Super-Sample Signal

When extracting cosmological information from power spectrum measurements, we must consider the impact of super-sample density fluctuations whose wavelengths are larger than the survey scale. These modes contribute to the mean density fluctuation $\delta_b$ in the survey and change the power spectrum in the same way as a change in the cosmological background. They can be simply included in cosmological parameter estimation and forecasts by treating $\delta_b$ as an additional cosmological parameter enabling efficient exploration of its impact. To test this approach, we consider here an idealized measurement of the matter power spectrum itself in the $\Lambda$CDM cosmology though our techniques can readily be extended to more observationally relevant statistics or other parameter spaces. Using sub-volumes of large-volume $N$-body simulations for power spectra measured with respect to either the global or local mean density, we verify that the minimum variance estimator of $\delta_b$ is both unbiased and has the predicted variance. Parameter degeneracies arise since the response of the matter power spectrum to $\delta_b$ and cosmological parameters share similar properties in changing the growth of structure and dilating the scale of features especially in the local case. For matter power spectrum measurements, these degeneracies can lead in certain cases to substantial error degradation and motivates future studies of specific cosmological observables such as galaxy clustering and weak lensing statistics with these techniques.