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The recent high precision maps of cosmic microwave anisotropies combined withmeasurements of the galaxy power spectrum from new large-scale redshift surveyshave allowed stringent bounds on the sum of the neutrino masses to be placed.The past analyses, however, have implicitly assumed that the spectrum ofprimordial density fluctuations is adiabatic and coherent, as predicted in thesimplest models of inflation. In this paper, we show that the limits hold evenif the assumption on the primordial power spectrum is relaxed to allow for acontribution of nonadiabatic, incoherent fluctuations such as would bepredicted by topological defects.Comment: 4 pages, to appear in Phys. Rev. D (R

Note on the robustness of the neutrino mass bounds from cosmology