Testing two-field inflation

Journal Article · Sat Jan 15 00:00:00 EST 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.023522· OSTI ID:21503943

Peterson, Courtney M ^[1]; Tegmark, Max ^[2]

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1. Department of Physics, Harvard University, Cambridge, Massachusetts 02138 (United States)
2. Department of Physics and MIT Kavli Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

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.

• OSTI ID: 21503943
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevD.83.023522; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
ENTROPY
LAGRANGIAN FUNCTION
RELICT RADIATION
SCALE INVARIANCE
SIMULATION
SPECTRA
TWO-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
ELECTROMAGNETIC RADIATION
FUNCTIONS
INVARIANCE PRINCIPLES
MICROWAVE RADIATION
PHYSICAL PROPERTIES
RADIATIONS
THERMODYNAMIC PROPERTIES