  In 1993 Foisy et al. proved that the optimal Euclidean planar double
bubble---the least-perimeter way to enclose and separate two given areas---is
three circular arcs meeting at 120 degrees. We consider the plane with density
$r^p$, joining the surge of research on manifolds with density after their
appearance in Perelman's 2006 proof of the Poincar\'e Conjecture. Dahlberg et
al. proved that the best single bubble in the plane with density $r^p$ is a
circle through the origin. We conjecture that the best double bubble is the
Euclidean solution with one of the vertices at the origin, for which we have
verified equilibrium (first variation or "first derivative" zero). To prove the
exterior of the minimizer connected, it would suffice to show that least
perimeter is increasing as a function of the prescribed areas. We give the
first direct proof of such monotonicity for the Euclidean case. Such arguments
were important in the 2002 Annals proof of the double bubble in Euclidean
3-space
