Cumulative Lyα luminosity functions. The blue (resp. red) lines show the cumulative luminosity functions at z = 5.7 (resp. z = 6.5) from Ouchi et al. (2008) (dotted-dashed lines), Hu et al. (2010) (plain lines) and Kashikawa et al. (2011) (dotted lines). The transitions to thin lines indicate the range of the luminosities probed by the observations. A fixed faint end slope of –1.5 is assumed. The parameter space probed by the HAWK-I observations is delimited by the black line, with the black dashed line corresponding to the HAWK-I observations and the null detection of the bright candidates of Hibon et al. (2010) mentioned in the text. The green dotted line corresponds to a 60% evolution in density of the Hu et al. (2010) LF, and the short-dashed-long-dashed line corresponds to a 60% evolution in luminosity of the Ouchi et al. (2010)z = 6.5 LF. The red filled diamond corresponds to the Iye et al. (2006) LAE detection at a redshift of 6.96. The black open diamonds correspond to the Vanzella et al. (2011) LAE detections at redshifts of 7.008 and 7.109. The magenta downward-pointing filled (resp. open) triangles are the photometric candidates at z = 7.7 from Tilvi et al. (2010) (resp. Krug et al. 2012).