising results with high quality and low latency. Despite it deeply exploiting the lexicon-representing capability of pre-trained language models, a crucial gap remains between language modeling and lexicon-weighting retrieval -- the former preferring certain or low-entropy words whereas the latter favoring pivot or high-entropy words -- becoming the main barrier to lexicon-weighting performance for large-scale retrieval. To bridge this gap, we propose a brand-new pre-training framework, lexicon-bottlenecked masked autoencoder (LexMAE), to learn importance-aware lexicon representations. Essentially, we present a lexicon-bottlenecked module between a normal language modeling encoder and a weakened decoder, where a continuous bag-of-words bottleneck is constructed to learn a lexicon-importance distribution in an unsupervised fashion. The pre-trained LexMAE is readily transferred to the lexicon-weighting retrieval via fine-tuning. On the ad-hoc retrieval benchmark, MS-Marco, it achieves 42.6% MRR@10 with 45.8 QPS for the passage dataset and 44.4% MRR@100 with 134.8 QPS for the document dataset, by a CPU machine. And LexMAE shows state-of-the-art zero-shot transfer capability on BEIR benchmark with 12 datasets.Comment: Appeared at ICLR 202

A complete FFT-based decomposition formalism for the redshift-space bispectrum

To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshift-space bispectrum. This approach preserves three fundamental properties of the Universe: statistical homogeneity, isotropy, and parity-symmetry, allowing us to efficiently separate the anisotropic signal induced by redshift-space distortions (RSDs) and the Alcock-Paczy\'{n}ski (AP) effect from the isotropic bispectrum. The relevant expansion coefficients in terms of the anisotropic signal are reduced to one multipole index $L$, and the $L> 0$ modes are induced only by the RSD or AP effects. Our formalism has two advantages: (1) we can make use of Fast Fourier Transforms (FFTs) to measure the bispectrum; (2) it gives a simple expression to correct for the survey geometry, i.e., the survey window function. As a demonstration, we measure the decomposed bispectrum from the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, and, for the first time, present a $14\sigma$ detection of the anisotropic bispectrum in the $L=2$ mode.Comment: 23 pages, 13 figure

Non-Circular beam correction to the CMB power spectrum

In the era of high precision CMB measurements, systematic effects are beginning to limit the ability to extract subtler cosmological information. The non-circularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. The effect of non-circular beam on the power spectrum is important at multipoles larger than the beam-width. For recent experiments with high angular resolution, optimal methods of power spectrum estimation are computationally prohibitive and sub-optimal approaches, such as the Pseudo-Cl method, are used. We provide an analytic framework for correcting the power spectrum for the effect of beam non-circularity and non-uniform sky coverage (including incomplete/masked sky maps). The approach is perturbative in the distortion of the beam from non-circularity allowing for rapid computations when the beam is mildly non-circular. When non-circular beam effect is important, we advocate that it is computationally advantageous to employ `soft' azimuthally apodized masks whose spherical harmonic transform die down fast with m.Comment: 12 pages, 2 figures; Proceedings of the Fundamental Physics With CMB workshop, UC Irvine, March 23-25, 2006, to be published in New Astronomy Review