We prove that, in a generic single-field model, the consistency relation for the 3-point function in the squeezed limit receives corrections that vanish quadratically in the ratio of the momenta, i.e. as (k L /k S )2 . This implies that a detection of a bispectrum signal going as 1/k 2 L in the squeezed limit, that is suppressed only by one power of k L compared with the local shape, would rule out all single-field models. The absence of this kind of terms in the bispectrum holds also for multifield models, but only if all the fields have a mass much smaller than H. The detection of any scale dependence of the bias, for scales much larger than the size of the haloes, would disprove all single-field models. We comment on the regime of squeezing that can be probed by realistic surveys.

We study the consequences of imposing an approximate Galilean symmetry on the Effective Theory of Inflation, the theory of small perturbations around the inflationary background. This approach allows us to study the effect of operators with two derivatives on each field, which can be the leading interactions due to non-renormalization properties of the Galilean Lagrangian. In this case cubic nonGaussianities are given by three independent operators, containing up to six derivatives, two with a shape close to equilateral and one peaking on flattened isosceles triangles. The four-point function is larger than in models with small speed of sound and potentially observable with the Planck satellite.

The role of the cosmic web in shaping galaxy properties is investigated in the GAMA spectroscopic survey in the redshift range 0.03 z 0.25. The stellar mass, u − r dust corrected colour and specific star formation rate (sSFR) of galaxies are analysed as a function of their distances to the 3D cosmic web features, such as nodes, filaments and walls, as reconstructed by DisPerSE. Significant mass and type/colour gradients are found for the whole population, with more massive and/or passive galaxies being located closer to the filament and wall than their less massive and/or star-forming counterparts. Mass segregation persists among the starforming population alone. The red fraction of galaxies increases when closing in on nodes, and on filaments regardless of the distance to nodes. Similarly, the star-forming population reddens (or lowers its sSFR) at fixed mass when closing in on filament, implying that some quenching takes place. Comparable trends are also found in the state-of-the-art hydrodynamical simulation HORIZON-AGN. These results suggest that on top of stellar mass and large-scale density, the traceless component of the tides from the anisotropic large-scale environment also shapes galactic properties. An extension of excursion theory accounting for filamentary tides provides a qualitative explanation in terms of anisotropic assembly bias: at a given mass, the accretion rate varies with the orientation and distance to filaments. It also explains the absence of type/colour gradients in the data on smaller, non-linear scales.