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Article
Report number	arXiv:1209.5701 ; CERN-PH-TH-2012-246 ; CPHT-RR-021.0512 ; CERN-PH-TH-2012-246
Title	Inflating in a Trough: Single-Field Effective Theory from Multiple-Field Curved Valleys
Author(s)	Burgess, C.P. (Perimeter Inst. Theor. Phys. ; McMaster U.) ; Horbatsch, M.W. (Mississippi U. ; McMaster U.) ; Patil, Subodh.P. (Ecole Polytechnique, CPHT ; CERN)
Publication	2013
Imprint	26 Sep 2012
Number of pages	28
Note	Comments: 28 pages + 3 appendices 28 pages + 3 appendices, references added and typos corrected, matches published version
In:	JHEP 01 (2013) 133
DOI	10.1007/JHEP01(2013)133
Subject category	Particle Physics - Theory
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.
Copyright/License	Preprint: © 2012-2024 CERN (License: CC-BY-3.0)

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