Constraining primordial non-Gaussianity with future galaxy surveys

TL;DR

This work forecasts how well future galaxy surveys can constrain primordial non-Gaussianity using two-point statistics. By applying a Fisher matrix framework to DES-like and Euclid-like configurations and incorporating 3D redshift-space clustering, 2D projected clustering, and cosmic shear (with cross-covariances), the authors quantify constraints on PNG shapes (local, equilateral, orthogonal) and on $f_{ m NL}$ and its scale dependence $n_{f_{ m NL}}$, while marginalising over standard cosmological parameters and nuisance biases. They show that including PNG in the analysis does not significantly degrade LCDM or dark-energy constraints, and that the strongest expected constraints on local PNG arise from the combination of weak lensing and photometric clustering, yielding $\sigma(f_{ m NL}) oughly 3$ and $\sigma(n_{f_{ m NL}}) oughly 0.12$ for Euclid-like surveys with Planck priors; orthogonal and equilateral constraints are weaker in clustering due to reduced bias scale-dependence, though lensing remains robust. The results are robust to halo-model uncertainties, redshift-bin choices, and reasonable updates to Euclid specifications, underscoring the potential of next-generation surveys to test inflationary scenarios. The study also highlights the value of incorporating cross-probes and planck priors to maximize PNG sensitivity across shapes and to probe scale-dependent features of non-Gaussianity.

Abstract

We study the constraining power on primordial non-Gaussianity of future surveys of the large-scale structure of the Universe for both near-term surveys (such as the Dark Energy Survey - DES) as well as longer term projects such as Euclid and WFIRST. Specifically we perform a Fisher matrix analysis forecast for such surveys, using DES-like and Euclid-like configurations as examples, and take account of any expected photometric and spectroscopic data. We focus on two-point statistics and we consider three observables: the 3D galaxy power spectrum in redshift space, the angular galaxy power spectrum, and the projected weak-lensing shear power spectrum. We study the effects of adding a few extra parameters to the basic LCDM set. We include the two standard parameters to model the current value for the dark energy equation of state and its time derivative, w_0, w_a, and we account for the possibility of primordial non-Gaussianity of the local, equilateral and orthogonal types, of parameter fNL and, optionally, of spectral index n_fNL. We present forecasted constraints on these parameters using the different observational probes. We show that accounting for models that include primordial non-Gaussianity does not degrade the constraint on the standard LCDM set nor on the dark-energy equation of state. By combining the weak lensing data and the information on projected galaxy clustering, consistently including all two-point functions and their covariance, we find forecasted marginalised errors sigma (fNL) ~ 3, sigma (n_fNL) ~ 0.12 from a Euclid-like survey for the local shape of primordial non-Gaussianity, while the orthogonal and equilateral constraints are weakened for the galaxy clustering case, due to the weaker scale-dependence of the bias. In the lensing case, the constraints remain instead similar in all configurations.

Figures (10)

• Figure 1: Comparison of the theoretical matter power spectra with the measurements from $N-$body simulations by PPH08, with local $f_{\mathrm{NL}}= 80$. The top panel shows the total $P_m(k)$ for the linear (red) and two non-linear models: the halo model (blue) and the model by Smith:2006ne (green). Below we plot the ratio $P_m(k)/P_{\mathrm{simulations}}(k)$. All curves are at $z=0$: a similar ($\sim 10 \%$) level of accuracy is obtained at other redshifts.
• Figure 2: Redshift distributions used for the forecasts of both photometric and spectroscopic data sets for the Euclid satellite and the DES. The photo-z distributions are given by an analytic function 1994MNRAS.270..245S, while the spectroscopic part is numerically estimated by 2010MNRAS.402.1330G, where the Euclid specified flux cut is used, $4 \cdot 10^{-16}$ erg s$^{-1}$ cm$^{-2}$. The distributions have been already convolved with the probability density function of redshift measurement errors.
• Figure 3: Summary of all observables used in this work for the fiducial model described in Section \ref{['sec:forec']}. In the upper panel, we show the projected 2D spectra for lensing, galaxy clustering, and their cross-spectra for photometric and spectroscopic surveys. In the bottom panel we show the 3D galaxy power spectrum. Note that the Limber approximation is inaccurate on large scales for the galaxy-galaxy spectra, as well as the linear-theory power spectrum is on the small scales (dashed lines). For the lensing and galaxy-lensing cases, the Limber approximation works well due to the wider distribution of the sources. The shaded areas represent cosmic-variance errors for a half-sky survey. A redshift bin centred around $z = 1$ is used in all cases.
• Figure 4: Fisher matrix forecasts for the Euclid-like survey, using weak lensing (photometric survey), 2D galaxy clustering (photometric and spectroscopic surveys), and 3D galaxy clustering (spectroscopic only). For lensing, the used multipoles are from $l_{\min} = 5$ to $l_{\max}=20~000$, while for clustering the maximum mode is $k_{\max} = 0.15$$h$/Mpc at $z=0$. The forecasted posteriors are marginalised over the other not shown parameters. The blue ellipses refer to Euclid only, while in red we show the results including Planck priors. Notice that the axes ranges are different, which is necessary given the different constraining power of the different observables.
• Figure 5: Full combination of Euclid-like data. Fisher matrix forecasts for the combination of weak lensing (photometric survey) plus 2D galaxy clustering (photometric and spectroscopic surveys). Both the range of used multipoles and the colour coding of the ellipses are as described above for the previous plots.