Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Local Nonlinear Transforms effectively Reveal Primordial Information in Large-Scale Structure

Yun Wang, Hao-Ran Yu, Yu Yu, Ping He

TL;DR

The paper tackles the problem that nonlinear gravitational evolution in the large-scale structure obscures primordial information by inducing non-Gaussianity in the density field. It introduces a Zel'dovich-based local nonlinear transform, the $\mathcal{Z}$-$\kappa$ transform, and shows that with $\kappa\approx6$ it Gaussianizes the density more effectively than the log transform, while recovering the linear power spectrum. The transformed power spectra, $P_{log}$ and $P_{\mathcal{Z}-6}$, exhibit near-diagonal covariances and have enhanced sensitivity to local primordial non-Gaussianity, enabling substantial improvements in $f_{NL}^{local}$ constraints when combined with the nonlinear spectrum and, potentially, Planck data. This approach opens a practical route to probing early-Universe physics with Stage-IV LSS surveys using two-point statistics, with forecasts suggesting $\sigma(f_{NL}^{local})$ could reach $\lesssim5$ for large enough volumes and tighter joint constraints with CMB data. Future work will extend the method to biased tracers and redshift-space distortions to incorporate realistic observational effects.

Abstract

To eliminate gravitational non-Gaussianity, we introduce the $\mathcal{Z}$-$κ$ transform, a simple local nonlinear transform of the matter density field that emulates the inverse of nonlinear gravitational evolution. Using $N$-body simulations, we show that the $\mathcal{Z}$-$κ$ transform with $κ=6$ or $κ\to\infty$ (i.e., log) substantially Gaussianizes the density distribution, and recovers the linear power spectrum. In an extended parameter space including primordial non-Gaussianity, summed neutrino mass, and $Λ$CDM parameters, Fisher analysis demonstrates that power spectra of transformed fields provide strong complementary constraints. A central result is that these power spectra can directly capture the local primordial non-Gaussianity imprinted in large-scale structure. This opens a new avenue for probing the physics of the early Universe with Stage-IV surveys using two-point statistics.

Local Nonlinear Transforms effectively Reveal Primordial Information in Large-Scale Structure

TL;DR

The paper tackles the problem that nonlinear gravitational evolution in the large-scale structure obscures primordial information by inducing non-Gaussianity in the density field. It introduces a Zel'dovich-based local nonlinear transform, the - transform, and shows that with it Gaussianizes the density more effectively than the log transform, while recovering the linear power spectrum. The transformed power spectra, and , exhibit near-diagonal covariances and have enhanced sensitivity to local primordial non-Gaussianity, enabling substantial improvements in constraints when combined with the nonlinear spectrum and, potentially, Planck data. This approach opens a practical route to probing early-Universe physics with Stage-IV LSS surveys using two-point statistics, with forecasts suggesting could reach for large enough volumes and tighter joint constraints with CMB data. Future work will extend the method to biased tracers and redshift-space distortions to incorporate realistic observational effects.

Abstract

To eliminate gravitational non-Gaussianity, we introduce the - transform, a simple local nonlinear transform of the matter density field that emulates the inverse of nonlinear gravitational evolution. Using -body simulations, we show that the - transform with or (i.e., log) substantially Gaussianizes the density distribution, and recovers the linear power spectrum. In an extended parameter space including primordial non-Gaussianity, summed neutrino mass, and CDM parameters, Fisher analysis demonstrates that power spectra of transformed fields provide strong complementary constraints. A central result is that these power spectra can directly capture the local primordial non-Gaussianity imprinted in large-scale structure. This opens a new avenue for probing the physics of the early Universe with Stage-IV surveys using two-point statistics.

Paper Structure

This paper contains 7 sections, 7 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction.
  2. Theory.
  3. Fisher formalism.
  4. Data set.
  5. Results.
  6. Conclusions.
  7. Acknowledgments.

Figures (3)

  • Figure 1: Gaussianization under different transformations. Top: mean absolute deviation between the transformed density PDF and the Gaussian distribution. The blue dashed line marks the deviation in the log limit, equal to 0.0248. Middle: PDFs of the normalized density fields $y_i=(\delta_i-\mu_i)/\sigma_i$ compared with the unit Gaussian (dashed line), in which $i\in\{\mathrm{nl}, \mathrm{log}, \mathcal{Z}$-$6 \}$. Bottom: ratios of the transformed power spectra to the smoothed initial power spectrum. A bias factor $P_\mathrm{nl}(k_f)/P_i(k_f)$ with $k_f=0.0089\, h\, \text{Mpc}^{-1}$ is applied to align spectra on large scales. PDFs and spectra are averaged over 100 fields of the fiducial Quijote simulations (see Data set).
  • Figure 2: Correlation matrix and parameter responses of power spectra. Left: auto and cross correlation coefficients $\mathcal{C}_{ij}/\sqrt{\mathcal{C}_{ii}\mathcal{C}_{jj}}$ for the nonlinear power spectrum $P_\mathrm{nl}(k)$, log power spectrum $P_\mathrm{log}(k)$, and $\mathcal{Z}$-6 power spectrum $P_{\mathcal{Z}-6}(k)$, at $z=0$. Right: numerical partial derivatives of different spectra with respect to PNG parameters $\{f_\mathrm{NL}^\mathrm{local}, f_\mathrm{NL}^\mathrm{equil}, f_\mathrm{NL}^\mathrm{ortho}\}$ and summed neutrino mass $M_\nu$. Solid/dashed lines indicate that the derivative is positive/negative. In the "$f_\mathrm{NL}^\mathrm{local}$" sub-plot, the black line shows the CAMB result for $P_\mathrm{lin}(k)/\mathcal{M}(k)$, rescaled by a constant factor to match $\partial P_\mathrm{log}/\partial f_\mathrm{NL}^\mathrm{local}$, in which $P_\mathrm{lin}(k)$ is the linear power spectrum at $z=0$, and $\mathcal{M}(k)=2k^2T(k)/(3\Omega_mH_0^2)$.
  • Figure 3: Fisher forecast constraints from power spectra. Left: joint and marginalized constraints on the parameters $\{f_\mathrm{NL}^\mathrm{local}$, $f_\mathrm{NL}^\mathrm{equil}$, $f_\mathrm{NL}^\mathrm{ortho}$, $M_\nu\}$ at $z=0$, using $P_\mathrm{nl}$, $P_\mathrm{log}$, $P_{\mathcal{Z}-6}$, and their combinations up to $k_\mathrm{max}=0.5\, h\mathrm{Mpc}^{-1}$. Right: dependence of the marginalized 1-$\sigma$ constraints on the maximum wavenumber $k_\mathrm{max}$. Although only a subset of parameters is shown here, all constraints are fully marginalized over the remaining $\Lambda$CDM parameters.