We study the small scale structure of axion dark matter in the post-inflationary scenario, which predicts the formation of low-mass, high density clumps of gravitationally bound axions called axion miniclusters. To this end we follow numerically the cosmological evolution of the axion field and the network of strings and domain walls until the density contrast is frozen. Our simulations, comprising up to 8192 3 points, are the largest studies of the axion field evolution in the non-linear regime presented so far. Axitons, pseudobreathers of the Klein-Gordon equation, are observed to form in our simulation at late times. Studying their properties analytically and numerically, we observe that in particular the earliest axitons contribute to density perturbations at the typical length scale of miniclusters. We analyse the small scale structure of the density field, giving the correlation length, power spectrum and the distribution of high density regions that will collapse into axion miniclusters. The final density field of our simulations can be used to calculate the minicluster mass fraction in simulations including gravity. In particular, we find that typical minicluster progenitors are smaller than previously thought and only of moderate, O(1) overdensity. We expect these miniclusters to have a rich sub-structure, emerging from small-scale fluctuations produced in the collapse of the string-wall network and from axitons. arXiv:1809.09241v2 [astro-ph.CO] 9 Apr 2019 3 In the low T regime the potential away from the minimum is not well-described by (2.2). However, it seems to be a good approximation above T ∼ 2Tc or, at least, the quartic coupling computed in [68] does. The fact that at these temperatures the axion field is mostly very close to θ ∼ 0 renders the inaccuracy of small importance to us in this paper, but, as we will see, it is not entirely irrelevant.4 Definitions in the literature differ slightly, for instance Sikivie and Kawasaki use 3H1 = mA as the defining scale. Fortunately for comparison's sake, this has only mild effect on the value of H1 as the temperature dependence of mA is quite strong.

We study the gravitational collapse of axion dark matter fluctuations in the postinflationary scenario, socalled axion miniclusters, with N-body simulations. Largely confirming theoretical expectations, overdensities begin to collapse in the radiation-dominated epoch and form an early distribution of miniclusters with masses up to 10 −12 M ⊙. After matter-radiation equality, ongoing mergers give rise to a steep powerlaw distribution of minicluster halo masses. The density profiles of well-resolved halos are Navarro-Frenk-White-like to good approximation. The fraction of axion dark matter in these bound structures is ∼0.75 at redshift z ¼ 100.

We perform a high statistics calculation of disconnected fermion loops on Graphics Processing Units for a range of nucleon matrix elements extracted using lattice QCD. The isoscalar electromagnetic and axial vector form factors, the sigma terms and the momentum fraction and helicity are among the quantities we evaluate. We compare the disconnected contributions to the connected ones and give the physical implications on nucleon observables that probe its structure.

We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from the connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical u, d, s, and c quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from a ≈ 0.06-0.15 fm. The up-and downquark masses in our simulations have equal masses m l . We obtain, in this world where all pions have the mass of the π 0 , 10 10 a ll µ (conn.) = 630.1(8.3), in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. We obtain for the total order (α 2 ) hadronic-vacuum polarization to the muon's anomalous magnetic moment 10 10 a HVP,LO µ = 691(8) u,d (1) s,c,b (13) other , where the errors are from the light-quark connected contribution, heavy-flavor connected contributions, and omitted effects listed above, respectively. Our result agrees with both ab-initio lattice-QCD calculations and phenomenological determinations from experimental e + e − -scattering data. It is 1.7σ below the "no new physics" value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of aµ with theoretical calculations of the other contributions. * christine.davies@glasgow.ac.uk † ruthv@fnal.gov