Inflation after False Vacuum Decay: Observational Prospects after Planck

We assess two potential signals of the formation of our universe by the decay of a false vacuum. Negative spatial curvature is one possibility, but the window for its detection is now small. However, another possible signal is a suppression of the CMB power spectrum at large angles. This arises from the steepening of the effective potential as it interpolates between a flat inflationary plateau and the high barrier separating us from our parent vacuum. We demonstrate that these two effects can be parametrically separated in angular scale. Observationally, the steepening effect appears to be excluded at large l; but it remains consistent with the slight lack of power below l about 30 found by the WMAP and Planck collaborations. We give two simple models which improve the fit to the Planck data; one with observable curvature and one without. Despite cosmic variance, we argue that future CMB polarization and most importantly large-scale structure observations should be able to corroborate the Planck anomaly if it is real. If we further assume the specific theoretical setting of a landscape of metastable vacua, as suggested by string theory, we can estimate the probability of seeing a low-l suppression in the CMB. There are significant theoretical uncertainties in such calculations, but we argue the probability for a detectable suppression may be as large as O(1), and in general is significantly larger than the probability of seeing curvature.
Comment: 34 pages plus appendices, 16 figures. v2: Corrections and clarifications to section 3.2, conclusions unchanged. References added