The Super-Sample Covariance of Line-Intensity Mapping Power Spectrum

In this work, we provide the first derivation of the line-intensity mapping (LIM) power spectrum super-sample covariance (SSC) from first principles, and also derive as a by-product the non-Gaussian in-box contributions to the covariance for the first time. Previous studies have typically modelled the LIM power spectrum covariance using either the Gaussian approximation or estimates obtained from mocks or the data itself, neglecting uncertainties related to whether the limited volume surveyed sits in a cosmological overdensity. This contribution, known as the SSC or, depending on the context, the field-to-field variance, cannot be estimated from the data, but it is crucial for a correct inference of global quantities, i.e., for ensemble-averaged parameters rather than the actual values just within the patch of the Universe observed. For our derivation, we employ a combination of the halo model and standard perturbation theory that allows us to capture the nonlinearity and non-Gaussianity of the covariance. After a successful validation of our predictions against painted N-body simulations, we explore different scenarios related to current and future LIM experiments, quantifying the relative importance of the non-Gaussian in-box and SSC. We find that the newly derived contributions to the LIM power spectrum covariance are crucial at intermediate and small scales, especially for cases in which the covariance is not dominated by instrumental noise. We find that the relative relevance of the SSC with respect to the other covariance contributions is roughly independent of the survey volume, but does depend on the specific response of the power spectrum to large-scale modes for each line and redshift. Therefore, the impact of the SSC will be increasingly significant for parameter inference from the current and the next generation high signal-to-noise LIM surveys.