Systematics of aligned axions

Abstract

We describe a novel technique that renders theories of N axions tractable, and more generally can be used to efficiently analyze a large class of periodic potentials of arbitrary dimension. Such potentials are complex energy landscapes with a number of local minima that scales as √ N !, and so for large N appear to be analytically and numerically intractable. Our method is based on uncovering a set of approximate symmetries that exist in addition to the N periods. These approximate symmetries, which are exponentially close to exact, allow us to locate the minima very efficiently and accurately and to analyze other characteristics of the potential. We apply our framework to evaluate the diameters of flat regions suitable for slow-roll inflation, which unifies, corrects and extends several forms of "axion alignment" previously observed in the literature. We find that in a broad class of random theories, the potential is smooth over diameters enhanced by N 3/2 compared to the typical scale of the potential. A Mathematica implementation of our framework is available online.

Barnacles and gravity

“…Another interesting extension would be to include the effects of finite temperature, especially as this may be relevant for electroweak baryogenesis. Finally, given progress in modelling random landscapes, for example see [23,24] for two recent approaches, it would be interesting to determine the likelihood and importance of barnacles in specific landscape models.…”

Axion landscape cosmology

“…Note that even for σ Q = O(1/ √ N ), which one may also be interested in (e.g. [6,11]), this inequality is satisfied. We conclude HM instantons are irrelevant for the decay of quadratic domain minima.…”

“…Let us consider a particularly simple axion potential to illustrate our technique for the systematic sampling of inflationary trajectories. The theory is discussed at length in the appendix D of [6], but here we have set the phases to zero. The relevant parameters Figure 2: Sample of tensor-to-scalar ratios r and spectral indices n s for the particular axion theory discussed in §3.2.…”

“…Our notation is that of [6]: bold represents a vector or matrix. Here V 0 is a constant, the Λ 4 I are the couplings of the axions to the non-perturbative effects, θ are the N axion fields, Q is a P × N rank N matrix containing integer charges Q I j , and δ I are constant phases.…”

“…In the later sections of the paper we will consider a minimal coupling to QCD or a U (1) with random, M GUT -suppressed couplings, and the effects of gravitational instantons with actions of order M Pl /f . With these parameters and the techniques of [6] we can test whether this landscape truly solves the CC problem -that is, whether those cosmological histories in which collapsed structures form (à la [1,3]) do in fact resemble our universe.…”