  In order to solve the problem of eternal acceleration, a model has been
recently proposed including both a negative cosmological constant $\Lambda$ and
a scalar field evolving under the action of an exponential potential. We
further explore this model by contrasting it against the Hubble diagram of Type
Ia supernovae, the gas mass fraction in galaxy clusters and the acoustic peak
and shift parameters. It turns out that the model is able to fit quite well
this large dataset so that we conclude that a negative $\Lambda$ is indeed
allowed and could represent a viable mechanism to halt eternal acceleration. In
order to avoid problems with theoretical motivations for both a negative
$\Lambda$ term and the scalar field, we reconstruct the gravity Lagrangian
$f(R)$ of a fourth order theory of gravity predicting the same dynamics (scale
factor and Hubble parameter) as the starting model. We thus end up with a
$f(R)$ theory able to both fit the data and solve the problem of eternal
acceleration without the need of unusual negative $\Lambda$ and ad hoc scalar
fields.
