We present a new near-field cosmological probe of the initial mass function ( IMF ) of the first stars .
Specifically , we constrain the lower-mass limit of the Population III ( Pop III ) IMF with the total number of stars in large , unbiased surveys of the Milky Way .
We model the early star formation history in a Milky Way-like halo with a semi-analytic approach , based on Monte-Carlo sampling of dark matter merger trees , combined with a treatment of the most important feedback mechanisms .
Assuming a logarithmically flat Pop III IMF and varying its low mass limit , we derive the number of expected survivors of these first stars , using them to estimate the probability to detect any such Pop III fossil in stellar archaeological surveys .
Following our analysis , the most promising region to find possible Pop III survivors is the stellar halo of the Milky Way , which is the best target for future surveys .
We find that if no genuine Pop III survivor is detected in a sample size of 4 \times 10 ^ { 6 } ( 2 \times 10 ^ { 7 } ) halo stars with well-controlled selection effects , then we can exclude the hypothesis that the primordial IMF extended down below 0.8 M _ { \odot } at a confidence level of 68 \% ( 99 \% ) .
With the sample size of the Hamburg/ESO survey , we can tentatively exclude Pop III stars with masses below 0.65 M _ { \odot } with a confidence level of 95 \% , although this is subject to significant uncertainties .
To fully harness the potential of our approach , future large surveys are needed that employ uniform , unbiased selection strategies for high-resolution spectroscopic follow-up .