LAGER Ly$\alpha$ Luminosity Function at $z\sim7$, Implications for
  Reionization
  We present a new measurement of the Ly$\alpha$ luminosity function at
redshift $z=6.9$, finding moderate evolution from $z=5.7$ that is consistent
with a fully or largely ionized $z\sim7$ intergalactic medium. Our result is
based on four fields of the LAGER (Lyman Alpha Galaxies in the Epoch of
Reionization) project. Our survey volume of $6.1\times10^{6}$ Mpc$^{3}$ is
double that of the next largest $z\sim 7$ survey. We combine two new LAGER
fields (WIDE12 and GAMA15A) with two previously reported LAGER fields (COSMOS
and CDFS). In the new fields, we identify $N=95$ new $z=6.9$ Ly$\alpha$
emitters (LAEs); characterize our survey's completeness and reliability; and
compute Ly$\alpha$ luminosity functions. The best-fit Schechter luminosity
function parameters for all four LAGER fields are in good general agreement.
Two fields (COSMOS and WIDE12) show evidence for a bright-end excess above the
Schechter function fit. We find that the Ly$\alpha$ luminosity density declines
at the same rate as the UV continuum LF from $z=5.7$ to $z=6.9$. This is
consistent with an intergalactic medium that was fully ionized as early as
redshift $z\sim 7$, or with a volume-averaged neutral hydrogen fraction of
$x_{HI} < 0.33$ at $1\sigma$.
