A Goldstone Boson Equivalence for Inflation
arxiv(2024)
摘要
The effective field theory of single-field inflation characterizes the
inflationary epoch in terms of a pattern of symmetry breaking. An operator
acquires a time-dependent vacuum expectation value, defining a preferred
spatial slicing. In the absence of dynamical gravity, the fluctuations around
the time-dependent background are described by the Goldstone boson associated
with this symmetry breaking process. With gravity, the Goldstone is eaten by
the metric, becoming the scalar metric fluctuation. In this paper, we will show
that in general single-field inflation, the statistics of scalar metric
fluctuations are given by the statistics of this Goldstone boson it decoupled
from gravity up to corrections that are controlled as an expansion in slow-roll
parameters. This even holds in the presence of additional parameters, like the
speed of sound, that naively enhance the impact of the gravitational terms. In
the process, we derive expressions for leading and sub-leading gravitational
corrections to all-orders in the Goldstone boson.
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