  We consider inflation in a universe with a positive cosmological constant and
a nonminimally coupled scalar field, in which the field couples both
quadratically and quartically to the Ricci scalar. When considered in the
Einstein frame and when the nonminimal couplings are negative, the field starts
in slow roll and inflation ends with an asymptotic value of the principal slow
roll parameter, $\epsilon_E=4/3$. Graceful exit can be achieved by suitably
(tightly) coupling the scalar field to matter, such that at late time the total
energy density reaches the scaling of matter, $\epsilon_E=\epsilon_m$. Quite
generically the model produces a red spectrum of scalar cosmological
perturbations and a small amount of gravitational radiation. With a suitable
choice of the nonminimal couplings, the spectral slope can be as large as
$n_s\simeq 0.955$, which is about one standard deviation away from the central
value measured by the Planck satellite. The model can be ruled out by future
measurements if any of the following is observed: (a) the spectral index of
scalar perturbations is $n_s>0.960$; (b) the amplitude of tensor perturbations
is above about $r\sim 10^{-2}$; (c) the running of the spectral index of scalar
perturbations is positive.
