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We study the evolving environment dependence of mass accretion by dark haloesin simulations of cold and warm dark matter (CDM and WDM) cosmologies. Thelatter allows us to probe the nature of halo growth at scales below the WDMhalf-mode mass, which form an extreme regime of nonlinear collisionlessdynamics and offer an excellent test-bed for ideas relating to hierarchicalgrowth. As environmental proxies, we use the local halo-centric matter density$\delta$ and tidal anisotropy $\alpha$, as well as large-scale halo bias $b_1$.Our analysis, while reproducing known trends for environment-dependentaccretion in CDM, as well as the comparison between accretion in CDM and WDM,reveals several interesting new features. As expected from excursion setmodels, WDM haloes have higher specific accretion rates, dominated by theaccretion of diffuse mass, as compared to CDM haloes. For low-mass WDM haloes,we find that the environment-dependence of both diffuse mass accretion as wellas accretion by mergers is almost fully explained by $\alpha$. For the othercases, $\delta$ plays at least a comparable role. We detect, for the firsttime, a significant and evolving assembly bias due to diffuse mass accretionfor low-mass CDM and WDM haloes (after excluding splashback objects), with a$z=0$ strength higher than with almost all known secondary variables andlargely explained by $\alpha$. Our results place constraints on semi-analyticalmerger tree algorithms, which in turn could affect the predictions of galaxyevolution models based on them.

Mass accretion rates and multi-scale halo environment in cold and warm dark matter cosmologies