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We study the topological susceptibility in 2+1 flavor QCD above the chiralcrossover transition temperature using Highly Improved Staggered Quark actionand several lattice spacings, corresponding to temporal extent of the lattice,$N_\tau=6,8,10$ and $12$. We observe very distinct temperature dependences ofthe topological susceptibility in the ranges above and below $250$ MeV. Whilefor temperatures above $250$ MeV, the dependence is found to be consistent withdilute instanton gas approximation, at lower temperatures the fall-off oftopological susceptibility is milder. We discuss the consequence of our resultsfor cosmology wherein we estimate the bounds on the axion decay constant andthe oscillation temperature if indeed the QCD axion is a possible dark mattercandidate.

The topological susceptibility in finite temperature QCD and axion cosmology