Signature of Primordial Non-Gaussianity on Matter Power Spectrum

TL;DR

This work analyzes how primordial non-Gaussianity modifies large-scale structure observables via perturbation theory, focusing on the matter power spectrum and galaxy bias. It compares local-type and equilateral-type non-Gaussianity, deriving the one-loop corrections and showing that $P(k)$ can deviate by roughly a few percent in the weakly non-linear regime, with the sign and amplitude depending on $f_{NL}$ and the bispectrum shape. Through Fisher-matrix forecasts for a future BAO survey, the authors find that non-Gaussianity can degrade constraints on the primordial spectral index $n_s$ and its running $\alpha$, with CMB priors helping to mitigate degeneracies; the BAO distance scale remains relatively robust to non-Gaussianity. The paper also studies how local biasing introduces a scale-dependent galaxy bias for local non-Gaussianity, while equilateral non-Gaussianity does not, highlighting the potential of bias measurements to distinguish inflationary scenarios and the need for simulations to calibrate bias in non-Gaussian contexts.

Abstract

Employing the perturbative treatment of gravitational clustering, we discuss possible effects of primordial non-Gaussianity on the matter power spectrum. As gravitational clustering develops, the coupling between different Fourier modes of density perturbations becomes important and the primordial non-Gaussianity which intrinsically possesses a non-trivial mode-correlation can affect the late-time evolution of the power spectrum. We quantitatively estimate the non-Gaussian effect on power spectrum from the perturbation theory. The potential impact on the cosmological parameter estimation using the power spectrum are investigated based on the Fisher-matrix formalism. In addition, on the basis of the local biasing prescription, non-Gaussian effects on the galaxy power spectrum are considered, showing that the scale-dependent biasing arises from a local-type primordial non-Gaussianity. On the other hand, an equilateral-type non-Gaussianity does not induce such scale-dependence because of weaker mode-correlations between small and large Fourier modes.

Figures (5)

• Figure 1: Ratio of the power spectrum to the smoothed reference spectrum for the local model (left) and the equilateral model with $\kappa=0$ (right), for $z=1$. The smooth spectra are obtained from the no-wiggle approximation of the linear transfer function according to Ref. EH1998. The lines from top to bottom respectively indicate $f_{\rm NL}=300$ (solid), $f_{\rm NL}=100$ (long-dashed), $f_{\rm NL}=0$ (dotted), $f_{\rm NL}=-100$ (short-dashed) and $f_{\rm NL}=-300$ (dot-dashed).
• Figure 2: Ratios of power spectrum, $P(k;f_{\rm NL}\ne0)/P(k;f_{\rm NL}=0)$, for $z=3$ (left), $2$ (middle) and $1$ (right). From top to bottom panels, the results for the local, equilateral with $\kappa=0, ~~0.3$, and $-0.3$ are shown, respectively. In each panel, we plot the cases with non-Gaussian parameter $f_{\rm NL}=+300$ (solid), $+100$ (long-dashed), $-100$ (short-dashed) and $-300$ (dot-dashed). The vertical arrows labeled by $k_{1\%}$ and $k_{3\%}$ indicate the maximum wave number below which the perturbation theory predictions are reliable with a precision of $1\%$ and $3\%$ level, respectively, according to the criteria (\ref{['eq:criteria']}) Nishimichi2008. As references, the error bars limited by the cosmic variance are plotted in the right panel, assuming the survey volume of $V_s=4\, (h^{-1}$Gpc$)^3$ (thin solid) and $V_s=10^2\, (h^{-1}$Gpc$)^3$ (thick solid).
• Figure 3: Predicted 1-$\sigma$ (68%C.L.) errors on the spectral index $n_s$ (left), running of the index $\alpha$ (middle), and distance scale $D_V/D_{V,{\rm true}}$ (right) as function of maximum wavenumber $k_{\rm max}$, assuming the survey parameters of $z=1.5$, $V_s=100h^{-3}$Gpc$^3$, $b_1=3.25$, and $n_{\rm gal}=10^{-4} h^{3}$Gpc$^{-3}$, as an illustrative example of space-based BAO missions. Here, we specifically treat the local model of primordial non-Gaussianity. The solid (prior 1), short-dashed (prior 2), and long-dashed (prior 3) lines represent the results under the different priors (see text for details). Thick lines show the one-dimensional errors marginalized over the four parameters (i.e., $n_s, \, \alpha, \, D_V/D_{V,{\rm true}},\, f_{\rm NL}$), and thin lines represents the error excluding the non-Gaussian parameter, $f_{\rm NL}$.
• Figure 5: Expected 1-$\sigma$ (68%C.L.) error on the distance scale as a function of maximum wavenumber (left) and two-dimensional joint $68\%$ C.L. constraints on $f_{\rm NL}$ of the local model and $D_V/D_{V,{\rm true}}$ fixing the maximum wavenumber to $k_{\rm max}=k_{1\%}\simeq0.131h$Mpc$^{-1}$ (right). Here, we specifically adopt the survey parameters of $z=1$, $V_s=4$$h^{-3}$Gpc$^3$, $b_1=2.0$, and $n_{\rm gal}=10^{-3}$$h^{3}$Mpc$^{-3}$, as a representative example of ground-based BAO surveys. The meaning of the lines are the same as in Figures \ref{['fig:1Derror_ns_nrun_Dv_ADEPT']} and \ref{['fig:2Derror_ns_nrun_Dv_ADEPT']}.
• Figure 6: Ratio of biasing factor, $b(k;z)/b_{\rm G}(k;z)$ given at $z=1$, in the case of the local model. Gaussian smoothing is adopted in order to compute the biased power spectra. $R=1h^{-1}$Mpc (left); $R=5h^{-1}$Mpc (middle); $R=10h^{-1}$Mpc (right)