HI intensity mapping is a new observational technique to survey the large-scale structure of matter using the 21 cm emission line of atomic hydrogen (HI). In this work, we simulate BINGO (BAO from Integrated Neutral Gas Observations) and SKA (Square Kilometre Array) phase-1 dish array operating in auto-correlation mode. For the optimal case of BINGO with no foregrounds, the combination of the HI angular power spectra with Planck results allows $w$ to be measured with a precision of $4%$, while the combination of the BAO acoustic scale with Planck gives a precision of $7%$. We consider a number of potentially complicating effects, including foregrounds and redshift dependent bias, which increase the uncertainty on $w$ but not dramatically; in all cases the final uncertainty is found to be $Delta w < 8%$ for BINGO. For the combination of SKA-MID in auto-correlation mode with Planck, we find that, in ideal conditions, $w$ can be measured with a precision of $4%$ for the redshift range $0.35 < z < 3$ (i.e., for the bandwidth of $Delta u = [350, 1050]$ MHz) and $2%$ for $0 < z < 0.49$ (i.e., $Delta u = [950, 1421]$ MHz). Extending the model to include the sum of neutrino masses yields a $95%$ upper limit of $sum m_ u < 0.24$ eV for BINGO and $sum m_ u < 0.08$ eV for SKA phase 1, competitive with the current best constraints in the case of BINGO and significantly better than them in the case of SKA.
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