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We exploit a suite of large N-body simulations (up to N=$4096^3$) performed with Abacus, of scale-free models with a range of spectral indices $n$, to better understand and quantify convergence of the matter power spectrum in dark matter only cosmological N-body simulations. Using self-similarity to identify converged regions, we show that the maximal wavenumber resolved at a given level of accuracy increases monotonically as a function of time. At the $1%$ level it starts at early times from a fraction of $k_Lambda$, the Nyquist wavenumber of the initial grid, and reaches at most, if the force softening is sufficiently small, $sim 2 k_Lambda$ at the very latest times we evolve to. At the $5%$ level accuracy extends up to slightly larger wavenumbers, of order $5k_Lambda$ at late times. Expressed as a suitable function of the scale-factor, accuracy shows a very simple $n$-dependence, allowing a straightforward extrapolation to place conservative bounds on the accuracy of N-body simulations of non-scale free models like LCDM. Quantitatively our findings are broadly in line with the conservative assumptions about resolution adopted by recent studies using large cosmological simulations (e.g. Euclid Flagship) aiming to constrain the mildly non-linear regime. On the other hand, we note that studies of the matter power spectrum in the literature have often used data at larger wavenumbers, where convergence to the physical result is poor. Even qualitative conclusions about clustering at small scales, e.g concerning the validity of the stable clustering approximation, may need revision in light of our results.
We study the cosmological power spectra (PS) of the differential and integral galaxy volume number densities $gamma_i$ and $gamma_i^{*}$, constructed with the cosmological distances $d_i$ $(i=A,G,L,Z)$, where $d_A$ is the angular diameter distance, $
The most commonly used estimators of the anisotropic galaxy power spectrum employ Fast Fourier transforms, and rely on a specific choice of the line-of-sight that breaks the symmetry between the galaxy pair. This leads to wide-angle effects, includin
A proposed method for dealing with foreground emission in upcoming 21-cm observations from the epoch of reionization is to limit observations to an uncontaminated window in Fourier space. Foreground emission can be avoided in this way, since it is li
A promising method for measuring the cosmological parameter combination fsigma_8 is to compare observed peculiar velocities with peculiar velocities predicted from a galaxy density field using perturbation theory. We use N-body simulations and semi-a
We present cosmological parameter measurements from the effective field theory-based full-shape analysis of the power spectrum of emission line galaxies (ELGs). First, we perform extensive tests on simulations and determine appropriate scale cuts for