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 \textit{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 \textit{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 $\rm Å$ introduce a redshift-dependent distance modulus bias that, if left uncorrected, propagates to $Δw_0 \sim -0.06$ and $Δw_a = -0.236$, which are larger than the forecast statistical uncertainties of $σ_{\rm stat, w_0} = 0.025$ and $σ_{\rm stat, w_a} = 0.114$, 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 $\rm Å$ -- produces negligible redshift-dependent bias, with a minimal spread in $w_a$ ($Δw_a = -0.0004, σ_{w_{a,\rm sys}} = 0.114)$, 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 \textit{Roman}.