A New Window on the H{\alpha} Luminosity Function and Star Formation Rate Density from 1.2 < z < 6.6 from JWST Medium-Band Photometry

We present the first self-consistent measurement of the H{\alpha} luminosity function over a wide redshift range, covering cosmic noon into the epoch of reionization. Our analysis utilizes a novel method based on James Webb Space Telescope (JWST) NIRCam medium-band imaging. We combine data from the CANUCS, JWST in Technicolor, and JUMPS surveys which offer deep, uniform imaging (29.5-30 AB, 3{\sigma}) with extensive NIRCam medium-band coverage, reaching up to 29 total filters (up to 20 JWST) when including ancillary Hubble Space Telescope (HST) ACS and WFC3/UVIS data. The superb spectral energy distribution (SED) sampling enables precise, reliable photometric redshift estimation (outlier fraction 1.7\%, {\sigma} N_MAD = 0.039 for this sample) as well as accurate continuum subtraction and line flux measurement verified by spectroscopic follow-up (no systematic offset, 0.23 dex scatter). We measure the H{\alpha} luminosity function (LF) from 1.25 < z < 6.6 by tracing the H{\alpha} emission line in 11 medium-band filters. The combination of depth, redshift coverage, and statistical power is unique, providing strong constraints on the shape of the LF over almost three orders of magnitude in luminosity. Our dense SED sampling enables us to reliably correct for dust attenuation and derive dust-corrected star formation rate functions as well as the evolution of the cosmic star formation rate density over the full redshift range. We recover the peak at z ~ 2 and a decrease toward z = 6, though with a higher normalization more in line with recent IR measurements than UV, though eclipsing both. This potential tension will be addressed in future work utilizing larger surveys with MIR coverage to better constrain the bright end of the luminosity function and the effects of dust.