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Axions currently provide the most compelling solution to the strong CPproblem. These particles may be copiously produced in the early universe,including via thermal processes. Therefore, relic axions constitute a hot darkmatter component and their masses are strongly degenerate with those of thethree active neutrinos, as they leave identical signatures in the differentcosmological observables. In addition, thermal axions, while still relativisticstates, also contribute to the relativistic degrees of freedom, parameterisedvia $N_{eff}$. We present the cosmological bounds on the relic axion andneutrino masses, exploiting the full Planck mission data, which includepolarization measurements. In the mixed hot dark matter scenario explored here,we find the tightest and more robust constraint to date on the sum of the threeactive neutrino masses, $\sum m_\nu <0.136$ eV at $95\%$ CL, obtained in thewell-known linear perturbation regime. The Planck Sunyaev-Zeldovich clusternumber count data further tightens this bound, providing a $95\%$ CL upperlimit of $\sum m_\nu <0.126$ eV in this very same mixed hot dark matter model,a value which is very close to the expectations in the inverted hierarchicalneutrino mass scenario. Using this same combination of data sets we find themost stringent bound to date on the thermal axion mass, $m_a<0.529$ eV at$95\%$ CL.

Cosmological Axion and neutrino mass constraints from Planck 2015 temperature and polarization data