Time-Symmetric Gravity Today: A Closed-Time-Path Kernel for Future–Mass Projection that Preserves the ΛCDM Background and Acts Only on Structure

We present a quantum-field-theory–consistent formulation of Future–Mass Projection (FMP), in which the present gravitational response depends on baryons plus a short, band-limited projection of their near future along worldlines. Unlike earlier phenomenological variants, the new formulation is derived from a Closed-Time-Path (CTP/Schwinger–Keldysh) influence functional, yielding a divergence-free bitensor kernel with finite horizon and vanishing DC offset. This construction automatically preserves the homogeneous background expansion and enforces local conservation. We fix the cosmological ratio R(z) ≡ ΩF /Ωb to the observed constant R0 = 5.4, so the background exactly matches ΛCDM; FMP then appears only in inhomogeneous sectors through a scale- and time-dependent linear-growth coupling μ(a, k) that reduces to GR in the k → 0 and local limits. We compare against the previous “projector×scalar” kernel used in galaxy fits and show how the CTP kernel (i) removes background drift, (ii) restores Noether conservation, (iii) remains safe in Solar- System/PPN and gravitational-wave–speed tests, and (iv) delivers falsifiable predictions for fσ8(z) suppression without disturbing BAO/SN/chronometer constraints. We outline concrete observational gates and provide a minimal parameterization suitable for immediate use in Boltzmann and LSS pipelines.