Halting eternal acceleration with an effective negative cosmological   constant
  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. 
Vincenzo F. Cardone, Rolando P. Cardenas, Yoelsy Leiva Nodal