What question did this study set out to answer?

This research aims to resolve discrepancies in late-time clustering amplitude within cosmological models.

April 16, 2026Open Access

Paper10S8 tension under B framework

Key Points

This research aims to resolve discrepancies in late-time clustering amplitude within cosmological models.
Developed a formal approach within the α–β–ϕ framework.
Varied the visible Lagrangian to derive modified Einstein equations.
Reduced equations to obtain modified Friedmann equations.
Implemented a non-minimal coupling to explore effective gravitational response.
Showed potential to lower late-time clustering amplitude.
Connected modified equations to existing visible action frameworks.
Developed a controlled perturbative completion for growth sector analysis.

Abstract

The S8 tension is a late-time structure problem: baseline CMB fits in ΛCDM prefer asomewhat larger clustering amplitude than several low-redshift weak-lensing and large-scale-structure analyses. This paper develops a formal route by which the α–β–ϕ framework can movethe late-time clustering amplitude downward while remaining connected to the same visibleaction used in the broader program. Starting from the visible Lagrangian, the action is variedstep by step to obtain modified Einstein equations and, after homogeneous reduction, modifiedFriedmann equations. The same non-minimal coupling F (ϕ)R then yields a background effectivegravitational response and motivates a controlled perturbative completion for the growth sector.The quantity

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