This paper presents new deep and wide narrow-band surveys undertaken with UKIRT , Subaru and the VLT ; a unique combined effort to select large , robust samples of H \alpha star-forming galaxies at z = 0.40 , 0.84 , 1.47 and 2.23 ( corresponding to look-back times of 4.2 , 7.0 , 9.2 and 10.6 Gyrs ) in a uniform manner over \sim 2 deg ^ { 2 } in the COSMOS and UDS fields .
The deep multi-epoch H \alpha surveys reach a matched 3 \sigma flux limit of \approx 3 M _ { \odot } yr ^ { -1 } out to z = 2.2 for the first time , while the wide area and the coverage over two independent fields allow to greatly overcome cosmic variance and assemble by far the largest samples of H \alpha emitters .
Catalogues are presented for a total of 1742 , 637 , 515 and 807 H \alpha emitters , robustly selected at z = 0.40 , 0.84 , 1.47 and 2.23 , respectively , and used to determine the H \alpha luminosity function and its evolution .
The faint-end slope of the H \alpha luminosity function is found to be \alpha = -1.60 \pm 0.08 over z = 0 - 2.23 , showing no significant evolution .
The characteristic luminosity of SF galaxies , L _ { H \alpha } ^ { * } , evolves significantly as \log L ^ { * } _ { H \alpha } ( z ) = 0.45 z + \log L ^ { * } _ { z = 0 } .
This is the first time H \alpha has been used to trace SF activity with a single homogeneous survey at z = 0.4 - 2.23 .
Overall , the evolution seen with H \alpha is in good agreement with the evolution seen using inhomogeneous compilations of other tracers of star formation , such as FIR and UV , jointly pointing towards the bulk of the evolution in the last 11 Gyrs being driven by a statistically similar SF population across cosmic time , but with a strong luminosity increase from z \sim 0 to z \sim 2.2 .
Our uniform analysis allows to derive the H \alpha star formation history of the Universe ( SFRH ) , showing a clear rise up to z \sim 2.2 , for which the simple parametrisation \log _ { 10 } \rho _ { SFR } = -2.1 ( 1 + z ) ^ { -1 } is valid over 80 per cent of the age of the Universe .
The results reveal that both the shape and normalisation of the H \alpha SFRH are consistent with the measurements of the stellar mass density growth , confirming that our H \alpha SFRH is tracing the bulk of the formation of stars in the Universe for z < 2.23 .
The star formation activity over the last \sim 11 Gyrs is responsible for producing \sim 95 per cent of the total stellar mass density observed locally , with half of that being assembled in 2 Gyrs between z = 1.2 – 2.2 , and the other half in 8 Gyrs ( since z < 1.2 ) .
If the star-formation rate density continues to decline with time in the same way as seen in the past \sim 11 Gyrs , then the stellar mass density of the Universe will reach a maximum which is only 5 per cent higher than the present-day value .