Chromatic Effects Across the Roman Focal Plane: Implications for Supernova Photometry and Measurements of Cosmological Parameters

Calibration uncertainties are the leading systematics in cosmological analyses using Type Ia supernovae (SNe Ia). For the $\mathit{\text{Nancy}}\mathit{\text{Grace}}\mathit{\text{Roman}}\mathit{\text{Space}}\mathit{\text{Telescope}}\mathit{\text{(Roman)}}$, we quantify the impact of chromatic effects on SNe Ia photometry and derived cosmological parameters, using simulated light curves from the High-Latitude Time Domain Survey. We investigate two sources of wavelength-dependent bias: focal plane array (FPA)-dependent wavelength shifts arising from spatial variations across $\mathit{\text{Roman’s}}$ 18 detectors, and coherent wavelength shifts corresponding to the measured $0.06\mathrm{\%}$ uncertainty in absolute filter wavelength calibration. Using simulated SNe Ia light curves, we find that the FPA-dependent shifts – which range from +6 to -80 $\mathring{\mathrm{A}}$ introduce a redshift-dependent distance modulus bias that, if left uncorrected, propagates to $\mathrm{\Delta }{w}_0\sim -0.06$ and $\mathrm{\Delta }{w}_a=-0.236$, which are larger than the forecast statistical uncertainties of ${\sigma }_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t},{\mathrm{w}}_0}=0.025$ and ${\sigma }_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t},{\mathrm{w}}_{\mathrm{a}}}=0.114$, rendering the survey systematics-limited. We probe the impact of chromatic effects by employing detector-specific filter curves that recover unbiased cosmological constraints; to remain below the statistical noise floor, FPA wavelength shifts must be characterized to within 20%. In contrast, a coherent 0.06% offset in filter wavelength calibration – ranging from -3 to -11 $\mathring{\mathrm{A}}$ – produces negligible redshift-dependent bias, with a minimal spread in $w_a$ ($\mathrm{\Delta }{w}_a=-0.0004,{\sigma }_{w_{a,\mathrm{s}\mathrm{y}\mathrm{s}}}=0.114)$, demonstrating that the achieved pre-launch calibration precision is sufficient for this systematic to remain subdominant. Our results establish that chromatic effects are a required component of SN Ia cosmology with $\mathit{\text{Roman}}$.