Searching for massive galaxies at

Aims. We constrain the space density and properties of massive galaxy candidates at redshifts of $z\geq3.5$ in the Great Observatories Origin Deep Survey North (GOODS-N) field. By selecting sources in the Spitzer + IRAC bands, a sample highly complete in stellar-mass is assembled, including massive galaxies that are very faint in the optical/near-IR bands and would be missed by samples selected at shorter wavelengths. Methods. The $z\geq3.5$ sample was selected to $m_{\rm AB}=23$ mag at $4.5~\mu$m using photometric redshifts obtained by fitting the galaxies spectral energy distribution at optical, near-IR bands, and IRAC bands. We also require that the brightest band (in AB scale) in which candidates are detected is the IRAC $8.0~\mu$m band to ensure that the near-IR $1.6~\mu$m (rest-frame) peak is falling in or beyond this band. Results. We found 53 $z~\geq3.5$ candidates, of masses in the range $M_{\star}\sim10^{10}{-}10^{11}~M_{\odot}$. At least ~81% of these galaxies are missed by traditional Lyman Break selection methods based on ultraviolet light. Spitzer + MIPS emission is detected for 60% of the sample of $z\geq3.5$ galaxy candidates. Although in some cases this might suggest a residual contamination from lower redshift star-forming galaxies or Active Galactic Nuclei, 37% of these objects are also detected in the sub-mm/mm bands in SCUBA, AzTEC, and MAMBO surveys, and have properties fully consistent with vigorous starburst galaxies at $z\geq3.5$. The comoving number density of galaxies with stellar masses of above 5 $\times$ $10^{10}~M_{\odot}$ (a reasonable stellar-mass completeness limit for our sample) is 2.6 $\times$ 10-5 Mpc-3 (using the volume within $3.5<z