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 Nancy Grace Roman Space Telescope (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 Roman's 18 detectors, and coherent wavelength shifts corresponding to the measured 0.06% 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 introduce a redshift-dependent distance modulus bias that, if left uncorrected, propagates to w 0 about-0.06 and w a = -0.236, which are larger than the forecast statistical uncertainties of sigma stat, w 0 = 0.025 and sigma stat, w 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 -- produces negligible redshift-dependent bias, with a minimal spread in w a (w a = -0.0004, sigma w a, sys = 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 Roman.