Inflation as Emergent Starobinsky Gravity in the Absolute Frame Theory: The Topological Tension as a Scalar–Tensor Field

Version of September 24th, 2026, following technical developments within the Absolute Frame Theory programme. We derive the inflationary sector of the Absolute Frame Theory (AFT) from its unified action and find that it is, to leading order, Starobinsky R² inflation, with the R² term emergent rather than postulated. A single chain of reasoning drives the result. The routing term of the interaction Lagrangian couples to the metric only through the volume density √(−g). Its sole possible gravitational footprint is a pure-trace term, degenerate with the cosmological constant and absorbed into the baseline by the thermodynamic-isolation axiom. It therefore does not gravitate as an independent source. The cosmic sector then reduces to the tension alone. Carried with the mandatory Howe–Tucker constant, the tension stress is linear in the embedding strain and contributes no cosmological term of its own. The stiff sector (w=+1) decelerates, and spatial embedding deformations carry only w=−1/3 (curvature-like). The single cosmological term is therefore the substratum density ρ_𝒜, fixed by the observed dark-energy scale and far below the density required to inflate. No fluid of the cosmic sector can inflate. The resolution therefore lies not on the right-hand side of the Friedmann equation but in the gravitational term itself. Because the gravitational coupling obeys G∝𝒯_𝒜⁻¹, the action contains a term 𝒯_𝒜 R, and the topological tension 𝒯_𝒜 is a Brans–Dicke scalar–tensor field. Its Einstein-frame dynamics, through the conformal map, produces a plateau potential. Since 𝒯_𝒜 enters only as a coefficient with no kinetic term (it is the Lagrange multiplier of the action-quantization constraint), the Brans–Dicke parameter is ω_BD=0, which is f(R) gravity. Moreover, we take the soft saturation constraint of the foundational axiom to carry a quadratic penalty, which yields a quadratic potential. That penalty is an assumption of this paper, not a consequence of the axiom. Together these give Starobinsky f(R)=R+R²/(6M²) to leading order, hence n_s≃1−2/N_ef and r≃12/N_ef², with the single scale M≃1.3×10⁻⁵ M_P≃3×10¹³ [GeV] fixed by the scalar amplitude A_s. Dark energy arises from a different degree of freedom of the same embedding spectrum: a cosmological-constant baseline Λ=8πGρ_𝒜 set by the substratum density, carrying the bulk of the dark-energy density. Added to it is a small ultralight thawing residual, of mass of order H_0. That residual displaces the equation of state gently into the thawing quadrant (w_0 slightly above −1, w_a<0) near a pure Λ, in the direction of DESI DR2. The scalar–tensor tension itself is chameleon-screened at late times, leaving local gravity standard. The cosmological constant itself is the small background density ρ_𝒜 of the substratum, fixed by the observed value and distinct from 𝒯_𝒜, dissolving the vacuum-catastrophe problem structurally rather than by fine-tuning. Inflation (the heavy ultraviolet scalaron) and dark energy (the light infrared mode) are thus the two extremes of one modal spectrum.