We search for galaxies with a strong Balmer break (Balmer break galaxies; BBGs) at z ∼ 6 over a 0.41 deg2 effective area in the COSMOS field. Based on rich imaging data, including data obtained with the Atacama Large Millimeter/submillimeter Array (ALMA), three candidates are identified by their extremely red K-[3.6] colors, as well as by nondetection in the X-ray, optical, far-infrared, and radio bands. The nondetection in the deep ALMA observations suggests that they are not dusty galaxies but BBGs at z ∼ 6, although contamination from active galactic nuclei at z ∼ 0 cannot be completely ruled out for the moment. Our spectral energy distribution analyses reveal that the BBG candidates at z ∼ 6 have stellar masses of ≈5 × 1010 M o˙ dominated by old stellar populations with ages of ⪆ 700 Myr. Assuming that all three candidates are real BBGs at z ∼ 6, we estimate the stellar mass density to be 2.4-1.3 +2.3× 10-4,M Mpc-3. This is consistent with an extrapolation from the lower-redshift measurements. The onset of star formation in the three BBG candidates is expected to be several hundred million yr before the observed epoch of z ∼ 6. We estimate the star formation rate density (SFRD) contributed by progenitors of the BBGs to be 2.4-12 × 10-5 M o˙ yr-1 Mpc-3 at z > 14 (99.7% confidence range). Our result suggests a smooth evolution of the SFRD beyond z = 8.
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