Fitting the Nonlinear Matter Bispectrum by the Halofit Approach

We provide a new fitting formula of the matter bispectrum in the nonlinear regime calibrated by high-resolution cosmological $N$-body simulations of $41$ cold dark matter ($w$CDM, $w=$ constant) models around the Planck 2015 best-fit parameters. As the parameterization in our fitting function is similar to that in Halofit, our fitting is named BiHalofit. The simulation volume is sufficiently large ($> 10 \, {\rm Gpc}^3$) to cover almost all measurable triangle bispectrum configurations in the universe. The function is also calibrated using one-loop perturbation theory at large scales ($k<0.3 \, h \, {\rm Mpc}^{-1}$). Our formula reproduced the matter bispectrum to within $10 \, (15) \, \%$ accuracy in the Planck 2015 model at wavenumber $k< 3 \, (10) \, h \, {\rm Mpc}^{-1}$ and redshifts $z=0-3$. The other $40$ $w$CDM models obtained poorer fits, with accuracy approximating $20 \, \%$ at $k<3 \, h \, {\rm Mpc}^{-1}$ and $z=0-1.5$ (the deviation includes the $10 \, \%$-level sample variance of the simulations). We also provide a fitting formula that corrects the baryonic effects such as radiative cooling and active galactic nucleus feedback, using the latest hydrodynamical simulation IllustrisTNG. We demonstrate that our new formula more accurately predicts the weak-lensing bispectrum than the existing fitting formulas. This formula will assist current and future weak-lensing surveys and cosmic microwave background lensing experiments. Numerical codes of the formula are available, written in Python, C and Fortran.