Abstract: Accurate power spectrum (or correlation function) covariance matrices are a crucial requirement for cosmological parameter estimation from large scale structure surveys. In order to minimize reliance on computationally expensive mock catalogs, it is important to have a solid analytic understanding of the different components that make up a covariance matrix. Considering the matter power spectrum covariance matrix, it has recently been found that there is a potentially dominant effect on mildly non-linear scales due to power in modes of size equal to and larger than the survey volume. This beat coupling effect has been derived analytically in perturbation theory and while it has been tested with simulations, some questions remain unanswered. Moreover, there is an additional effect of these large modes, which has so far not been included in analytic studies, namely the effect on the estimated average density which enters the power spectrum estimate. In this article, we work out analytic, perturbation theory based expressions including both the beat coupling and this local average effect and we show that while, when isolated, beat coupling indeed causes large excess covariance in agreement with the literature, in a realistic scenario this is compensated almost entirely by the local average effect, leaving only similar to 10% of the excess. We test our analytic expressions by comparison to a suite of large N-body simulations, using both full simulation boxes and subboxes thereof to study cases without beat coupling, with beat coupling and with both beat coupling and the local average effect. For the variances, we find excellent agreement with the analytic expressions for k < 0.2 hMpc(-1) at z = 0.5, while the correlation coefficients agree to beyond k = 0.4 hMpc(-1). As expected, the range of agreement increases towards higher redshift and decreases slightly towards z = 0. We finish by including the large-mode effects in a full covariance matrix description for arbitrary survey geometry and confirming its validity using simulations. This may be useful as a stepping stone towards building an actual galaxy (or other tracer's) power spectrum covariance matrix.

Abstract: Addressing the origin of the astrophysical neutrino flux observed by IceCube is of paramount importance. Gamma-Ray Bursts (GRBs) are among the few astrophysical sources capable of achieving the required energy to contribute to such neutrino flux through p gamma interactions. In this work, ANTARFS data have been used to search for upward going muon neutrinos in spatial and temporal coincidence with 784 GRBs occurred from 2007 to 2017. For each GRB, the expected neutrino flux has been calculated in the framework of the internal shock model and the impact of the lack of knowledge on the majority of source redshifts and on other intrinsic parameters of the emission mechanism has been quantified. It is found that the model parameters that set the radial distance where shock collisions occur have the largest impact on neutrino flux expectations. In particular, the bulk Lorentz factor of the source ejecta and the minimum variability time-scale are found to contribute significantly to the GRB-neutrino flux uncertainty. For the selected sources, ANTARES data have been analysed by maximizing the discovery probability of the stacking sample through an extended maximum-likelihood strategy. Since no neutrino event passed the quality cuts set by the optimization procedure, 90 per cent confidence level upper limits (with their uncertainty) on the total expected diffuse neutrino flux have been derived, according to the model. The GRB contribution to the observed diffuse astrophysical neutrino flux around 100 TeV is constrained to be less than 10 percent.