Effects of long-wavelength fluctuations in large galaxy surveys

In order to capture as much information as possible large galaxies surveys have been increasing their volume and redshift depth. To face this challenge theory has responded by making cosmological simulations of huge computational volumes with equally increasing numbers of dark matter particles and supercomputing resources. Thus, it is taken for granted that the ideal situation is when a single computational box encompasses the whole volume of the observational survey, e.g. ∼ 50 h^{-3} Gpc^3 for the DESI and Euclid surveys. Here we study the effects of missing long waves in a finite volume using several relevant statistics: the abundance of dark matter haloes, the probability distribution function (PDF), the correlation function and power spectrum, and covariance matrices. Finite volume effects can substantially modify the results if the computational volumes are less than ∼ (500 h^{-1Mpc})^3. However, the effects become extremely small and practically can be ignored when the box size exceeds ∼1 Gpc³. We find that the average power spectra of dark matter fluctuations show remarkable lack of dependence on the computational box size with less than 0.1 per cent differences between 1 and 4 h^{-1 Gpc} boxes. No measurable differences are expected for the halo mass functions for these volumes. The covariance matrices are scaled trivially with volume, and small corrections due to supersample modes can be added. We conclude that there is no need to make those extremely large simulations when a box size of 1-1.5 h^{-1Gpc} is sufficient to fulfil most of the survey science requirements.