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  1. Abstract A number of recent, low-redshift, lensing measurements hint at a universe in which the amplitude of lensing is lower than that predicted from the ΛCDM model fit to the data of the Planck CMB mission. Here we use the auto- and cross-correlation signal of unWISE galaxies and Planck CMB lensing maps to infer cosmological parameters at low redshift. In particular, we consider three unWISE samples (denoted as "blue", "green" and "red") at median redshifts z ∼ 0.6, 1.1 and 1.5, which fully cover the Dark Energy dominated era. Our cross-correlation measurements, with combined significance S / N  ∼ 80, are used to infer the amplitude of low-redshift fluctuations, σ 8 ; the fraction of matter in the Universe, Ω m ; and the combination S 8  ≡ σ 8 (Ω m /0.3) 0.5 to which these low-redshift lensing measurements are most sensitive. The combination of blue, green and red samples gives a value S m  = 0.784 ± 0.015, that is fully consistent with other low-redshift lensing measurements and in 2.4σ tension with the CMB predictions from Planck. This is noteworthy, because CMB lensing probes the same physics as previous galaxy lensing measurements, but with very different systematics, thus providing an excellent complement to previous measurements.

    Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise three-dimensional map of our Universe. The survey effective volume reaches $\sim 20\, h^{-3}\, \mathrm{Gpc}^{3}$. It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. AbacusSummit is a suite of high-resolution dark-matter-only simulations designed for this purpose, with $200\, h^{-3}\, \mathrm{Gpc}^{3}$ (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide a more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi-N-body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variance than the expected DESI statistical variance at the scales we are interested in, e.g. $k \lt 0.3\, h\, \mathrm{Mpc}^{-1}$ for the halo power spectrum. In addition, it can significantly suppress the sample variance of the halo bispectrum. We further generalize the method for other cosmologies with only one realization in AbacusSummit suite to extend the effectivemore »volume ∼20 times. In summary, our proposed strategy of combining high-fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data.

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