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ABSTRACT Covering $$\sim 5600\, \deg ^2$$ to rms sensitivities of ∼70−100 $$\mu$$Jy beam−1, the LOFAR Two-metre Sky Survey Data Release 2 (LoTSS-DR2) provides the largest low-frequency (∼150 MHz) radio catalogue to date, making it an excellent tool for large-area radio cosmology studies. In this work, we use LoTSS-DR2 sources to investigate the angular two-point correlation function of galaxies within the survey. We discuss systematics in the data and an improved methodology for generating random catalogues, compared to that used for LoTSS-DR1, before presenting the angular clustering for ∼900 000 sources ≥1.5 mJy and a peak signal-to-noise ≥ 7.5 across ∼80 per cent of the observed area. Using the clustering, we infer the bias assuming two evolutionary models. When fitting angular scales of $$0.5 \le \theta \lt 5{^\circ }$$, using a linear bias model, we find LoTSS-DR2 sources are biased tracers of the underlying matter, with a bias of $$b_{\rm C}= 2.14^{+0.22}_{-0.20}$$ (assuming constant bias) and $$b_{\rm E}(z=0)= 1.79^{+0.15}_{-0.14}$$ (for an evolving model, inversely proportional to the growth factor), corresponding to $$b_{\rm E}= 2.81^{+0.24}_{-0.22}$$ at the median redshift of our sample, assuming the LoTSS Deep Fields redshift distribution is representative of our data. This reduces to $$b_{\rm C}= 2.02^{+0.17}_{-0.16}$$ and $$b_{\rm E}(z=0)= 1.67^{+0.12}_{-0.12}$$ when allowing preferential redshift distributions from the Deep Fields to model our data. Whilst the clustering amplitude is slightly lower than LoTSS-DR1 (≥2 mJy), our study benefits from larger samples and improved redshift estimates. 

We present images obtained with LABOCA on the APEX telescope of a sample of 22 galaxies selected via their red Herschel SPIRE 250-, 350- and $$500\textrm{-}\mu\textrm{m}$$ colors. We aim to see if these luminous, rare and distant galaxies are signposting dense regions in the early Universe. Our $$870\textrm{-}\mu\textrm{m}$$ survey covers an area of $$\approx0.8\,\textrm{deg}^2$$ down to an average r.m.s. of $$3.9\,\textrm{mJy beam}^{-1}$$, with our five deepest maps going $$\approx2\times$$ deeper still. We catalog 86 DSFGs around our 'signposts', detected above a significance of $$3.5\sigma$$. This implies a $$100\pm30\%$$ over-density of $$S_{870}>8.5\,\textrm{mJy}$$ DSFGs, excluding our signposts, when comparing our number counts to those in 'blank fields'. Thus, we are $$99.93\%$$ confident that our signposts are pinpointing over-dense regions in the Universe, and $$\approx95\%$$ confident that these regions are over-dense by a factor of at least $$\ge1.5\times$$. Using template SEDs and SPIRE/LABOCA photometry we derive a median photometric redshift of $$z=3.2\pm0.2$$ for our signposts, with an interquartile range of $$z=2.8\textrm{-}3.6$$. We constrain the DSFGs likely responsible for this over-density to within $$|\Delta z|\le0.65$$ of their respective signposts. These 'associated' DSFGs are radially distributed within $$1.6\pm0.5\,\textrm{Mpc}$$ of their signposts, have median SFRs of $$\approx(1.0\pm0.2)\times10^3\,M_{\odot}\,\textrm{yr}^{-1}$$ (for a Salpeter stellar IMF) and median gas reservoirs of $$\sim1.7\times10^{11}\,M_{\odot}$$. These candidate proto-clusters have average total SFRs of at least $$\approx (2.3\pm0.5)\times10^3\,M_{\odot}\,\textrm{yr}^{-1}$$ and space densities of $$\sim9\times10^{-7}\,\textrm{Mpc}^{-3}$$, consistent with the idea that their constituents may evolve to become massive ETGs in the centers of the rich galaxy clusters we see today.