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

Although the large-scale perturbations beyond a finite-volume survey region are not direct observables, these affect measurements of clustering statistics of small-scale (sub-survey) perturbations in the large-scale structure, compared with the ensemble average, via the mode-coupling effect. In this paper we show that the large-scale tides induced by scalar perturbations cause apparent anisotropic distortions in the redshift-space power spectrum of galaxies in a way depending on an alignment between the tides, the wavevector of small-scale modes and the line-of-sight direction. Using the perturbation theory of structure formation, we derive the $\textit{response}$ function of the redshift-space power spectrum to the large-scale tides. We then investigate the impact of the large-scale tides 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 tides 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 tides can be constrained at an accuracy better than the CDM prediction, if the effects up to a larger wavenumber in the nonlinear regime can be included.