Constraining equilateral-type primordial non-Gaussianities from imaging surveys

We investigate expected constraints on equilateral-type primordial non-Gaussianities from future/ongoing imaging surveys, making use of the fact that they enhance the halo/galaxy bispectrum on large scales. As model parameters to be constrained, in addition to $f_{\mathrm{NL}}^{\text{equil}}$, which is related to the primordial bispectrum, we consider $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}$, which is related to the primordial trispectrum that appeared in the effective field theory of inflation. After calculating the angular bispectra of the halo/galaxy clustering and weak gravitational lensing based on the integrated perturbation theory, we perform Fisher matrix analysis for three representative surveys. We find that among the three surveys, the tightest constraints come from Large Synoptic Survey Telescope; its expected $1\sigma$ errors on $f_{\mathrm{NL}}^{\text{equil}}$ and $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}$ are respectively given by $7.0\times 10^2$ and $4.9\times 10^7$. Although this constraint is somewhat looser than the one from the current cosmic microwave background observation, since we obtain it independently, we can use this constraint as a cross-check. We also evaluate the uncertainty with our results caused by using several approximations and discuss the possibility to obtain tighter constraint on $f_{\mathrm{NL}}^{\text{equil}}$ and $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}$.

Figure 1

Forecast results of equilateral-type primordial non-Gaussian parameters by HSC (left), DES (middle), and LSST (right). In each panel, marginalized $1\sigma$ error contours on $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}-f_{\mathrm{NL}}^{\text{equil}}$ planes are shown. Light blue contours represent the constraints from the autoangular bispectrum of halo/galaxy clustering, while the blue contours indicate the constraints when we add cross-angular bispectra between halos and weak lensing. Notice that the plotted range of the error contours is changed in each panel, for clarity.

Figure 2

Sensitivity of the marginalized $1\sigma$ errors on $f_{\mathrm{NL}}^{\text{equil}}$ (left), $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}$ (right) to the parameters ${\ell }_{\max }$. Solid (dashed) lines represent marginalized (unmarginalized) $1\sigma$ errors on equilateral-type primordial non-Gaussian parameters for HSC (blue), DES (red), and LSST (green).

Figure 3

Relative errors between exact and large-scale-limit formulas of the autoangular bispectrum of halo/galaxy clustering. Each line shows the relative errors of individual contributions of the bispectrum from nonlinear gravitational evolution (black solid), primordial bispectrum (red dashed), and primordial trispectrum (blue dotted). For simplicity, redshift ($z=1$) and halo mass $(M_h=10^{13}{M}_{\odot }/h)$ are fixed.