Primordial physics from large-scale structure beyond the power spectrum

Abstract

We study constraints on primordial mode-coupling from the power spectrum, squeezed-limit bispectrum and collapsed trispectrum of matter and halos. We describe these statistics in terms of long-wavelength 2-point functions involving the matter/halo density and position-dependent power spectrum. This allows us to derive simple, analytic expression for the information content, treating constraints from scale-dependent bias in the halo power spectrum on the same footing as those from higher order statistics. In particular, we include non-Gaussian covariance due to long-short mode-coupling from non-linear evolution, which manifests itself as long-mode cosmic variance in the position-dependent power spectrum. We find that bispectrum forecasts that ignore this cosmic variance may underestimate σ(fNL) by up to a factor ∼3 for the matter density (at z=1) and commonly a factor ∼2 for the halo bispectrum. Constraints from the bispectrum can be improved by combining it with the power spectrum and trispectrum. The reason is that, in the position-dependent power spectrum picture, the bispectrum and trispectrum intrinsically incorporate multitracer cosmic variance cancellation, which is optimized in a joint analysis. For halo statistics, we discuss the roles of scale-dependent bias, matter mode-coupling, and non-linear, non-Gaussian biasing (b^((h))_(11)). While scale-dependent bias in the halo power spectrum is already very constraining, higher order halo statistics are competitive in the regime where stochastic noise in the position-dependent halo power spectrum is low enough for cosmic variance cancellation to be effective, i.e.~for large halo number density and large k_(max). This motivates exploring this regime observationally.