How bursty star formation shapes spectral diversity at high redshifts: breaking degeneracies in early galaxy formation

JWST has revealed an unexpected abundance of z>10 galaxies and striking spectral diversity. Here, we model bursty star formation histories (SFHs) to explore how they shape this diversity and whether spectroscopy can discriminate between explanations for the UV luminosity function (UVLF) excess. We find strong burstiness ($σ_{UV}(M_h=10^{10}M_\odot)$~0.9 mag), increasing toward low halo masses, is required to reproduce the z~6 UVLF and observed fractions of galaxies in recent star formation upturns and downturns, traced by SFR$_3$/SFR$_{50}$. This burstiness naturally reproduces UVLFs and SFR upturn and downturn fractions over z~6-11. With increasing redshift, we predict galaxies in recent upturns (SFR$_3$/SFR$_{50}>5$) increasingly dominate the UVLF bright end, reflecting rising accretion rates and burstier low-mass halos. This results in higher median emission-line equivalent widths (EWs), bluer UV slopes and weaker Balmer breaks at fixed $M_{UV}$, while distributions of these properties broaden. We find the downturn fraction (SFR$_3$/SFR$_{50}<0.2$) is particularly sensitive to stochasticity: increasing towards faint $M_{UV}$ if burstiness increases in lower mass halos, and evolving with redshift only if stochasticity does. However, the model underpredicts the z~14 UVLF, so we explore two models which match the UVLF: increased burstiness and increased star formation efficiency. From z=10 to 14, at fixed $M_{UV}$, increased burstiness predicts the downturn fraction increases by ~2x and the weak-emitter fraction (H$β$ EW<50Å) by ~1.5x. By contrast, the increased efficiency model predicts a constant downturn fraction and declining weak-emitter fraction. Overall, our results indicate burstiness is important for explaining spectral diversity and evolution at z~6-14, and that spectroscopic samples spanning a broad $M_{UV}$ range can establish its role in the z~14 UVLF excess.