Fast and Exact Spin-s Spherical Harmonic Transforms

We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the computation of several distinct spin transforms simultaneously. Specifically, only one set of special functions is computed for transforms of quantities with any spin, namely the Wigner d-matrices evaluated at {\pi}/2, which may be computed with efficient recursions. For any spin the computation scales as O(L^3) where L is the band-limit of the function. Our publicly available numerical implementation permits very high accuracy at modest computational cost. We discuss applications to the Cosmic Microwave Background (CMB) and gravitational lensing.Comment: 22 pages, preprint format, 5 figure

Halo Concentration and the Dark Matter Power Spectrum

We explore the connection between halo concentration and the dark matter power spectrum using the halo model. We fit halo model parameters to non-linear power spectra over a large range of cosmological models. We find that the non-linear evolution of the power spectrum generically prefers the concentration at non-linear mass scale to decrease with the effective slope of the linear power spectrum, in agreement with the direct analysis of the halo structure in different cosmological models. Using these analyses, we compute the predictions for non-linear power spectrum beyond the current resolution of N-body simulations. We find that the halo model predictions are generically below the analytical non-linear models, suggesting that the latter may overestimate the amount of power on small scales.Comment: 7 pages, 6 figures, MNRAS accepte

Sunyaev-Zeldovich effect in WMAP and its effect on cosmological parameters

We use multi-frequency information in first year WMAP data to search for the Sunyaev-Zeldovich (SZ) effect. WMAP has sufficiently broad frequency coverage to constrain SZ without the addition of higher frequency data: the SZ power spectrum amplitude is expected to increase 50% from W to Q frequency band. This, in combination with the low noise in WMAP, allows us to strongly constrain the SZ contribution. We derive an optimal frequency combination of WMAP cross-spectra to extract SZ in the presence of noise, CMB, and radio point sources, which are marginalized over. We find that the SZ contribution is less than 2% (95% c.l.) at the first acoustic peak in W band. Under the assumption that the removed radio point sources are not correlated with SZ this limit implies sigma_8<1.07 at 95% c.l. We investigate the effect on the cosmological parameters of allowing an SZ component. We run Monte Carlo Markov Chains with and without an SZ component and find that the addition of SZ does not affect any of the cosmological conclusions. We conclude that SZ does not contaminate the WMAP CMB or change cosmological parameters, refuting the recent claims that they may be corrupted.Comment: 10 pages, 5 figures, 2 tables. Submitted to Phys. Rev.