A Planck-Scale Momentum Cutoff for Flat-Background Spin-2 Gravity: Deser Bootstrap, UV Finiteness, and FLRW Singularity Resolution

We study a massless spin-2 field on a flat Minkowski background with a single axiom: all field modes satisfy |k| ≤ ℓ_P⁻¹. Three results follow. First, the Deser self-consistency bootstrap, applied to the mode-restricted field, yields the Einstein–Hilbert action with fields restricted to the compact Fourier domain; classical solutions are the band-limited projections of the corresponding GR solutions. Second, all graviton loop integrals over the compact domain [0, ℓ_P⁻¹] are finite, providing power-counting UV finiteness pending gauge consistency. Third, the band-limited projection of the radiation-dominated FLRW scale factor is a_reg(η) = (2/π)[(η/ℓ_P) Si(η/ℓ_P) + cos(η/ℓ_P)] (dimensionless). This function has a positive global minimum a_reg(0) = 2/π > 0, established by the strict positivity of Si(u) for u > 0; the corresponding minimum proper-length scale is (2/π) ℓ_P, and the FLRW Kretschmann invariant evaluates at the bounce to K_reg(0) = (3/4)π⁴ ℓ_P⁻⁴ ≈ 73.06 ℓ_P⁻⁴. Computing G_μν[g_reg] directly shows that a_reg satisfies the cutoff-restricted Einstein equations with effective stress-energy T^eff_μν that vanishes at the bounce (de Sitter-like instantaneous state) and recovers radiation for |η| ≫ ℓ_P. The bounce is a dynamical solution of the cutoff-restricted theory, not merely a kinematic construction.