Dark Matter in the Absolute Frame Theory: A Two-Component Origin, the Pilot-Wave Scale, and Matter-Parity Stabilization
Year: 2026
Type: preprint
Abstract: The Absolute Frame Theory (AFT) proposes that the observable four-dimensional manifold $\mathcal{M}$ is continuously immersed in an $N$-dimensional Euclidean substratum $\mathcal{A}$ through a map $X:\mathcal{M} \to\mathcal{A}$, with gravity emerging as the entropic tension of the embedding and quantum probability as the aliasing of a deterministic pilot wave $\Psi$ on $\mathcal{A}$. We develop the dark-matter sector of this framework into a set of quantitative, falsifiable statements while marking explicitly the limits of what is derivable. The proposal is composite. A first, galactic component is the cumulative restoring tension of the embedding, which sources a non-Newtonian acceleration that traces the baryonic distribution and reproduces, at the qualitative level, the observed radial-acceleration relation, with a characteristic scale set by the single substratum density $\rho_{\mathcal{A}}$ that also fixes the cosmological constant. A second, cosmological component is the tower of Standard-Model--neutral transverse modes of the embedding; their spectrum is discrete (a confinement, not a compactification), and the bare neutral scale coincides with one of the two scalars to which the pilot wave reduces. We show that this intrinsic scale is not constructible from the substratum elastic moduli---both are energy densities, and in the transverse fluctuation problem the tension cancels---and the scale is thereby identifiability-limited from $\mathcal{M}$. It is, however, pinned by the right-handed-neutrino seesaw: the gauged $B-L$ of the Pati--Salam factor must break, forcing Majorana neutrinos, and the observed light-neutrino scale together with the $\mathrm{SU}(4)_c$ relation $m_D\simeq m_{\rm top}$ places the intrinsic scale at $m_{\mathcal{A}}\sim10^{14}~[\mathrm{GeV}]$---superheavy, and of the order of the inflationary scale of the same embedding spectrum. We then show that stability of a superheavy relic requires an exact protection that the residual matter parity $\mathbb{Z}_2=(-1)^{3(B-L)}$ does not by itself provide, and we conclude that a viable cold particle is a genuine dark-sector addition---a vector-like sterile lepton, stabilized by a discrete parity and with a mass near the inflationary scale where gravitational production yields the observed abundance---which the framework does not derive but whose scale, production, and consistency it fixes. We state the resulting falsifiable predictions: a discrete dark-matter mass spectrum, a baryon-tracing galactic anomaly, a superheavy gravitationally produced relic, and self-interaction bounded by the representation content of the embedding.
Author: Valenzuela, Patricio E.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162959639
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