Oscillating bispectra and galaxy clustering: A novel probe of inflationary physics with large-scale structure

Many models of inflation predict oscillatory features in the bispectrum of primordial fluctuations. Since it has been shown that primordial non-Gaussianity can lead to a scale-dependent halo bias, we investigate the effect of oscillations in the three-point function on the clustering of dark-matter halos. Interestingly, we find that features in the inflaton potential such as oscillations or sharp steps get imprinted in the mass dependence of the non-Gaussian halo bias. In this paper, we focus on models displaying a sharp feature in the inflaton potential as well as resonant non-Gaussianity. In both cases, we find a strong scale dependence for the non-Gaussian halo bias with a slope similar to that of the local model. In the resonant case, we find that the non-Gaussian bias oscillates with halo mass, a novel feature that is unique to this type of models. In the case of a sharp feature in the inflaton potential, we find that the clustering of halos is enhanced at the mass scale corresponding to the Fourier mode that exited the horizon when the inflaton was crossing the feature in the potential. Both of these are new effects that open the possibility of characterizing the inflationary potential with large-scale-structure surveys. We briefly discuss the prospects for detecting these non-Gaussian effects.

Figure 1

Non-Gaussian correction to the halo bias for the resonant non-Gaussianity model as a function of scale. We evaluate the bias for $M={10}^{13}{M}_{\odot }/h$ at $z=0$. We take $f_{\mathrm{NL}}^{\mathrm{res}}={10}^{-3}{C}_{\omega }^{5/2}$ and evaluate the Gaussian bias $b_1$ using the Sheth-Tormen mass function [34].

Figure 2

Non-Gaussian spectral moment ${\sigma }_W^2$ for the resonant model as a function of halo mass. We evaluate this spectral moment for $k={10}^{-3}h{\mathrm{Mpc}}^{-1}$ at $z=0$.

Figure 3

Non-Gaussian correction to the halo bias for the resonant non-Gaussianity model as a function of halo mass. We evaluate the bias for $k={10}^{-3}h{\mathrm{Mpc}}^{-1}$ at $z=0$. We take $f_{\mathrm{NL}}^{\mathrm{res}}={10}^{-3}{C}_{\omega }^{5/2}$ and evaluate the Gaussian bias $b_1$ using the Sheth-Tormen mass function. For comparison, we also show the bias for local non-Gaussianity with $f_{\mathrm{NL}}^{\mathrm{local}}=2$.

Figure 4

Absolute value of the non-Gaussian spectral moment ${\sigma }_W^2$ for the feature model as a function of halo mass. We evaluate this spectral moment for $k={10}^{-3}h{\mathrm{Mpc}}^{-1}$ at $z=0$ and use $\Delta k_f/k_f=0.01$.

Figure 5

The two contributions to the non-Gaussian halo bias correction as a function of mass for the model with a feature at $k_f=0.5h{\mathrm{Mpc}}^{-1}$. We evaluate ${\sigma }_W^2$ for $k={10}^{-3}h{\mathrm{Mpc}}^{-1}$ at $z=0$ and use $\Delta k_f/k_f=0.01$. The Gaussian bias $b_1$ is derived using the Sheth-Tormen mass function.

Figure 6

Mass dependence of the non-Gaussian correction to the halo bias for the model with a feature in the inflaton potential. We evaluate the bias for $k={10}^{-3}h{\mathrm{Mpc}}^{-1}$ at $z=0$ and use $\Delta k_f/k_f=0.01$. We take $f_{\mathrm{NL}}^{\mathrm{feat}}=10$ and evaluate the Gaussian bias $b_1$ using the Sheth-Tormen mass function. For comparison, we also show the bias for the local model of non-Gaussianity with $f_{\mathrm{NL}}^{\mathrm{local}}=-10$.

Figure 7

Scale dependence of the non-Gaussian correction to the halo bias for the model with a feature in the inflaton potential. We evaluate the bias for $M=1.5(4\pi /3)\overline{\rho }{k}_f^{-3}$ at $z=0$ and use $\Delta k_f/k_f=0.01$. We take $f_{\mathrm{NL}}^{\mathrm{feat}}=10$ and evaluate the Gaussian bias $b_1$ using the Sheth-Tormen mass function. For comparison, we also show the non-Gaussian bias correction from the local model evaluated at $M={10}^{13}{M}_{\odot }/h$ and $f_{\mathrm{NL}}^{\mathrm{local}}=100$.

Figure 8

Comparison between $\Delta b_I(M)$ obtained with a spherical tophat filter and with a Gaussian filter. We evaluate the bias for $k={10}^{-3}h{\mathrm{Mpc}}^{-1}$ at $z=0$ and use $\Delta k_f/k_f=0.01$ and $k_f=0.5h{\mathrm{Mpc}}^{-1}$. We take $f_{\mathrm{NL}}^{\mathrm{feat}}=10$.