USSFT Paper XIII: Inflation and the U-Field Phase Transition. Non-Minimal Inflation from the Locked Lagrangian

The USSFT Lagrangian, as locked in Paper I, contains a non-minimal gravitational coupling (1/2) xi R Phi^2 alongside the symmetry-breaking potential V(Phi) = (lambda_U/4)(Phi^2 - Phi_0^2)^2. We show that this structure naturally supports a period of cosmic inflation via the well-known non-minimal ("xi-inflation") mechanism: in the Einstein frame, the effective potential develops an asymptotically flat plateau at large field values, enabling slow-roll inflation without introducing any new fields or parameters beyond those already present in the series. In the large-xi (attractor) regime, the leading predictions for n_s and r are fixed primarily by the plateau form and the e-fold number N, while the scalar amplitude constrains the combination lambda_U/xi^2 (status (B) for these relations; individual parameter values remain (C) until the Paper V dictionary pins them). The discrete lattice provides a natural UV cutoff that supplies a candidate UV completion for the would-be unitarity-bound sector (amplitude-level demonstration: (C)) and offers a concrete regulator for trans-Planckian modes (vacuum selection/adiabaticity: (C)). We interpret the onset of inflation as a phase transition in U-field configuration space, a change in the constraint state of the eternal lattice, not the creation of the field itself. The Z_2 domain wall problem inherent in the symmetry-breaking potential, detailed reheating dynamics, and lattice vacuum selection for trans-Planckian modes remain at (C) status. This is the thirteenth paper in the 18-paper USSFT technical series, in the middle of the Cosmology block (Papers XII-XV); it builds on the locked Lagrangian of Paper I (DOI: 10.5281/zenodo.19622931) and the gravitational sector of Paper XII (DOI: 10.5281/zenodo.19689591).