Determine finite-affinity real-time SU(3) transport kernels

Determine the finite-affinity real-time SU(3) drift, susceptibility, and frequency- and momentum-dependent noise kernels governing gauge-helicity and quark-axial transport in Standard-Model warm inflation, in order to replace the local linear-response Gaussian closure with a parameter-free microscopic prediction.

Background

The calculation models QCD sphaleron drift, hard gauge-helicity relaxation, susceptibilities, and stochastic reaction noise using a local linear-response transport closure. However, the relevant inflationary trajectories reach large sphaleron and perturbative affinities, so the linear relation between drift and fluctuations is extrapolated beyond its controlled regime.

The authors identify finite-affinity real-time SU(3) transport data as the principal missing microscopic input. These data would determine whether gauge screening only deforms the viable Standard-Model warm-inflation trajectory, selects a narrower attractor, or changes the existence of the strong warm branch.

References

At finite affinity, the net drift, susceptibility, equation of state, event statistics, and frequency-dependent noise kernel are independent real-time QCD data.

— Gauge Backreaction in Standard Model Warm Inflation  (2609.35756 - Dejrah et al., 28 Sep 2026) in Introduction; Section 3, paragraph “Equilibrium consistency and the finite affinity”; Section 6, Discussion and conclusions

A controlled inclusion of \Delta\mathcal F_{\rm resp}, its pressure, and their perturbations would require the corresponding nonlinear susceptibility at finite affinity, which is presently unknown.

— Gauge Backreaction in Standard Model Warm Inflation  (2609.35756 - Dejrah et al., 28 Sep 2026) in Section 2, subsection “Operational definition and matching of hard gauge helicity,” paragraph “Thermodynamic energy stored in the response variable”; Section 3, paragraph “Energy conservation for stochastic reaction sources”

Establishing \omega\,\tau_{\rm corr}\ll1, in particular for modes near horizon crossing, requires the frequency-dependent real-time QCD response and noise kernels that are not presently available.

— Gauge Backreaction in Standard Model Warm Inflation  (2609.35756 - Dejrah et al., 28 Sep 2026) in Section 3, opening paragraphs on stochastic fluctuations from reaction channels

The missing microscopic object in the present scalar transport calculation is the finite-temperature QCD transverse-traceless anisotropic stress \Pi_{\lambda}{\rm TT}, including its unequal-time correlator.

— Gauge Backreaction in Standard Model Warm Inflation  (2609.35756 - Dejrah et al., 28 Sep 2026) in Section 3, paragraph “Spectral extraction”; Section 6, Discussion and conclusions