71 research outputs found
A bias to CMB lensing measurements from the bispectrum of large-scale structure
The rapidly improving precision of measurements of gravitational lensing of
the Cosmic Microwave Background (CMB) also requires a corresponding increase in
the precision of theoretical modeling. A commonly made approximation is to
model the CMB deflection angle or lensing potential as a Gaussian random field.
In this paper, however, we analytically quantify the influence of the
non-Gaussianity of large-scale structure lenses, arising from nonlinear
structure formation, on CMB lensing measurements. In particular, evaluating the
impact of the non-zero bispectrum of large-scale structure on the relevant CMB
four-point correlation functions, we find that there is a bias to estimates of
the CMB lensing power spectrum. For temperature-based lensing reconstruction
with CMB Stage-III and Stage-IV experiments, we find that this lensing power
spectrum bias is negative and is of order one percent of the signal. This
corresponds to a shift of multiple standard deviations for these upcoming
experiments. We caution, however, that our numerical calculation only evaluates
two of the largest bias terms and thus only provides an approximate estimate of
the full bias. We conclude that further investigation into lensing biases from
nonlinear structure formation is required and that these biases should be
accounted for in future lensing analyses.Comment: 15+19 pages, 9 figures. Comments welcom
Rotation method for accelerating multiple-spherical Bessel function integrals against a numerical source function
A common problem in cosmology is to integrate the product of two or more
spherical Bessel functions (sBFs) with different configuration-space arguments
against the power spectrum or its square, weighted by powers of wavenumber.
Naively computing them scales as with the number of
configuration space arguments and the grid size, and they cannot be
done with Fast Fourier Transforms (FFTs). Here we show that by rewriting the
sBFs as sums of products of sine and cosine and then using the product to sum
identities, these integrals can then be performed using 1-D FFTs with scaling. This "rotation" method has the potential to
accelerate significantly a number of calculations in cosmology, such as
perturbation theory predictions of loop integrals, higher order correlation
functions, and analytic templates for correlation function covariance matrices.
We implement this approach numerically both in a free-standing,
publicly-available \textsc{Python} code and within the larger,
publicly-available package \texttt{mcfit}. The rotation method evaluated with
direct integrations already offers a factor of 6-10 speed-up over the
naive approach in our test cases. Using FFTs, which the rotation method
enables, then further improves this to a speed-up of
over the naive approach. The rotation method should be useful in light of
upcoming large datasets such as DESI or LSST. In analysing these datasets
recomputation of these integrals a substantial number of times, for instance to
update perturbation theory predictions or covariance matrices as the input
linear power spectrum is changed, will be one piece in a Monte Carlo Markov
Chain cosmological parameter search: thus the overall savings from our method
should be significant
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