The extended epoch of galaxy formation: age dating of ~3600 galaxies
  with 2<z<6.5 in the VIMOS Ultra-Deep Survey
  We aim at improving constraints on the epoch of galaxy formation by measuring
the ages of 3597 galaxies with spectroscopic redshifts 2<z<6.5 in the VIMOS
Ultra Deep Survey (VUDS). We derive ages and other physical parameters from the
simultaneous fitting with the GOSSIP+ software of observed UV rest-frame
spectra and photometric data from the u-band up to 4.5 microns using composite
stellar population models. We conclude from extensive simulations that at z>2
the joint analysis of spectroscopy and photometry combined with restricted age
possibilities when taking into account the age of the Universe substantially
reduces systematic uncertainties and degeneracies in the age derivation. We
find galaxy ages ranging from very young with a few tens of million years to
substantially evolved with ages up to ~1.5-2 Gyr. The formation redshifts z_f
derived from the measured ages indicate that galaxies may have started forming
stars as early as z_f~15. We produce the formation redshift function (FzF), the
number of galaxies per unit volume formed at a redshift z_f, and compare the
FzF in increasing redshift bins finding a remarkably constant 'universal' FzF.
The FzF is parametrized with (1+z)^\zeta, with \zeta~0.58+/-0.06, indicating a
smooth 2 dex increase from z~15 to z~2. Remarkably this observed increase is of
the same order as the observed rise in the star formation rate density (SFRD).
The ratio of the SFRD with the FzF gives an average SFR per galaxy of
~7-17Msun/yr at z~4-6, in agreement with the measured SFR for galaxies at these
redshifts. From the smooth rise in the FzF we infer that the period of galaxy
formation extends from the highest possible redshifts that we can probe at z~15
down to redshifts z~2. This indicates that galaxy formation is a continuous
process over cosmic time, with a higher number of galaxies forming at the peak
in SFRD at z~2 than at earlier epochs. (Abridged)
