Local Primordial non-Gaussian Bias from Time Evolution

Primordial non-Gaussianity (PNG) is a signature of fundamental physics in the early universe that is probed by cosmological observations. It is well known that the local type of PNG generates a strong signal in the two-point function of large-scale structure tracers, such as galaxies. This signal, often termed ``scale-dependent bias'' is a generic feature of modulation of gravitational structure formation by a large-scale mode. It is less well-appreciated that the coefficient controlling this signal, $b_{\phi}$, is closely connected to the time evolution of the tracer number density. This correspondence between time evolution and local PNG can be simply explained for a universal tracer whose mass function only depends on peak height, and more generally for non-universal tracers in the separate universe picture, which we validate in simulations. We also describe how to recover the bias of tracers subject to a survey selection function, and perform a simple demonstration on simulated galaxies. Since the local PNG amplitude in $n-$point statistics ($f_{\rm NL}$) is largely degenerate with the coefficient $b_{\phi}$, this proof of concept study demonstrates that galaxy survey data can allow for more optimal and robust extraction of local PNG information from upcoming surveys.