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Characterizing the full probability distribution of anomalous metric contributions

Characterize the full probability distribution of stochastic deviations from the Newtonian potential within the classical-quantum gravity path-integral framework beyond the γ1 and γ2 truncation, including identification of additional significant terms and their correlations (for example via a Kosambi–Karhunen–Loève analysis), in order to robustly relate these fluctuations to dark-matter-like phenomenology.

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Background

The analysis shows that, under a static spherically symmetric ansatz, the path integral induces a bivariate normal distribution in γ1 and γ2 (linear and quadratic in r). The authors caution that higher-order or additional terms could contribute and that fitting power series alone may be misleading without understanding the full fluctuation distribution.

They suggest a principal-component approach (e.g., Kosambi–Karhunen–Loève) to identify the dominant stochastic modes across scales, but emphasize that currently they lack knowledge of what further terms materially contribute.

References

Here, the full normal distribution reflected in Eq.~eq:Faction may provide some insight into the distribution of what is currently taken to be dark matter, but one must be careful since anything can be fit to a power series, and a fuller understanding of the probability distribution is required, as we don't know what other terms may contribute.

— Anomalous contribution to galactic rotation curves due to stochastic spacetime (2402.19459 - Oppenheim et al., 29 Feb 2024) in Main text, in the discussion beginning “Let us now highlight the weaknesses of the calculation.”