Regularization and width of temporal delta-function singularities

Characterize and derive the physically admissible regularization (width, profile, and degree of singularity) of the temporal delta functions δ(a−η) and δ′(a−η) that represent the proposed time shells, including quantitative bounds that ensure the spikes are sufficiently narrow to evade direct detection yet reproduce the required averaged Friedmann dynamics.

Background

The model’s dynamics rely on idealized delta-function spikes in the mass-energy density and pressure as functions of the expansion factor. The author discusses observational constraints, such as the need for the spikes to be narrower than current redshift resolution, but explicitly notes that the exact degree of singularity is not known.

Determining a physically motivated regularization is essential both for consistency with measurements and for constructing simulations or analytical treatments that use smooth approximations of the singular behavior.