Aims. The aim of this work is to constrain the evolution of the fraction of Lya emitters among UV selected star forming galaxies at 2<z<6, and to measure the stellar escape fraction of Lya photons over the same redshift range. Methods. We exploit the ultradeep spectroscopic observations collected by the VIMOS Ultra Deep Survey (VUDS) to build an unique, complete and unbiased sample of 4000 spectroscopically confirmed star forming galaxies at 2<z<6. Our galaxy sample UV luminosities brighter than M* at 2<z<6, and luminosities down to one magnitude fainter than M* at 2<z<3.5. Results. We find that 80% of the star forming galaxies in our sample have EW0(Lya)<10A, and correspondingly fesc(Lya)<1%. By comparing these results with literature, we conclude that the bulk of the Lya luminosity at 2<z<6 comes from galaxies that are fainter in the UV than those we sample in this work. The strong Lya emitters constitute, at each redshift, the tail of the distribution of the galaxies with extreme EW0(Lya) and fesc(Lya) . This tail of large EW0 and fesc(Lya) becomes more important as the redshift increases, and causes the fraction of Lya with EW0> 25A to increase from 5% at z=2 to 30% at z=6, with the increase being relatively stronger beyond z=4. We observe no difference, for the narrow range of UV luminosities explored in this work, between the fraction of strong Lya emitters among galaxies fainter or brighter than M*, although the fraction for the FUV faint galaxies evolves faster, at 2<z<3.5, than for the bright ones. We do observe an anticorrelation between E(B-V) and fesc(Lya): generally galaxies with high fesc(Lya) have also small amounts of dust (and viceversa). However, when the dust content is low (E(B-V)<0.05) we observe a very broad range of fesc(Lya), ranging from 10^-3 to 1. This implies that the dust alone is not the only regulator of the amount of escaping Lya photons.
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