Constraints on the spacetime variation of the fine-structure constant using DESI emission-line galaxies

We present strong constraints on the spacetime variation of the fine-structure constant $\alpha$ using the Dark Energy Spectroscopic Instrument (DESI). In this pilot work, we utilize $\sim110,000$ galaxies with strong and narrow O III $\lambda\lambda$4959,5007 emission lines to measure the relative variation $\Delta\alpha/\alpha$ in space and time. The O III doublet is arguably the best choice for this purpose owing to its wide wavelength separation between the two lines and its strong emission in many galaxies. Our galaxy sample spans a redshift range of $0<z<0.95$, covering half of all cosmic time. We divide the sample into subsamples in 10 redshift bins ($\Delta z=0.1$), and calculate $\Delta\alpha/\alpha$ for the individual subsamples. The uncertainties of the measured $\Delta\alpha/\alpha$ are roughly between $2\times10^{-6}$ and $2\times10^{-5}$. We find an apparent $\alpha$ variation with redshift at a level of $\Delta\alpha/\alpha=(2\sim3)\times10^{-5}$. This is highly likely to be caused by systematics associated with wavelength calibration, since such small systematics can be caused by a wavelength distortion of $0.002-0.003$ \AA, which is beyond the accuracy that the current DESI data can achieve. We refine the wavelength calibration using sky lines for a small fraction of the galaxies, but it does not change our main results. We further probe the spatial variation of $\alpha$ in small redshift ranges, and do not find obvious, large-scale structures in the spatial distribution of $\Delta\alpha/\alpha$. As DESI is ongoing, we will include more galaxies, and by improving the wavelength calibration, we expect to obtain a better constraint that is comparable to the strongest current constraint.