In recent years it has been noted that the perturbative treatment of the statistics of fluctuations may fail to make correct predictions for the abundance of primordial black holes (PBHs). Moreover, it has been shown in some explicit single-field examples that the nonperturbative effects may lead to an exponential tail for the probability distribution function (PDF) of fluctuations responsible for PBH formation—in contrast to the PDF being Gaussian, as suggested by perturbation theory. In this paper, we advocate that the so-called <italic>&#948;N</italic> formalism can be considered as a simple, yet effective, tool for the nonperturbative estimate of the tail of the PDF. We discuss the criteria a model needs to satisfy so that the results of the classical <italic>&#948;N</italic> formalism can be trusted and most possible complications due to the quantum nature of fluctuations can be avoided. As a proof of concept, we then apply this method to a simple example and show that the tail of the PDF can be even <italic>heavier</italic> than exponential, leading to a significant enhancement of the PBH formation probability, compared with the predictions of the perturbation theory. Our results, along with other related findings, motivate the invention of new, nonperturbative methods for the problem and open up new ideas on generating PBHs with notable abundance.

Iran

Sina Hooshangi

Mohammad Hossein Namjoo

Mahdiyar Noorbala

Rare events are nonperturbative: Primordial black holes from heavy-tailed distributions

In this paper we develop a formalism for studying the nonrelativistic limit of relativistic field theories in a systematic way. By introducing a simple, nonlocal field redefinition, we transform a given relativistic theory, describing a real, self-interacting scalar field, into an equivalent theory, describing a complex scalar field that encodes at each time both the original field and its conjugate momentum. Our low-energy effective theory incorporates relativistic corrections to the kinetic energy as well as the backreaction of fast-oscillating terms on the behavior of the dominant, slowly varying component of the field. Possible applications of our new approach include axion dark matter, though the methods developed here should be applicable to the low-energy limits of other field theories as well.

United States

Alan H. Guth

David I. Kaiser

Relativistic corrections to nonrelativistic effective field theories

Standard Clocks in the primordial epoch leave a special type of features in the primordial perturbations, which can be used to directly measure the scale factor of the primordial universe as a function of time a(t) , thus discriminating between inflation and alternatives. We have started to search for such signals in the Planck 2013 data using the key predictions of the Standard Clock. In this Letter, we summarize the key predictions of the Standard Clock and present an interesting candidate example in Planck 2013 data. Motivated by this candidate, we construct and compute full Standard Clock models and use the more complete prediction to make more extensive comparison with data. Although this candidate is not yet statistically significant, we use it to illustrate how Standard Clocks appear in Cosmic Microwave Background (CMB) and how they can be further tested by future data. We also use it to motivate more detailed theoretical model building.