We explore the effect of a cubic correction $g_{\mathrm{NL}}{\varphi }^3$ on the mass function and bias of dark matter haloes extracted from a series of large N-body simulations and compare it to theoretical predictions. Such cubic terms can be motivated in scenarios like the curvaton model, in which a large cubic correction can be produced while simultaneously keeping the quadratic $f_{\mathrm{NL}}{\varphi }^2$ correction small. The deviation from the Gaussian halo mass function is in reasonable agreement with the theoretical predictions. The scale-dependent bias correction $\Delta b_{\kappa }(k,g_{\mathrm{NL}})$ measured from the auto- and cross-power spectrum of haloes, is similar to the correction in $f_{\mathrm{NL}}$ models, but the amplitude is lower than theoretical expectations. Using the compilation of LSS data in [A. Slosar et al., J. Cosmol. Astropart. Phys. 08 (2008) 031], we obtain for the first time a limit on $g_{\mathrm{NL}}$ of $-3.5\times {10}^5<g_{\mathrm{NL}}<+8.2\times {10}^5$ (at 95% CL). This limit will improve with the future LSS data by 1–2 orders of magnitude, which should test many of the scenarios of this type.

• Received 15 July 2009

DOI:https://doi.org/10.1103/PhysRevD.81.023006