Catching the Cosmic Sign Flip: Background and Growth Tests of Smooth Sign Switching Lambda s CDM

Recent baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI), in combination with CMB and supernova data, show a mild preference for dynamical dark energy over flat CDM. They can also drive the best-fit effective neutrino mass to unphysical negative values, motivating models that mimic this effect through late-time expansion physics. The sign-switching cosmological constant (s CDM) model addresses this by introducing an AdS-like negative vacuum energy density at high redshifts (z > z) that transitions to a dS-like positive density at low redshifts. While original fits assumed a discontinuous step function transition, we generalise the dynamics using a smooth hyperbolic tangent parametrisation, (z) proportional to [(z - z)]. We constrain the transition redshift z and smoothness parameter using background distance data from DES-SN5YR (with Dovekie recalibration) and DESI 2024 BAO. We further incorporate a compact redshift space distortion (RSD) f sigma 8 compilation. The joint data do not prefer the smooth sign-switching model over flat CDM, yielding nearly identical chi 2 min values, while information criteria penalise the additional parameters. The transition smoothness remains unconstrained and dominated by the prior volume (= 24.75+17.42-17.48), indicating that current data cannot distinguish between a sharp transition and a smooth dynamical crossover. This work does not directly constrain the physical sum of neutrino masses sum m nu; rather, it shows that current late-time background and growth data alone cannot resolve the transition details. We discuss the implications of this null detection and present projections for next-generation surveys.