What question did this study set out to answer?

The aim is to study scalar perturbations in saturating bounce cosmology with effective Friedmann dynamics.

May 13, 2026Open Access

Scalar Perturbation Obstruction in Saturating Bounce Cosmology: Frobenius Analysis, Five-Route Completion Audit, and Parameter Triangle

Key Points

The aim is to study scalar perturbations in saturating bounce cosmology with effective Friedmann dynamics.
Conducted a Frobenius analysis of the scalar perturbation equation.
Introduced a class-level symplectic obstruction theorem for single-field effective bounces.
Performed a five-route completion audit and a post-bounce parameter-triangle analysis.
Identified structural obstruction in the scalar sector linked to Mukhanov–Sasaki field divergence at H = 0.
Demonstrated that the tensor sector remains regular through the bounce.
Clarified that the work does not provide a complete trans-bounce scalar perturbation theory or UV-complete quantum gravity theory.

Abstract

This preprint studies scalar perturbations in a minimal saturating bounce cosmology with effective Friedmann dynamics of the form: H² = (8π/3)ρeff(1 − ρeff/ρsat). The tensor sector remains regular through the bounce, while the scalar sector exhibits a structural obstruction associated with divergence of the Mukhanov–Sasaki pump field at H = 0. The paper presents:- a Frobenius analysis of the scalar perturbation equation,- a class-level symplectic obstruction theorem for single-field effective bounces,- a five-route completion audit,- and a post-bounce parameter-triangle analysis. The work explicitly does not claim a complete trans-bounce scalar perturbation theory or a UV-complete theory of quantum gravity.

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