  There is a class of higher derivative gravity theories that are in some sense
natural extensions of cosmological Einstein's gravity with a unique maximally
symmetric classical vacuum and only a massless spin-2 excitation about the
vacuum and no other perturbative modes. These theories are of the Born-Infeld
determinantal form. We show that the macroscopic dynamical entropy as defined
by Wald for bifurcate Killing horizons in these theories are equivalent to the
geometric Bekenstein-Hawking entropy (or more properly Gibbons-Hawking entropy
for the case of de Sitter spacetime) but given with an effective gravitational
constant which encodes all the information about the background spacetime and
the underlying theory. We also show that the higher curvature terms increase
the entropy. We carry out the computations in generic n-dimensions including
the particularly interesting limits of three, four and infinite number of
dimensions. We also give a preliminary discussion about the black hole entropy
in generic dimensions for the BI theories.
