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[O III]$\lambda\lambda$4960,5008 doublet are often the strongest narrowemission lines in starburst galaxies and quasi-stellar objects (QSOs), and thusare a promising probe to possible variation of the fine-structure constant$\alpha$ over cosmic time. Previous such studies using QSOs optical spectrawere limited to $z<1$. In this work, we constructed a sample of 40 spectra ofLy$\alpha$ emitting galaxies (LAEs) and a sample of 46 spectra of QSOs at$1.09<z<3.73$ using the VLT/X-Shooter near-infrared spectra publicly available.We measured the wavelength ratios of the two components of the spin-orbitdoublet and accordingly calculated $\alpha(z)$ using two methods. Analysis onall of the 86 spectra yielded $\Delta\alpha/\alpha=(-3\pm6)\times10^{-5}$ withrespect to the laboratory $\alpha$ measurements, consistent with no variationover the explored time interval. If assuming a uniform variation rate, weobtained $\alpha^{-1}{\rm d}\alpha/{\rm d}t = (-3\pm6)\times10^{-15}$ yr$^{-1}$within the last 12 Gyrs. Extensive tests indicate that $\alpha$ variation couldbe better constrained using starburst galaxies' spectra than using QSO spectrain future studies.

Time Variation of Fine-Structure Constant Constrained by [O III] Emission-Lines at 1.1