A preprint reports that a nonperturbative lattice calculation gave a higher primordial curvature spectrum—the spectrum of initial curvature fluctuations—than a perturbative calculation in a selected ultra-slow-roll, single-field scalar Gauss–Bonnet inflation model. The difference became significant when the spectrum’s peak reached about 10^-2, and the model’s peak frequency lay in the band studied by pulsar-timing arrays.
The difference appears at high amplitude
The study fed both versions of the primordial spectrum into calculations of scalar-induced gravitational waves, or SIGWs: a predicted gravitational-wave background calculated from those primordial fluctuations. The resulting energy-density spectra showed clearly significant lattice effects when the primordial spectrum had a large amplitude.
A finite numerical scan
The perturbative comparison solved the model’s background and mode equations numerically. It initialized modes deep inside the Hubble sphere, followed them through horizon exit and continued until the curvature mode approached a constant.
The lattice calculation evolved fields on a discretized cubic box, using a discretized Laplacian and an effective lattice momentum for the power-spectrum calculation. Initial fluctuations were generated with a truncated-Wigner stochastic procedure that included Box–Muller generation and a fast Fourier transform, while a nonperturbative delta-N method extracted the final curvature perturbation.
The scan fixed f at 7.0, Lambda at 0.0065, xi1 at 9.6 and phic at 30.0, then tested 14 alpha settings between 1.1331 × 10^7 and 1.13412 × 10^7.
The lattice size was N = 200. Evolution began at keff,min = 1.3aH and ended at keff,max = aH/200; the authors described larger lattice sizes as computationally infeasible. They also evaluated metric perturbations and found their magnitudes below 10^-8 in the reported setup, supporting their omission from the main lattice calculation.
From the lattice to PTA data
For the pulsar-timing comparison, the analysis used the first 14 frequency bins of the NANOGrav 15-year HD-correlated free spectrum, represented by a kernel-density estimate, or KDE. Bayesian inference used bilby and dynesty.
The comparison included models with and without a supermassive-black-hole-binary, or SMBHB, contribution. It also considered a mixed model in which SMBHBs and SIGWs both contributed to the signal.
Lattice corrections mainly changed the posterior—the resulting distribution of plausible parameter values—in the region with large alpha-minus-alpha0 offsets. At smaller offsets, the lattice and perturbative results were essentially identical and had little effect on the posterior.
Using Bayes factors, which are evidence ratios for competing models, the lattice-corrected analysis reported a larger SGB-model factor relative to SMBHB and a larger portion of the scanned parameter space compatible with PTA observations.
A result tied to one setup
The analysis is a theoretical model comparison against selected PTA frequency bins, not a direct gravitational-wave detection. Its conclusions are confined to the specified SGB setup, the 14-point alpha scan and the N = 200 lattice. The PTA comparison also used a selected data representation and a uniform prior from 9000 to 10200 for alpha-minus-alpha0.
The report does not give a numerical correction ratio or uncertainty interval for the spectral difference, nor an uncertainty for the Bayesian evidence. That leaves open whether the reported pattern persists at larger lattice sizes, across other parameter choices or with different PTA model assumptions.
The document identifies itself as an arXiv version-one preprint dated 20 August 2026.
Paper data and sources
Original title: Inflation on the lattice: scalar Gauss-Bonnet single field inflation
Authors: Fei-Yu Chen, Jing-Zhi Zhou, Zhi-Chao Li, Di Wu
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text