  Modern numerical hydrodynamics tools have recently enabled detailed
examinations of binaries accreting from prograde circumbinary disks. These have
re-framed the current understanding of binary-disk interactions and disk driven
orbital evolution. We present the first full-domain grid-based hydrodynamics
simulations of equal-mass, eccentric binaries accreting from retrograde
circumbinary disks. We study binary eccentricities that span $e=0.0$ to $e =
0.8$ continuously, and explore the influence of retrograde accretion on the
binary orbital response, disk morphology, and observational properties. We find
that, at all eccentricities, retrograde accretion shrinks the binary semi-major
axis and pumps its eccentricity leading to the previously identified
possibility of highly eccentric mergers. Contrary to past studies and models,
we observe gravitational forces to dominate the binary's orbital evolution as
opposed to the physical accretion of mass and momentum. Retrograde accretion
variability also differs strongly from prograde solutions. Preeminently,
binaries with $e > 0.55$ reveal a unique two-period, double-peaked accretion
signature that has not previously been identified. We additionally find
evidence for the emergence of retrograde Lindblad resonances at large
eccentricities in accordance with predictions from linear theory. Our results
suggest that some astrophysical binaries for which retrograde accretion is
possible will experience factors-of-a-few times faster orbital decay than in
prograde disks and will have their eccentricities pumped beyond the limits
found from prograde solutions. Such effects could lead to rapid inward
migration for some young stellar binaries, the detection of highly-eccentric
LISA mergers, and the tentatively observed turnover at the low-frequency end of
the gravitational wave background.
