Inflating in a Trough: Single-Field Effective Theory from Multiple-Field Curved Valleys

Abstract

We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective low-energy approximation involving only the light field, $\ell$. (Typically only one of these -- the mass of the heavy field transverse to the trough -- is used in the literature when justifying the truncation of heavy fields.) We explicitly compute the resulting effective field theory, which has the form of a $P(\ell ,X)$ model, with $X=-1/2(\partial \ell {)}^2$, as a function of these scales. This gives the leading ways each scale contributes to any low-energy dynamics, including (but not restricted to) those relevant for cosmology. We check our results with the special case of a homogeneous roll near the valley floor, placing into a broader context recent cosmological calculations that show how the truncation approximation can fail. By casting our results covariantly in field space, we provide a geometrical criterion for model-builders to decide whether or not the single-field and/or the truncation approximation is justified, identify its leading deviations, and to efficiently extract cosmological predictions.

28 pages + 3 appendices, references added and typos corrected, matches published version

References in corpus (13)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Effective Field Theory for Inflation
• String Cosmology: A Review
• Introduction to Effective Field Theory
• Mass hierarchies and non-decoupling in multi-scalar field dynamics
• Heavy fields, reduced speeds of sound and decoupling during inflation
• Strongly Coupled Perturbations in Two-Field Inflationary Models
• Curvature Perturbation Spectrum in Two-field Inflation with a Turning Trajectory
• Brane Inflation : String Theory viewed from the Cosmos

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