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We examine the motion of light fields near the bottom of a potential valleyin a multi-dimensional field space. In the case of two fields we identify threegeneral scales, all of which must be large in order to justify an effectivelow-energy approximation involving only the light field, $\ell$. (Typicallyonly one of these -- the mass of the heavy field transverse to the trough -- isused in the literature when justifying the truncation of heavy fields.) Weexplicitly compute the resulting effective field theory, which has the form ofa $P(\ell,X)$ model, with $X = - 1/2(\partial \ell)^2$, as a function of thesescales. This gives the leading ways each scale contributes to any low-energydynamics, including (but not restricted to) those relevant for cosmology. Wecheck our results with the special case of a homogeneous roll near the valleyfloor, placing into a broader context recent cosmological calculations thatshow how the truncation approximation can fail. By casting our resultscovariantly in field space, we provide a geometrical criterion formodel-builders to decide whether or not the single-field and/or the truncationapproximation is justified, identify its leading deviations, and to efficientlyextract cosmological predictions.

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