Quintessence with quadratic coupling to dark matter
  We introduce a new form of coupling between dark energy and dark matter that
is quadratic in their energy densities. Then we investigate the background
dynamics when dark energy is in the form of exponential quintessence. The three
types of quadratic coupling all admit late-time accelerating critical points,
but these are not scaling solutions. We also show that two types of coupling
allow for a suitable matter era at early times and acceleration at late times,
while the third type of coupling does not admit a suitable matter era.
