  Many inflationary theories introduce new scalar, vector, or tensor degrees of
freedom that may then affect the generation of primordial density
perturbations. Here we show how to search a galaxy (or 21-cm) survey for the
imprint of primordial scalar, vector, and tensor fields. These new fields
induce local departures to an otherwise statistically isotropic two-point
correlation function, or equivalently, nontrivial four-point correlation
functions (or trispectra, in Fourier space), that can be decomposed into
scalar, vector, and tensor components. We write down the optimal estimators for
these various components and show how the sensitivity to these modes depends on
the galaxy-survey parameters. New probes of parity-violating early-Universe
physics are also presented.
