Primordial Power Spectrum and Bispectrum from Lattice Simulations of Axion-U(1) Inflation

Abstract

We present primordial non-Gaussianity predictions from a new high-precision code for simulating axion-U(1) inflation on a discrete lattice. We measure the primordial scalar curvature power spectrum and bispectrum from our simulations, determining their dependence on both scale and axion-gauge coupling strength. Both the gauge-sourced power spectrum and the bispectrum exhibit a strong blue tilt due to our choice of an $α$-attractor inflaton potential. We provide fitting functions for the power spectrum and bispectrum that accurately reproduce these statistics across a wide range of scales and coupling strengths. While our fitting function for the bispectrum has a separable form, results from high-resolution simulations demonstrate that the full shape is not separable. Thus, our simulations generate realizations of primordial curvature perturbations with nontrivial correlators that cannot be generated using standard techniques for primordial non-Gaussianity. We derive bounds on the axion-gauge coupling strength based on the bispectrum constraints from the cosmic microwave background, demonstrating a new method for constraining inflationary primordial non-Gaussianity by simulating the nonlinear dynamics.

Figures (12)

• Figure 1: Absolute value of the time-dependent parameter $\xi(\tau)$ defined in Eq. \ref{['eq:xi_eps']} at horizon crossing, $-k\tau=1$, for several axion-gauge coupling strengths, $g_{\rm cs}$. The top axis shows the number of $e$-folds relative to when the pivot scale exits the horizon.
• Figure 2: Time evolution of the power spectra of the vacuum curvature perturbations (top-left), the sourced curvature perturbations (top-right), the left-handed gauge modes (bottom-left), and right-handed gauge modes (bottom-right). The color bar indicates time as the number of $e$-folds relative to when the pivot scale exits the horizon. These power spectra were measured from a single pair of simulations with $g_{\rm cs}=750~M_{\rm Pl}^{-1}$, $L_{\rm box}=10^3~{\rm Mpc}$, and $N_{\rm grid}=256$.
• Figure 3: Power spectra from simulations with fixed $N_{\rm grid}=256$ and different box lengths and axion-gauge coupling strengths. In the upper panel, the red data points at the top show the unsourced vacuum power, which agrees with the target primordial power spectrum (black dot-dashed line). The other data points show the sourced power spectra. All power spectra are shown for three box lengths: $L_{\rm box}=10^4~{\rm Mpc}$ (leftmost, light color), $10^3~{\rm Mpc}$ (middle), and $10^2~{\rm Mpc}$ (rightmost, dark color). The dashed lines show the fitting function from Eq. \ref{['eq:pkfit']}, jointly fit to all the simulated sourced power spectra with scale cuts (the vertical gray dot-dashed lines) described in the main text. The middle panel displays the ratio of total power to vacuum power, illustrating the small-scale enhancement from the axion-gauge coupling. The bottom panel shows the fractional residuals to the fitting function.
• Figure 4: 2D contours showing the parameters estimated from the joint fit of the sourced power spectrum model in Eq. \ref{['eq:pkfit']} to simulation data with $N_{\rm grid}=256$, box lengths $L_{\rm box}\, {\rm Mpc}^{-1} \in \{10^4, 10^3, 10^2\}$, and axion-gauge coupling strengths $g_{\rm cs}\,M_{\rm Pl} \in \{665, 700, 725, 750, 770\}$.
• Figure 5: The shape of the sourced curvature fluctuation bispectrum for simulations with box length $L_{\rm box}=10^3~{\rm Mpc}$ and axion-gauge coupling strength $g_{\rm cs}=750~M_{\rm Pl}^{-1}$. The bispectrum is parameterized with $k_1\leq k_2\leq k_3$, so $k_3$ sets the maximum wavenumber. The bispectrum peaks when $k_1 = k_2 = k_3$, or the upper-right corner in each of these plots.