High-redshift cosmology with oxygen lines from H$\alpha$ surveys

A new generation of cosmological experiments will spectroscopically detect the H$\alpha$ line from ELGs at optical/near-infrared frequencies. Other emission lines will also be present, which may come from the same H$\alpha$ sample or constitute a new galaxy sample altogether. Our goal is to assess the value, for cosmological investigation, of galaxies at $z\gtrsim2$ present in H$\alpha$ galaxy surveys and identifiable by the highly redshifted ultra-violet and optical lines - namely the OII line and the OIII doublet in combination with the H$\beta$ line. We use state-of-the-art luminosity functions to estimate the number density of OIIIb and OII ELGs. We study the constraining power of these high-redshift galaxy samples on cosmological parameters such as the BAO amplitude, $H(z)$, $D_{\rm A}(z)$, $f\sigma_8(z)$, and $b\sigma_8(z)$ for different survey designs. We present a strong science case for extracting the OIIIb sample, which we consider as an independent probe of the Universe in the redshift range $2-3$. Moreover, we show that the OII sample can be used to measure the BAO and growth of structure above $z=3$; albeit it may be shot-noise dominated, it will nonetheless provide valuable tomographic information. We discuss the scientific potential of a sample of galaxies which, so far, has been mainly considered as a contaminant in H$\alpha$ galaxy surveys. Our findings indicate that planned H$\alpha$ surveys should include the extraction of these oxygen-line samples in their pipeline, to enhance their scientific impact on cosmology.