Geometric dark matter from Residual Spacetime Deformations: Covariant infinite-derivative completion, cosmological evolution, and relic abundance

We formulate Residual Spacetime Deformations (RSDs) as a covariant quadratic spin-two dark sector with a constant-scale infinite-derivative kinetic completion. The construction replaces the minimally covariantized Fierz–Pauli operator by a curvature-completed Hermitian operator and dresses the complete massive operator with a zero-free entire form factor. The stationary spectrum contains the single Fierz–Pauli pole with the healthy local Fierz–Pauli residue, while the FLRW scalar–vector–tensor reduction identifies the constraint system and the five quadratic massive polarizations on its nondegenerate stable domain. During inflation, the canonically normalized transverse-traceless strain acquires a nearly scale-invariant spectrum and freezes outside the horizon. A covariant scalar-clock profile describes the effective transition to a constant post-inflationary mass and separates classical coherent transfer from helicity-resolved particle production. In the regime 𝐻 ≪ 𝑀 0 , the massive TT strain oscillates with an 𝑎 − 3 / 2 envelope, its averaged pressure vanishes, and its density redshifts as 𝑎 − 3 . We derive the coherent relic density, give the general helicity-resolved form of any produced component, obtain the leading nonrelativistic wave-pressure/Jeans scale, and formulate the anisotropic-stress and TT-projector isocurvature response. For the coherent abundance-normalization point 𝑍 o s c / 𝑍 i n f = 1 , ℐ c l = 6 0 , 𝐻 i n f = 1 ⁢ 0 1 3 G e V , and 𝛺 p r o d ⁢ ℎ 2 = 0 , 𝛺 𝛥 ⁢ ℎ 2 = 0 . 1 2 is obtained at 𝑀 0 ≃ 1 . 5 × 1 0 − 6 e V ; CMB isocurvature and the full FLRW scalar stability conditions remain independent restrictions on observational viability. The resulting framework connects inflationary tensor-strain initial conditions to a pressureless geometric dark component while making explicit the domain in which the quadratic spin-two EFT is controlled.