2010/05/31 by Courtney M. Peterson, Max Tegmark · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Anisotropy #CMB cold spot #Classical mechanics #Cosmic microwave background #Cosmology and Gravitation Theories #Covariant transformation #Curvature #Geometry #Geophysics and Gravity Measurements #Mathematical physics #Mathematics #Observable #Physics #Quantum mechanics #Solar and Space Plasma Dynamics #Statistical physics #Theoretical physics #astro-ph.CO #hep-th
paper · pdf · doi:10.1103/physrevd.83.023522
published as Phys.Rev.D83:023522,2011 · 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 figures
arxiv created 2010/10/29 · openalex publication_date 2011/01/25 · arxiv updated 2011/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive accurate semianalytic formulas for the power spectra from two-field inflation assuming an arbitrary potential and arbitrary noncanonical 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 evolution of modes can be inferred mostly from the background kinematics and the geometry of the field manifold. From these expressions, we derive semianalytic formulas for the curvature, isocurvature, and cross spectra, and the standard 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 general features of the inflationary Lagrangian translate into distinct features in the observable power spectra. In particular, we find that key features of the power spectra can be directly read off from the nature of the roll path, the curve the field vector rolls along with respect to the two-dimensional field manifold. For example, models whose roll path makes a sharp turn around 60 e-foldings before the end of inflation tend to be ruled out because they produce stronger departures from scale invariance than are allowed by the latest CMB observations. Finally, we apply our formalism to confront four classes of two-field models with WMAP data, including doubly quadratic and quartic potentials and nonstandard kinetic terms, showing how whether a model is ruled out or not depends not only on certain features of the inflationary Lagrangian, but also on the initial conditions. Ultimately, for a two-field model to be consistent with observations, we show that it must possess the right balance of certain kinematical and dynamical behaviors, which we reduce to a set of functions that represent the main characteristics of any two-field model of inflation.