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We present the results of our search for high‐redshift Lyman‐break galaxies over the GOODS‐South field. We use  Hubble Space Telescope (HST) ‐ACS data in   B ,  V ,  i ′  &amp;  z ′, Very Large Telescope (VLT)‐ISAAC  J  and  Ks ,  Spitzer –Infrared Array Camera ( IRAC ) 3.6, 4.5, 5.8 and 8.0 μm data in conjunction with the new HAWK‐I  Y ‐band science verification data to search for dropout galaxies in the redshift range  6 &lt;  z  &lt; 9 . We survey ≈119 arcmin 2  to   Y AB  = 25.7 (5σ ), of which 37.5 arcmin 2  reaches   Y AB  = 25.9 . Candidate  z ′ and  Y  dropouts were selected on the basis of a colour cut of  ( Y − J )  AB   &gt; 0.75  mag and  ( z ′− Y )  AB   &gt; 1.0  mag, respectively. We find no robust  Y ‐drops ( z ≈ 9) brighter than   J AB   &lt; 25.4 . In our search for  z ′‐band dropouts  ( z ≈ 6.5– 7.5) , we identify four possible candidates, two with  z ′‐drop colours and clear  Spitzer – IRAC  detections and two less likely candidates. We also identify two previously known Galactic T‐dwarf stellar contaminants with these colours, and two likely transient objects seen in the  Y ‐band data. The implications if all or none of our candidates is real on the ultraviolet galaxy luminosity functions at   z  &gt; 6.5  are explored. We find our number of  z ′‐drop candidates to be insufficient based on the expected number of  z ′ drops in a simple no‐evolution scenario from the   z = 3  Lyman‐break galaxy luminosity function but we are consistent with the observed luminosity function at   z ≈ 6  (if all our candidates are real). However, if one or both of our best  z ′‐drop candidates are not   z  &gt; 6.5  galaxies, this would demand evolution of the luminosity function at early epochs, in the sense that the number density of ultraviolet luminous star‐forming galaxies at   z  &gt; 7  is less than at   z ∼ 6 . We show that the future surveys to be conducted with the European Southern Observatory VISTA telescope over the next 5 yr will be able to measure the bulk of the luminosity function for both  z ′ and  Y  dropouts and thus provide the strongest constraints on the level of star‐formation within the epoch of reionization.

Constraints on star‐forming galaxies at z ≥ 6.5 from HAWK‐I Y ‐band imaging of GOODS‐South