[Paper Review] Primordial physics from large-scale structure beyond the power spectrum

Roland de Putter|arXiv (Cornell University)|Feb 19, 2018

Cosmology and Gravitation TheoriesPhysics and Astronomy16 citations

TL;DR

This paper develops a unified framework to extract primordial physics from large-scale structure using higher-order statistics beyond the power spectrum, including the bispectrum and trispectrum. It shows that non-Gaussian cosmic variance from long-short mode coupling in non-linear evolution can reduce constraints on $f_{\rm NL}$ by up to a factor of 3 if ignored, and that joint analysis of power spectrum, bispectrum, and trispectrum optimizes cosmic variance cancellation, significantly improving $f_{\rm NL}$ constraints for both matter and halos.

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 $σ(f_{ m NL})$ by up to a factor $\sim 3$ for the matter density (at $z=1$) and commonly a factor $\sim 2$ 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 ($b_{11}^{(h)}$). 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 $k_{ m max}$. This motivates exploring this regime observationally.

Motivation & Objective

• To unify constraints on primordial mode-coupling ($f_{\rm NL}$) from the power spectrum, bispectrum, and trispectrum using a common formalism.
• To quantify the impact of non-Gaussian cosmic variance from long-short mode coupling in non-linear evolution on $f_{\rm NL}$ forecasts.
• To demonstrate that joint analysis of power spectrum, bispectrum, and trispectrum optimizes cosmic variance cancellation and improves $f_{\rm NL}$ constraints.
• To include the effects of scale-dependent bias, non-linear biasing ($b_{11}^{(h)}$), and halo stochastic noise in the position-dependent power spectrum formalism.
• To show that ignoring non-Gaussian cosmic variance in bispectrum forecasts can underestimate $\sigma(f_{\rm NL})$ by up to a factor of 3 for matter and 2 for halos.

Proposed method

• Formulates all statistics (power spectrum, bispectrum, trispectrum) in terms of long-wavelength $2$-point functions involving matter/halo density and position-dependent power spectrum.
• Derives analytic expressions for information content by treating scale-dependent bias and higher-order statistics on equal footing.
• Incorporates non-Gaussian covariance from long-short mode coupling due to non-linear evolution as long-mode cosmic variance in the position-dependent power spectrum.
• Models halo stochastic noise as non-Gaussian and derives its mode-coupling contributions to the bispectrum and trispectrum using bias parameters $b^{(h)}_{\delta_{L}\epsilon_{S}}$, $b^{(h)}_{\epsilon_{L}\delta_{S}}$, and $b^{(h)}_{\epsilon^{2}}$.
• Uses the position-dependent power spectrum formalism to show that the bispectrum and trispectrum naturally incorporate multitracer cosmic variance cancellation.
• Derives explicit expressions for shot noise contributions to the bispectrum, including terms from non-Gaussian halo stochasticity, and validates them against standard results.

Experimental results

Research questions

• RQ1 How does non-Gaussian cosmic variance from long-short mode coupling affect $f_{\rm NL}$ constraints in the bispectrum?
• RQ2 Can the power spectrum, bispectrum, and trispectrum be treated within a unified formalism for $f_{\rm NL}$ constraints?
• RQ3 To what extent does joint analysis of multiple statistics improve $f_{\rm NL}$ constraints through cosmic variance cancellation?
• RQ4 How do halo stochastic noise and non-linear biasing affect the position-dependent power spectrum and higher-order statistics?
• RQ5 What is the quantitative impact of ignoring non-Gaussian cosmic variance in standard bispectrum forecasts?

Key findings

• Non-Gaussian cosmic variance from long-short mode coupling in non-linear evolution can reduce $\sigma(f_{\rm NL})$ constraints by up to a factor of 3 if ignored, particularly for the matter density at $z=1$.
• For the halo bispectrum, ignoring this cosmic variance leads to an underestimation of $\sigma(f_{\rm NL})$ by a factor of approximately 2.
• Joint analysis of the power spectrum, bispectrum, and trispectrum optimizes multitracer cosmic variance cancellation, significantly improving $f_{\rm NL}$ constraints.
• The position-dependent power spectrum formalism naturally incorporates cosmic variance cancellation in the bispectrum and trispectrum, making joint analysis more effective than individual statistics.
• Higher-order halo statistics (bispectrum and trispectrum) are competitive with the power spectrum only when stochastic noise is low, i.e., for high halo number density and large $k_{\rm max}$.
• The paper derives explicit expressions for shot noise contributions to the halo bispectrum, including non-Gaussian terms from Poisson noise, and validates them against standard results.