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We carried out the largest ($>3.5\times10^5$ Mpc$^3$, 26 deg$^2$) H$\alpha$narrow band survey to date at $z\sim0.2$ in the SA22, W2 and XMMLSSextragalactic fields. Our survey covers a large enough volume to overcomecosmic variance and to sample bright and rare H$\alpha$ emitters up to anobserved luminosity of $\sim10^{42.4}$ erg s$^{-1}$, equivalent to $\sim11M_\odot$ yr$^{-1}$. Using our sample of $220$ sources brighter than$>10^{41.4}$ erg s$^{-1}$ ($>1 M_\odot$ yr$^{-1}$), we derive H$\alpha$luminosity functions, which are well described by a Schechter function with$\phi^* = 10^{-2.85\pm0.03}$ Mpc$^{-3}$ and $L^*_{H\alpha} = 10^{41.71\pm0.02}$erg s$^{-1}$ (with a fixed faint end slope $\alpha=-1.35$). We find thatsurveys probing smaller volumes ($\sim3\times10^4$ Mpc$^3$) are heavilyaffected by cosmic variance, which can lead to errors of over $100$ per cent inthe characteristic density and luminosity of the H$\alpha$ luminosity function.We derive a star formation rate density of $\rho_\mathrm{SFRD} =0.0094\pm0.0008$ $M_\odot$ yr$^{-1}$, in agreement with the redshift-dependentH$\alpha$ parametrisation from Sobral et al. (2013). The two-point correlationfunction is described by a single power law $\omega(\theta) = (0.159\pm0.012)\theta^{(-0.75\pm0.05)}$, corresponding to a clustering length of $r_0 =3.3\pm0.8$ Mpc/h. We find that the most luminous H$\alpha$ emitters at$z\sim0.2$ are more strongly clustered than the relatively fainter ones. The$L^*_{H\alpha}$ H$\alpha$ emitters at $z\sim0.2$ in our sample reside in$\sim10^{12.5-13.5}$ $M_\odot$ dark matter haloes. This implies that the moststar forming galaxies always reside in relatively massive haloes or group-likeenvironments and that the typical host halo mass of star-forming galaxies isindependent of redshift if scaled by $L_\mathrm{H\alpha}/L^*_{H\alpha}(z)$, asproposed by Sobral et al. (2010).

A large narrow band H$\alpha$ survey at $z\sim0.2$: the bright end of the luminosity function, cosmic variance and clustering across cosmic time