Euclid preparation

The extraction of cosmological information from two-point statistics critically relies on the assumed form of their likelihood. Although a Gaussian likelihood is generally adopted, the first paper of this series showed that the distribution of power-spectrum estimates exhibits non-Gaussian features on both large and small scales ( k < 0.5 h /Mpc), with their amplitudes depending on the survey volume, masking, and shot noise. In this work, we account for this skewness in parameter inference by modelling the likelihood through an Edgeworth expansion. This procedure involves the complete skewness tensor, composed of one-point, two-point, and three-point correlators. To simplify the calculations of this expansion, we performed a change in the basis, which reduced the precision matrix to the identity. In this basis, the off-diagonal elements of the skewness tensor are consistent with zero, while the amplitude of its diagonal match the level expected for a Gaussian underlying field. We performed a parameter inference with this likelihood model and found that including only the diagonal part of the skewness is sufficient; whereas incorporating the full skewness tensor injects noise without improving accuracy. Despite the estimated excess skewness in the original basis, the cosmological constraints remain effectively unchanged when adopting a Gaussian likelihood or considering the more complete Edgeworth expansion, with variations in the figure of merit of cosmological parameters between the two cases below 5%. This result remains unchanged against variations of the survey volume and geometry, scale-cut, as well as the two-point statistics (i.e. power spectrum or correlation function). Using 10 000 cloned Euclid large mocks based on realistic galaxy catalogues with characteristics approximating future Euclid data, we found no detectable excess skewness on intermediate scales, due to the level of shot noise expected for the Euclid spectroscopic sample. We conclude that the Gaussian likelihood assumption is robust for Euclid two-point statistics analyses in both Fourier and the configuration space.

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