We derive semi-analytic formulae for the power spectra of two-field inflation
assuming an arbitrary potential and non-canonical kinetic terms, and we use
them both to build phenomenological intuition and to constrain classes of
two-field models using WMAP data. Using covariant formalism, we first develop a
framework for understanding the background field kinematics and introduce a
"slow-turn" approximation. Next, we find covariant expressions for the
evolution of the adiabatic/curvature and entropy/isocurvature modes, and we
discuss how the mode evolution can be inferred directly from the background
kinematics and the geometry of the field manifold. From these expressions, we
derive semi-analytic formulae for the curvature, isocurvature, and cross
spectra, and the spectral observables, all to second-order in the slow-roll and
slow-turn approximations. In tandem, we show how our covariant formalism
provides useful intuition into how the characteristics of the inflationary
Lagrangian translate into distinct features in the power spectra. In
particular, we find that key features of the power spectra can be directly read
off of the nature of the roll path, the curve the field vector rolls along with
respect to the field manifold. For example, models whose roll path makes a
sharp turn 60 e-folds before inflation ends tend to be ruled out because they
produce strong departures from scale invariance. Finally, we apply our
formalism to confront four classes of two-field models with WMAP data,
including doubly quadratic and quartic potentials and non-standard kinetic
terms, showing how whether a model is ruled out depends not only on certain
features of the inflationary Lagrangian, but also on the initial conditions.
Ultimately, models must possess the right balance of kinematical and dynamical
behaviors, which we capture in a set of functions that can be reconstructed
from spectral observables.Comment: Revised to match accepted PRD version: Improved discussion of
background kinematics and multi-field effects, added tables summarizing key
quantities and their links to observables, more detailed figures, fixed typos
in former equations (103) and (117). 49 PRD pages, 11 figure
