We used Early Release Science ( ERS ) observations taken with the Wide Field Camera 3 ( WFC3 ) in the GOODS-S field to study the galaxy stellar mass function ( GSMF ) at 0.6 \leq z < 4.5 .
Deep WFC3 near-IR data ( for Y as faint as 27.3 , J and H as faint as 27.4 AB mag at 5 \sigma ) , as well as deep K _ { S } ( as faint as 25.5 at 5 \sigma ) Hawk-I band data , provide an exquisite data set with which determine in an unprecedented way the low-mass end of the GSMF , allowing an accurate probe of masses as low as M _ { * } \simeq 7.6 \cdot 10 ^ { 9 } M _ { \odot } at z \sim 3 .
Although the area used is relatively small ( \sim 33 arcmin ^ { 2 } ) , we found generally good agreement with previous studies on the entire mass range .
Our results show that the slope of the faint-end increases with redshift , from \alpha = -1.44 \pm 0.03 at z \sim 0.8 to \alpha = -1.86 \pm 0.16 at z \sim 3 , although indications exist that it does not steepen further between z \sim 3 and z \sim 4 .
This result is insensitive to any uncertainty in the M ^ { * } parameter .
The steepness of the GSMF faint-end solves the well-known disagreement between the stellar mass density ( SMD ) and the integrated star formation history at z > 2 .
However , we confirm the that there appears to be an excess of integrated star formation with respect to the SMD at z < 2 , by a factor of \sim 2 - 3 .
Our comparison of the observations with theoretical predictions shows that the models forecast a greater abundance of low mass galaxies , at least up to z \sim 3 , as well as a dearth of massive galaxies at z \sim 4 with respect to the data , and that the predicted SMD is generally overestimated at z \lesssim 2 .