HETDEX [OII] galaxies at $z\le 0.48$: Growth of structures from power spectrum multipoles

We use the monopole and quadrupole power spectra of [\ion{O}{2}]-emitting galaxies in the HETDEX Public Data Release 1 to constrain the growth of cosmic structures at $z\le 0.48$. We interpret the power spectra using a simulation-based model built from the Mucho-Uchuu-1G $N$-body simulation. The best-fit model reproduces the observed power spectra remarkably well up to $k_{\mathrm{m}\mathrm{a}\mathrm{x}}=0.7h{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$, and goodness-of-fit tests confirm that the HETDEX [\ion{O}{2}] clustering is consistent with the $\mathit{\text{Planck}}$ flat $\mathrm{\Lambda }$CDM cosmology. We test the general relativity (GR) prediction for the linear growth index, $\gamma \simeq 0.55$. When the Alcock-Paczyński parameters are held fixed at their fiducial values, we find consistency with the GR prediction, $\gamma =0.55\pm 0.05$. And, when the AP parameters are allowed to vary, $\gamma =0.60\pm 0.07$, which is consistent with both the GR prediction and the suppressed growth rate reported by \citet{Nguyen_2023}. These results establish HETDEX [\ion{O}{2}] galaxies as a competitive, independent low-redshift probe of the growth of structures and motivate future full cosmological inference.