A JWST View of Cosmic Star Formation from $z\sim 0$ to 9 with Hydrogen Recombination Lines in the COSMOS and GOODS-N fields

We combine wide-area COSMOS-3D observations with deeper GOODS-N data from JWST/NIRCam F444W wide-field slitless spectroscopy to trace cosmic star formation over $z\sim 0$–9. The observations cover approximately $0.33{\mathrm{d}\mathrm{e}\mathrm{g}}^2$ in COSMOS and $60.9{\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{m}\mathrm{i}\mathrm{n}}^2$ in GOODS-N, with typical $3\sigma$ integrated line-flux limits of $3.2\times {10}^{-18}$ and $1.04\times {10}^{-18}\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{s}}^{-1}\mathrm{c}{\mathrm{m}}^{-2}$, respectively. The common $3.9$–$5.0\mu$m wavelength window probes Br$\alpha$, Br$\beta$, Pa$\alpha$, Pa$\beta$, H$\alpha$, and H$\beta$ across the local Universe, cosmic noon, and reionization. Our final sample contains 9146 galaxies, including 7883 in COSMOS and 1263 in GOODS-N. COSMOS constrains luminous emitters, while GOODS-N extends the luminosity functions toward fainter sources. We measure dust-corrected line luminosities, account for line-detection completeness, and convert the six lines to equivalent H$\alpha$ luminosities assuming Case B recombination. Schechter fits reveal an increase in the characteristic H$\alpha$-equivalent luminosity toward cosmic noon. Integrating the resulting star formation rate functions above $0.24M_{\odot }{\mathrm{y}\mathrm{r}}^{-1}$, we trace the cosmic star formation rate density from the local Universe to reionization. The combined Brackett, Paschen, and Balmer measurements are broadly consistent with the canonical UV- and IR-based cosmic star formation history at $z\lesssim 6$. Fixed-slope tests show that the H$\beta$ estimate at $z\sim 8$ remains sensitive to the external photometric faint-end constraint and extrapolation below our spectroscopic limit. These measurements provide complementary constraints on the distribution and integrated rate of star formation across cosmic time.