For Gaussian primordial fluctuations the relationship between galaxy and matter overdensities, bias, is most often assumed to be local at the time of observation in the large-scale limit. This hypothesis is however unstable under time evolution, we provide proofs under several (increasingly more realistic) sets of assumptions. In the simplest toy model galaxies are created locally and linearly biased at a single formation time, and subsequently move with the dark matter (no velocity bias) conserving their comoving number density (no merging). We show that, after this formation time, the bias becomes unavoidably non-local and non-linear at large scales. We identify the non-local gravitationally induced fields in which the galaxy overdensity can be expanded, showing that they can be constructed out of the invariants of the deformation tensor (Galileons), the main signature of which is a quadrupole field in second-order perturbation theory. In addition, we show that this result persists if we include an arbitrary evolution of the comoving number density of tracers. We then include velocity bias, and show that new contributions appear; these are related to the breaking of Galilean invariance of the bias relation, a dipole field being the signature at second order.We test these predictions by studying the dependence of halo overdensities in cells of fixed dark matter density: measurements in simulations show that departures from the mean bias relation are strongly correlated with the non-local gravitationally induced fields identified by our formalism, suggesting that the halo distribution at the present time is indeed more closely related to the mass distribution at an earlier rather than present time. However, the non-locality seen in the simulations is not fully captured by assuming local bias in Lagrangian space. The effects on non-local bias seen in the simulations are most important for the most biased halos, as expected from our predictions.Accounting for these effects when modeling galaxy bias is essential for correctly describing the dependence on triangle shape of the galaxy bispectrum, and hence constraining cosmological parameters and primordial non-Gaussianity. We show that using our formalism we remove an important systematic in the determination of bias parameters from the galaxy bispectrum, particularly for luminous galaxies.

The primary components of two new candidate events (GW190403 051519 and GW190426 190642) fall in the mass gap predicted by pair-instability supernova theory. We also expand the population of binaries with significantly asymmetric mass ratios reported in GWTC-2 by an additional two events (q < 0.61 and q < 0.62 at 90% credibility for GW190403 051519 and GW190917 114630 respectively), and find that 2 of the 8 new events have effective inspiral spins χ eff > 0 (at 90% credibility), while no binary is consistent with χ eff < 0 at the same significance.

We study the scale-dependence of halo bias in generic (non-local) primordial non-Gaussian (PNG) initial conditions of the type motivated by inflation, parametrized by an arbitrary quadratic kernel. We first show how to generate non-local PNG initial conditions with minimal overhead compared to local PNG models for a general class of primordial bispectra that can be written as linear combinations of separable templates. We run cosmological simulations for the local, and non-local equilateral and orthogonal models and present results on the scale-dependence of halo bias. We also derive a general formula for the Fourier-space bias using the peak-background split (PBS) in the context of the excursion set approach to halos and discuss the difference and similarities with the known corresponding result from local bias models. Our PBS bias formula generalizes previous results in the literature to include non-Markovian effects and non-universality of the mass function and are in better agreement with measurements in numerical simulations than previous results for a variety of halo masses, redshifts and halo definitions. We also derive for the first time quadratic bias results for arbitrary non-local PNG, and show that non-linear bias loops give small corrections at large-scales. The resulting well-behaved perturbation theory paves the way to constrain non-local PNG from measurements of the power spectrum and bispectrum in galaxy redshift surveys.

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