Inflationary origin of anomalous metric contributions (conjecture)

Establish whether the anomalous large-scale contributions to the static spherically symmetric metric—specifically the linear γ1 r and quadratic γ2 r^2 terms that modify geodesics and galactic rotation curves in the classical-quantum stochastic gravity framework—originate from early-time metric fluctuations generated and stretched during cosmic inflation, by deriving their production, evolution, and persistence within a Friedman–Robertson–Walker cosmology consistent with the theory’s path-integral action.

Background

The paper develops a classical-quantum path-integral approach in which the metric is classical but undergoes stochastic evolution, leading to deviations from general relativity at low accelerations. In static, spherically symmetric settings, the resulting most-probable contributions to the metric include linear and quadratic terms (γ1 r and γ2 r^2), analogous to features used to fit galactic rotation curves without dark matter.

The authors posit that, given the scales involved, these anomalous contributions may not be actively fluctuating today but could reflect early-time fluctuations that were imprinted during inflation. Establishing this requires a cosmological (rather than purely static) treatment to trace how such fluctuations are generated and survive to late times.