  Correlations between intrinsic properties of gamma-ray burst (GRB) light
curves provide clues to the nature of the central engine, the jet, and a
possible means to standardise GRBs for cosmological use. Here we report on the
discovery of a correlation between the intrinsic early time luminosity,
$L_{G,\rm 10s}$, measured at rest frame 10s, and the average decay rate
measured from rest frame 10s onward, $\alpha_{G,\rm avg>10s}$, in a sample of
13 Fermi Large Array Telescope (LAT) long GRB light curves. We note that our
selection criteria, in particular the requirement for a redshift to construct
luminosity light curves, naturally limits our sample to energetic GRBs. A
Spearman's rank correlation gives a coefficient of -0.74, corresponding to a
confidence level of 99.6%, indicating that brighter afterglows decay faster
than less luminous ones. Assuming a linear relation with $\log(L_{G,\rm 10s})$,
we find $\alpha_{G,\rm avg>10s} = -0.31_{-0.09}^{+0.12}\log(L_{G,\rm 10s}) +
14.43_{-5.97}^{+4.55}$. The slope of -0.31 is consistent at $1\sigma$ with
previously identified correlations in the optical/UV and X-ray light curves. We
speculate that differences in the rate at which energy is released by the
central engine or differences in observer viewing angle may be responsible for
the correlation.
