  The physical properties inferred from the SEDs of z>3 galaxies have been
influential in shaping our understanding of early galaxy formation and the role
galaxies may play in cosmic reionization. Of particular importance is the
stellar mass density at early times which represents the integral of earlier
star formation. An important puzzle arising from the measurements so far
reported is that the specific star formation rates (sSFR) evolve far less
rapidly than expected in most theoretical models. Yet the observations
underpinning these results remain very uncertain, owing in part to the possible
contamination of rest-optical broadband light from strong nebular emission
lines. To quantify the contribution of nebular emission to broad-band fluxes,
we investigate the SEDs of 92 spectroscopically-confirmed galaxies in the
redshift range 3.8<z<5.0 chosen because the H-alpha line lies within the
Spitzer/IRAC 3.6 um filter. We demonstrate that the 3.6 um flux is
systematically in excess of that expected from stellar continuum, which we
derive by fitting the SED with population synthesis models. No such excess is
seen in a control sample at 3.1<z<3.6 in which there is no nebular
contamination in the IRAC filters. From the distribution of our 3.6 um flux
excesses, we derive an H-alpha equivalent width (EW) distribution. The mean
rest-frame H-alpha EW we infer at 3.8<z<5.0 (270 A) indicates that nebular
emission contributes at least 30% of the 3.6 um flux. Via our
empirically-derived EW distribution we correct the available stellar mass
densities and show that the sSFR evolves more rapidly at z>4 than previously
thought, supporting up to a 5x increase between z~2 and 7. Such a trend is much
closer to theoretical expectations. Given our findings, we discuss the
prospects for verifying quantitatively the nebular emission line strengths
prior to the launch of the James Webb Space Telescope.
