Impact of large-scale tides on cosmological distortions via redshift-space power spectrum

Although large-scale perturbations beyond a finite-volume survey region are not direct observables, these affect measurements of clustering statistics of small-scale (subsurvey) perturbations in large-scale structure, compared with the ensemble average, via the mode-coupling effect. In this paper we show that a large-scale tide induced by scalar perturbations causes apparent anisotropic distortions in the redshift-space power spectrum of galaxies in a way depending on an alignment between the tide, wave vector of small-scale modes and line-of-sight direction. Using the perturbation theory of structure formation, we derive a response function of the redshift-space power spectrum to large-scale tide. We then investigate the impact of large-scale tide on estimation of cosmological distances and the redshift-space distortion parameter via the measured redshift-space power spectrum for a hypothetical large-volume survey, based on the Fisher matrix formalism. To do this, we treat the large-scale tide as a signal, rather than an additional source of the statistical errors, and show that a degradation in the parameter is restored if we can employ the prior on the rms amplitude expected for the standard cold dark matter (CDM) model. We also discuss whether the large-scale tide can be constrained at an accuracy better than the CDM prediction, if the effects up to a larger wave number in the nonlinear regime can be included.