n this thesis we first calculate the relation between QCD axion mass and decay constant at high precision, employing effective chiral lagrangian techniques. In particular we include the O(αem) and NNLO corrections in the chiral expansion, which amount to 0.65(21)% and -0.71(29)% respectively. Both corrections are one order of magnitude smaller than the known NLO ones, confirming the very good convergence of the chiral expansion and its reliability. Using the latest estimates for the light quark masses, the current uncertainty is dominated by the one of the low-energy constant l7. When combined with possible improvements on the light quark mass ratio and l7 from lattice QCD, the
axion mass could be determined with per-mille accuracy as a function of the its decay constant. Second, with the goal of predicting the numerical value of the axion decay constant (and therefore the axion mass) based on the axion DM relic abundance, we study the system of axion strings that forms in the early Universe if the Peccei-Quinn symmetry is restored after inflation. Understanding the dynamics of this system is a necessary condition for a reliable prediction of the axion DM abundance in the post-inflationary scenario. Using numerical simulations, we establish the existence of an asymptotic solution to which the system is attracted independently of the initial conditions. We study in detail the properties of this solution, including the average number of strings per Hubble patch, the distribution
of loops and long strings, the way that different types of radiation are emitted, and the shape of the spectrum of axions produced. We find clear evidence of logarithmic violations of the scaling properties of the attractor solution. We also find that, while most of the axions are emitted with momenta of order Hubble, most of the axion energy density is contained in axions with energy of order the string core scale, at least in the parameter range available in the simulation. While such a spectrum would lead to a negligible number density of relic axions from strings when extrapolated to the physical parameter region, we show that the presence of small logarithmic corrections to the spectrum shape could completely alter such a conclusion. A detailed understanding of the evolution of the axion
spectrum is therefore crucial for a reliable estimate of the relic axion abundance from strings.
