Enabling Polyspectra via Stochastic Realizations of Inverse Decay Curvature Perturbations in Axion Inflation

Current and upcoming galaxy-redshift surveys offer a promising path for constraining inflationary physics. These constraints are often imposed by relating correlations of the primordial curvature perturbation to the late-time galaxy. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It matters because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. These constraints are often imposed by relating correlations of the primordial curvature perturbation to the late-time galaxy correlation functions. The primordial correlators can either be computed analytically, or via realizations of the primordial curvature perturbations that are initialized on a grid and evolved.

In this work we take a hybrid approach, initializing the fields in the Bunch-Davies vacuum. And then imposing time evolution through direct numerical integration.

Our method efficiently generates realizations of the inverse decay primordial curvature perturbations for axion inflation---an inflationary model in which a pseudoscalar inflaton. Depending on the choice of parameter $ξ\in\{2, 2.5, 3\}$, which controls gauge field particle production in this model, our method generates realizations with an average runtime.

We compute the power spectrum and bispectrum from these realizations and find a surprisingly large discrepancy between our result and previous work that used an approximation for. This new method enables not only rapid computation of higher order polyspectra, but also generation of initial conditions for large-scale structure analyses.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

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Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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