JWST COSMOS-3D: Spectroscopic Census and Luminosity Function of [O III] Emitters at 6.75<z<9.05 in COSMOS

We present a spectroscopically-selected [OIII]+Hb emitters catalogue at 6.75<z<9.05 and the resulting [OIII] 5008 ÅLuminosity Function (LF) in the COSMOS field. We leverage the 0.3 deg$^{2}$ covered to date by COSMOS-3D using NIRCam/WFSS F444W (90% of the survey) to perform the largest spectroscopic search for [OIII] emitters at 6.75<z<9.05. We present our catalogue of 237 [OIII] emitters and their associated completeness function. The inferred constraints on the [OIII] LF enable us to characterise the knee of the [OIII] LF, resulting in improved [OIII] LF constraints at z~7,8. Notably, we find evidence for an accelerated decline of the [OIII] luminosity density between z~7 and z~8, which could be expected if the metallicity of [OIII] emitters, as well as the cosmic star-formation rate density, is declining at these redshifts. We find that theoretical models that reproduce the z~7,8 [OIII] LF do not reproduce well the [OIII] equivalent width distribution, pointing to potential challenges in the modelling of[OIII] and other nebular lines in the early Universe. Finally, we provide the first constraints on the cosmic variance of [OIII] emitters, estimating at 15% the relative uncertainty for the z~7,8 [OIII] LF in the 0.3 deg$^2$ field. This estimate is in good agreement with that inferred from clustering, and shows that the [OIII] LF derived from smaller extragalactic legacy fields is strongly affected by cosmic variance. Our results highlight the fundamental role that wide-area JWST slitless surveys play to map the galaxy large-scale structure down into the reionisation era, serving as a springboard for a variety of science cases.