  Measuring the environments of massive galaxies at high redshift is crucial to
understanding galaxy evolution and the conditions that gave rise to the
distribution of matter we see in the Universe today. While high-$z$ radio
galaxies (H$z$RGs) and quasars tend to reside in protocluster-like systems, the
environments of their radio-quiet counterparts are relatively unexplored,
particularly in the submillimetre, which traces dust-obscured star formation.
In this study we search for 850 $\mu$m-selected submillimetre galaxies in the
environments of massive ($M_{\star} > 10^{11} M_{\odot}$), radio-quiet ($L_{500
{\rm MHz}} \lesssim 10^{25}$ W Hz$^{-1}$) galaxies at $z \sim 1\text{--}3$
using S2COSMOS data. By constructing number counts in circular regions of
radius 1--6 arcmin and comparing with blank-field measurements, we find no
significant overdensities of SMGs around massive radio-quiet galaxies at any of
these scales, despite being sensitive down to overdensities of $\delta \sim
0.4$. To probe deeper than the catalogue we also examine the distribution of
peaks in the SCUBA-2 SNR map, which reveals only tentative signs of any
difference in the SMG densities of the radio-quiet galaxy environments compared
to the blank field, and only on smaller scales (1$^{\prime}$ radii,
corresponding to $\sim0.5$ Mpc) and higher SNR thresholds. We conclude that
massive, radio-quiet galaxies at cosmic noon are typically in environments with
$\delta\lesssim0.4$, which are either consistent with the blank field or
contain only weak overdensities spanning sub-Mpc scales. The contrast between
our results and studies of H$z$RGs with similar stellar masses and redshifts
implies an intrinsic link between the wide-field environment and radio AGN
luminosity at high redshift.
