Observations of the microwave background fluctuations suggest a scale-dependent amplitude asymmetry of roughly $2.5\sigma$ significance. Inflationary explanations for this “anomaly” require non-Gaussian fluctuations which couple observable modes to those on much larger scales. In this paper, we describe an analysis of such scenarios which significantly extends previous treatments. We identify the non-Gaussian “response function” which characterizes the asymmetry and show that it is nontrivial to construct a model which yields a sufficient amplitude; many independent fine-tunings are required, often making such models appear less likely than the anomaly they seek to explain. We present an explicit model satisfying observational constraints and determine for the first time how large its bispectrum would appear to a Planck-like experiment. Although this model is merely illustrative, we expect it is a good proxy for the bispectrum in a sizeable class of models which generate a scale-dependent response using a large $\eta$ parameter.

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• Cosmic microwave background
• Inflation