Derive the foam pedestal and amplitude from first-principles quantum gravity

Derive the spectral-pedestal shape and foam amplitude from a first-principles quantum-gravity theory, rather than calibrating them phenomenologically through the temporal autocorrelation of spacetime foam.

Background

The paper models time-varying spacetime foam through a stochastic arrival-time jitter with temporal autocorrelation function $C_\alpha(\tau)$. In the dynamical-foam regime, this jitter suppresses the coherent spectral component by $e^{-\sigma_\phi^2(\nu)}$ and redistributes the removed flux into a broad spectral pedestal. The pedestal shape depends on the short-time behavior of $C_\alpha$, while its amplitude is governed by phenomenological parameters such as the cumulative foam variance.

The authors use this phenomenological framework to constrain the foam exponent from GRB and CMB spectroscopy. They emphasize that the CMB interpretation, including the separation of the foam signal from chemical-potential and temperature distortions, depends on the as-yet-unavailable first-principles determination of both the pedestal profile and the overall foam amplitude.