Context :

Aims : We perform a deep search for galaxies in the redshift range 6.5 \leq z \leq 7.5 , to measure the evolution of the number density of luminous galaxies in this redshift range and derive useful constraints on the evolution of their Luminosity Function .

Methods : We present here the first results of an ESO Large Program , that exploits the unique combination of area and sensitivity provided in the near–IR by the camera Hawk-I at the VLT .
We have obtained two Hawk-I pointings on the GOODS South field for a total of \sim 32 observing hours , covering \sim 90 ~ { } arcmin ^ { 2 } .
The images reach Y = 26.7 mags for the two fields .
We have used public ACS images in the z band to select z-dropout galaxies with the colour criteria Z - Y \geq 1 , Y - J < 1.5 and Y - K < 2 .
The other public data in the UBVRIJK bands are used to reject possible low redshift interlopers .
The output has been compared with extensive Monte Carlo simulations to quantify the observational effects of our selection criteria as well as the effects of photometric errors .

Results : We detect 7 high quality candidates in the magnitude range Y = 25.5 - 26.7 .
This interval samples the critical range for M _ { * } at z > 6 ( M _ { 1500 } \simeq - 19.5 to -21.5 ) .
After accounting for the expected incompleteness , we rule out at a 99 % confidence level a luminosity function constant from z=6 to z=7 , even including the effects of cosmic variance .
For galaxies brighter than M _ { 1500 } = -19.0 we derive a luminosity density \rho _ { UV } = 1.5 ^ { +2.0 } _ { -0.9 } \times 10 ^ { 25 } erg~ { } s ^ { -1 } ~ { } Hz ^ { -1 } ~ { } Mpc ^ { -3 } , implying a decrease by a factor 3.5 from z = 6 to z \simeq 6.8 .
On the basis of our findings , we make predictions for the surface densities expected in future surveys , based on ULTRA-VISTA , HST-WFC3 or JWST-NIRCam , evaluating the best observational strategy to maximise their impact .

Conclusions :