The inflationary origin of the Cold Spot anomaly

Single-field inflation, arguably the simplest and most compelling paradigm for the origin of our Universe, is strongly supported by the recent results of the Planck satellite and the BICEP2 experiment. The results from Planck, however, also confirm the presence of a number of anomalies in the Cosmic Microwave Background (CMB), whose origin becomes problematic in single-field inflation. Among the most prominent and well-tested of these anomalies is the Cold Spot, which constitutes the only significant deviation from gaussianity in the CMB. Planck's non-detection of primordial non-gaussianity on smaller scales thus suggests the existence of a physical mechanism whereby significant non-gaussianity is generated on large angular scales only. In this letter, we address this question by developing a localized version of the inhomogeneous reheating scenario, which postulates the existence of a scalar field able to modify the decay of the inflaton on localized spatial regions only. We demonstrate that if the Cold Spot is due to an overdensity in the last scattering surface, the localization mechanism offers a feasible explanation for it, thus providing a physical mechanism for the generation of localized non-gaussianity in the CMB. If, on the contrary, the Cold Spot is caused by a newly discovered supervoid (as recently claimed), we argue that the localization mechanism, while managing to enhance underdensities, may well shed light on the rarity of the discovered supervoid.Comment: 12 pages, 4 figures. v3 Comments and references added. It matches published versio

Optimal State-Contingent Unemployment Insurance

Since the probability of finding a job is affected not only by individual effort but also by the aggregate state of the economy, designing unemployment insurance payments conditional on the business cycle could be valuable. This paper answers a fundamental question related to this issue: How should the payments vary with the aggregate state of the economy?Unemployment Insurance; Aggregate Fluctuations; Recursive Contracts and Moral Hazard

Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via M\"{o}bius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.Comment: 13 pages. No figure. Accepted for publication in Symmetr