The Renormalization Group for Large-Scale Structure: Origin of Galaxy Stochasticity
arxiv(2024)
摘要
The renormalization group equations for large-scale structure (RG-LSS)
describe how the bias and stochastic (noise) parameters – both of matter and
biased tracers such as galaxies – evolve as a function of the cutoff Λ
of the effective field theory. In previous work, we derived the RG-LSS
equations for the bias parameters using the Wilson-Polchinski framework. Here,
we extend these results to include stochastic contributions, corresponding to
terms in the effective action that are higher order in the current J. We show
that the RG equations exhibit an interesting, previously unnoticed structure at
all orders in J, which implies that a single nonlinear bias term immediately
generates all stochastic moments through RG evolution. We then derive the
nonlinear RG evolution of the (leading-derivative) stochastic parameters for
all n-point functions, and show that this evolution is controlled by a
different, lower scale than the nonlinear scale. This has implications for the
optimal choice of the renormalization scale when comparing the theory with data
to obtain cosmological constraints.
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