We present realistic forecasts for the constraining power of the Nancy Grace Roman Space Telescope on fundamental cosmological parameters, with particular emphasis on the absolute neutrino mass scale, using full-shape analyses of the galaxy power spectrum. We analyze simulated light cone mock catalogs of $\mathrm{H}\alpha$ emission-line galaxies spanning the redshift range $0.5<z<2$ over $2400{\mathrm{deg}}^2$, designed to reproduce the expected properties of the Roman High Latitude Wide Area Spectroscopic Survey. We perform parameter inference on the galaxy power spectrum multipoles using two complementary theoretical frameworks: a model-dependent approach based on the effective field theory of large-scale structure (EFT of LSS) within $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$), and a model-independent phenomenological approach that makes no assumptions about the background cosmological model. In the $\mathrm{\Lambda }\mathrm{CDM}$ analysis, we find $m_{\nu }<0.380(0.162)\mathrm{eV}$ at 95(68)% CL using big bang nucleosynthesis (BBN) prior and a broad prior on $n_s$, which tightens to $m_{\nu }<0.276(0.121)\mathrm{eV}$ when Planck priors on ${\omega }_b$, ${\omega }_{\mathrm{cdm}}$, and $n_s$ are added. Our forecasts show that Roman can additionally constrain $H_0$, ${\mathrm{\Omega }}_m$, and ${\sigma }_8$ with precisions of 1.3%, 4.3%, and 2.9% in line with stage IV galaxy survey measurements and forecasts. In the model-independent analysis, we demonstrate that the phenomenological model can robustly recover unbiased measurements of the angular diameter distance, the Hubble parameter, and the growth of structure across all redshift bins, in the same range of scales as the EFT model, and obtain $m_{\nu }<0.63(0.36)\mathrm{eV}$ at 95(68)% CL when Planck priors are included.

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• Dark energy
• Dark matter
• Evolution of the Universe
• Large scale structure of the Universe