Sutter et al. have responded to the criticisms we made of their cosmic void catalogue in our recent paper presenting an alternative catalogue (Nadathur & Hotchkiss 2013). Unfortunately, their response contains several statements which are incorrect, as we point out in this note.
We consider methods with which to answer the question is any observed galaxy cluster too unusual for Lambda-CDM? After emphasising that many previous attempts to answer this question will overestimate the confidence level at which Lambda-CDM can be r
uled out, we outline a consistent approach to these rare clusters, which allows the question to be answered. We define three statistical measures, each of which are sensitive to changes in cluster populations arising from different modifications to the cosmological model. We also use these properties to define the equivalent mass at redshift zero for a cluster --- the mass of an equally unusual cluster today. This quantity is independent of the observational survey in which the cluster was found, which makes it an ideal proxy for ranking the relative unusualness of clusters detected by different surveys. These methods are then used on a comprehensive sample of observed galaxy clusters and we confirm that all are less than 2-sigma deviations from the Lambda-CDM expectation. Whereas we have only applied our method to galaxy clusters, it is applicable to any isolated, collapsed, halo. As motivation for future surveys, we also calculate where in the mass redshift plane the rarest halo is most likely to be found, giving information as to which objects might be the most fruitful in the search for new physics.
Multiple inflation is a model based on N=1 supergravity wherein there are sudden changes in the mass of the inflaton because it couples to flat direction scalar fields which undergo symmetry breaking phase transitions as the universe cools. The resul
ting brief violations of slow-roll evolution generate a non-gaussian signal which we find to be oscillatory and yielding f_NL ~ 5-20. This is potentially detectable by e.g. Planck but would require new bispectrum estimators to do so. We also derive a model-independent result relating the period of oscillations of a phase transition during inflation to the period of oscillations in the primordial curvature perturbation generated by the inflaton.
The form of the inflationary potential is severely restricted if one requires that it be natural in the technical sense, i.e. terms of unrelated origin are not required to be correlated. We determine the constraints on observables that are implied in
such natural inflationary models, in particular on $r$, the ratio of tensor to scalar perturbations. We find that the naturalness constraint does not require $r$ to be lare enough to be detectable by the forthcoming searches for B-mode polarisation in CMB maps. We show also that the value of $r$ is a sensitive discriminator between inflationary models.
