Inflation as Temporal Resolution: No Inflaton Required - Multi-Mode Cascade Mechanism in the Spectral Fractal-Temporal Theory

Can the Spectral Fractal-Temporal Theory (STFT) produce inflation without an inflaton field? We first establish a no-go result: standard slow-roll inflation on the STFT confining potential U₀(σ) = Λ₀e−λσ + Λ_b eνσ is excluded. The consistency relation r = 8(1 − n_s) is a hard floor for exponential potentials, giving r ≈ 0.28 for n_s = 0.965 — incompatible with BICEP/Keck (r < 0.036). We verify numerically that no combination of slow-roll, curvaton, trapped, or hybrid mechanisms produces viable (n_s, r) anywhere in the (ν, R) parameter space. This negative result applies to any single-field model on a sum-of-exponentials potential. We then show that the STFT provides a fundamentally different mechanism with three components: (1) Horizon problem: solved by temporal resolution. In the primordial low-density universe, the temporal field τ > 1 (time flows faster in weak gravitational fields). The causal horizon d = ∫ c τ(t') dt' is enlarged by the factor ⟨τ⟩, reducing the required number of e-folds from ~60 to ~60/⟨τ⟩. No inflaton needed. (2) Quasi-exponential expansion: produced by the multi-mode post-rebound cascade. Following the elastic quantum bounce (from the negative vacuum pressure P_vac = −A(L)ρ^√2 at ρ_crit = ρ_P/8), each fractal level n of the √2 texture tower contributes a decaying mode with rate Γ_n = 2^n/t₀. The superposition of N_max modes produces destructive interference in the slow-roll parameter: ε ~ 2−N_max. This is analogous to an explosion in a negative-pressure chamber: the medium assists the expansion, the confining walls provide restoring force, and energy cascades through the √2 hierarchy. (3) Primordial perturbation spectrum: generated by progressive mode freeze-out. As σ → σ_* (stabilization), the texture modes with m_n > H freeze out sequentially, reducing the effective mode count. This Kibble-Zurek mechanism produces: n_s − 1 = −α ln 2, r = 16 × 2−N_max where α is the mode freeze-out rate per e-fold and N_max is the total number of active modes. These two observables are decoupled — there is no consistency relation r = f(n_s). This is structurally distinct from all single-field inflation models. For n_s = 0.9649 (Planck 2018): α ≈ 0.051, meaning approximately one mode freezes every ~20 e-folds — physically reasonable. For N_max = 10–13: r = 0.016–0.002, within reach of LiteBIRD (σ_r ~ 10⁻³). Log-periodic modulations at ω_f = 2π/ln√2 ≈ 18.1 in the CMB power spectrum are an intrinsic prediction, not an ad hoc addition. The same √2 tower that drives inflation also provides dark matter (partially frozen modes, Chronostasis mechanism, 47/50 SPARC fit) and dark energy (stabilized branch vacuum energy, w > −1). This creates cross-epoch consistency tests: the modes generating perturbations at z ~ 10³⁰ are the same modes shaping galaxy rotation curves at z ~ 0. Five falsification criteria are provided: (1) detection of a consistency relation r = f(n_s), (2) r at a value not matching 16 × 2−N for integer N, (3) absence of log-periodic modulations at ω_f ≈ 18.1, (4) significant spectral running, (5) phantom dark energy (w < −1 at >5σ).