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 Phi² alongside the symmetry-breaking potential V (Phi) = (lambdaU/4) (Phi² - Phi₀²) 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 nₛ and r are fixed primarily by the plateau form and the e-fold number N, while the scalar amplitude constrains the combination lambdaU/xi² (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 Z₂ 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. 19622932) and the gravitational sector of Paper XII (DOI: 10. 5281/zenodo. 19689592).