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April 17, 2026Open Access

Inflation Without an Inflaton: Deriving nₛ = 0. 9649 from Network Critical Geometry in Granular Entropic Physics

Key Points

The aim is to derive the scalar spectral index n_s from network critical geometry in Granular Entropic Physics without conventional inflaton fields.
Analyzed the critical dynamics of a bipartite tetrahedral network.
Used the critical exponent from the 3D Ising universality class to derive n_s.
Compared results to traditional inflation models like Starobinsky R^2.
Derived n_s = 0.9649 consistent with Planck measurements.
Calculated tensor-to-scalar ratio r ~ 0.004 and running alpha_s ~ -10^-3.
Demonstrated that the framework addresses bounce cosmology and emergent gravity.

Abstract

This paper derives the scalar spectral index nₛ = 0. 9649 from the critical dynamics of a bipartite tetrahedral network in Granular Entropic Physics (GEP), without introducing an inflaton field or continuous free parameters. The result follows from the critical exponent of the 3D Ising universality class: nₛ = 1 - eta, where eta = 0. 0363 +/- 0. 0003, giving nₛ in the range 0. 9634-0. 9640, consistent with Planck 2018 (nₛ = 0. 9649 +/- 0. 0042). This is a postdiction. The tensor-to-scalar ratio r ~ 0. 004 and running alphaₛ ~ -10^-3 are forward predictions testable by LiteBIRD (2030). The paper compares GEP inflation with Starobinsky R² inflation and discusses how the same GEP framework addresses bounce cosmology, emergent gravity, and fermion mass in separate publications.

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Štěpán Sekanina (Wed,) studied this question.

synapsesocial.com/papers/69e1cfcb5cdc762e9d858c8b https://doi.org/https://doi.org/10.5281/zenodo.19591124

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